fft_kernelstring.cpp 55.5 KB
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#include <stdio.h> 
#include <stdlib.h> 
#include <math.h> 
#include <iostream> 
#include <sstream> 
#include <string.h> 
#include <assert.h> 
#include "fft_internal.h" 
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#include <clFFT.h> 
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using namespace std; 
  
#define max(A,B) ((A) > (B) ? (A) : (B)) 
#define min(A,B) ((A) < (B) ? (A) : (B)) 
  
static string  
num2str(int num) 
{ 
    char temp[200]; 
    sprintf(temp, "%d", num); 
    return string(temp); 
} 
  
// For any n, this function decomposes n into factors for loacal memory tranpose  
// based fft. Factors (radices) are sorted such that the first one (radixArray[0]) 
// is the largest. This base radix determines the number of registers used by each 
// work item and product of remaining radices determine the size of work group needed. 
// To make things concrete with and example, suppose n = 1024. It is decomposed into 
// 1024 = 16 x 16 x 4. Hence kernel uses float2 a[16], for local in-register fft and  
// needs 16 x 4 = 64 work items per work group. So kernel first performance 64 length 
// 16 ffts (64 work items working in parallel) following by transpose using local  
// memory followed by again 64 length 16 ffts followed by transpose using local memory 
// followed by 256 length 4 ffts. For the last step since with size of work group is  
// 64 and each work item can array for 16 values, 64 work items can compute 256 length 
// 4 ffts by each work item computing 4 length 4 ffts.  
// Similarly for n = 2048 = 8 x 8 x 8 x 4, each work group has 8 x 8 x 4 = 256 work 
// iterms which each computes 256 (in-parallel) length 8 ffts in-register, followed 
// by transpose using local memory, followed by 256 length 8 in-register ffts, followed 
// by transpose using local memory, followed by 256 length 8 in-register ffts, followed 
// by transpose using local memory, followed by 512 length 4 in-register ffts. Again, 
// for the last step, each work item computes two length 4 in-register ffts and thus 
// 256 work items are needed to compute all 512 ffts.  
// For n = 32 = 8 x 4, 4 work items first compute 4 in-register  
// lenth 8 ffts, followed by transpose using local memory followed by 8 in-register 
// length 4 ffts, where each work item computes two length 4 ffts thus 4 work items 
// can compute 8 length 4 ffts. However if work group size of say 64 is choosen,  
// each work group can compute 64/ 4 = 16 size 32 ffts (batched transform).  
// Users can play with these parameters to figure what gives best performance on 
// their particular device i.e. some device have less register space thus using 
// smaller base radix can avoid spilling ... some has small local memory thus  
// using smaller work group size may be required etc 
  
static void  
getRadixArray(unsigned int n, unsigned int *radixArray, unsigned int *numRadices, unsigned int maxRadix) 
{ 
    if(maxRadix > 1) 
    { 
        maxRadix = min(n, maxRadix); 
        unsigned int cnt = 0; 
        while(n > maxRadix) 
        { 
            radixArray[cnt++] = maxRadix; 
            n /= maxRadix; 
        } 
        radixArray[cnt++] = n; 
        *numRadices = cnt; 
        return; 
    } 
  
    switch(n)  
    { 
        case 2: 
            *numRadices = 1; 
            radixArray[0] = 2; 
            break; 
             
        case 4: 
            *numRadices = 1; 
            radixArray[0] = 4; 
            break; 
             
        case 8: 
            *numRadices = 1; 
            radixArray[0] = 8; 
            break; 
             
        case 16: 
            *numRadices = 2; 
            radixArray[0] = 8; radixArray[1] = 2;  
            break; 
             
        case 32: 
            *numRadices = 2; 
            radixArray[0] = 8; radixArray[1] = 4; 
            break; 
             
        case 64: 
            *numRadices = 2; 
            radixArray[0] = 8; radixArray[1] = 8; 
            break; 
             
        case 128: 
            *numRadices = 3; 
            radixArray[0] = 8; radixArray[1] = 4; radixArray[2] = 4; 
            break; 
             
        case 256: 
            *numRadices = 4; 
            radixArray[0] = 4; radixArray[1] = 4; radixArray[2] = 4; radixArray[3] = 4; 
            break; 
             
        case 512: 
            *numRadices = 3; 
            radixArray[0] = 8; radixArray[1] = 8; radixArray[2] = 8; 
            break;           
             
        case 1024: 
            *numRadices = 3; 
            radixArray[0] = 16; radixArray[1] = 16; radixArray[2] = 4; 
            break;   
        case 2048: 
            *numRadices = 4; 
            radixArray[0] = 8; radixArray[1] = 8; radixArray[2] = 8; radixArray[3] = 4; 
            break; 
        default: 
            *numRadices = 0; 
            return; 
    } 
} 
  
static void 
insertHeader(string &kernelString, string &kernelName, clFFT_DataFormat dataFormat) 
{ 
    if(dataFormat == clFFT_SplitComplexFormat)  
        kernelString += string("__kernel void ") + kernelName + string("(__global float *in_real, __global float *in_imag, __global float *out_real, __global float *out_imag, int dir, int S)\n"); 
    else  
        kernelString += string("__kernel void ") + kernelName + string("(__global float2 *in, __global float2 *out, int dir, int S)\n"); 
} 
  
static void  
insertVariables(string &kStream, int maxRadix) 
{ 
    kStream += string("    int i, j, r, indexIn, indexOut, index, tid, bNum, xNum, k, l;\n"); 
    kStream += string("    int s, ii, jj, offset;\n"); 
    kStream += string("    float2 w;\n"); 
    kStream += string("    float ang, angf, ang1;\n"); 
    kStream += string("    __local float *lMemStore, *lMemLoad;\n"); 
    kStream += string("    float2 a[") +  num2str(maxRadix) + string("];\n"); 
    kStream += string("    int lId = get_local_id( 0 );\n"); 
    kStream += string("    int groupId = get_group_id( 0 );\n"); 
} 
  
static void 
formattedLoad(string &kernelString, int aIndex, int gIndex, clFFT_DataFormat dataFormat) 
{ 
    if(dataFormat == clFFT_InterleavedComplexFormat) 
        kernelString += string("        a[") + num2str(aIndex) + string("] = in[") + num2str(gIndex) + string("];\n"); 
    else 
    { 
        kernelString += string("        a[") + num2str(aIndex) + string("].x = in_real[") + num2str(gIndex) + string("];\n"); 
        kernelString += string("        a[") + num2str(aIndex) + string("].y = in_imag[") + num2str(gIndex) + string("];\n"); 
    } 
} 
  
static void 
formattedStore(string &kernelString, int aIndex, int gIndex, clFFT_DataFormat dataFormat) 
{ 
    if(dataFormat == clFFT_InterleavedComplexFormat) 
        kernelString += string("        out[") + num2str(gIndex) + string("] = a[") + num2str(aIndex) + string("];\n"); 
    else 
    { 
        kernelString += string("        out_real[") + num2str(gIndex) + string("] = a[") + num2str(aIndex) + string("].x;\n"); 
        kernelString += string("        out_imag[") + num2str(gIndex) + string("] = a[") + num2str(aIndex) + string("].y;\n"); 
    } 
} 
  
static int 
insertGlobalLoadsAndTranspose(string &kernelString, int N, int numWorkItemsPerXForm, int numXFormsPerWG, int R0, int mem_coalesce_width, clFFT_DataFormat dataFormat) 
{ 
    int log2NumWorkItemsPerXForm = (int) log2(numWorkItemsPerXForm); 
    int groupSize = numWorkItemsPerXForm * numXFormsPerWG; 
    int i, j; 
    int lMemSize = 0; 
     
    if(numXFormsPerWG > 1) 
        kernelString += string("        s = S & ") + num2str(numXFormsPerWG - 1) + string(";\n"); 
     
    if(numWorkItemsPerXForm >= mem_coalesce_width) 
    {            
        if(numXFormsPerWG > 1) 
        { 
            kernelString += string("    ii = lId & ") + num2str(numWorkItemsPerXForm-1) + string(";\n"); 
            kernelString += string("    jj = lId >> ") + num2str(log2NumWorkItemsPerXForm) + string(";\n"); 
            kernelString += string("    if( !s || (groupId < get_num_groups(0)-1) || (jj < s) ) {\n"); 
            kernelString += string("        offset = mad24( mad24(groupId, ") + num2str(numXFormsPerWG) + string(", jj), ") + num2str(N) + string(", ii );\n"); 
            if(dataFormat == clFFT_InterleavedComplexFormat) 
            { 
                kernelString += string("        in += offset;\n"); 
                kernelString += string("        out += offset;\n"); 
            } 
            else 
            { 
                kernelString += string("        in_real += offset;\n"); 
                kernelString += string("        in_imag += offset;\n"); 
                kernelString += string("        out_real += offset;\n"); 
                kernelString += string("        out_imag += offset;\n"); 
            } 
            for(i = 0; i < R0; i++) 
                formattedLoad(kernelString, i, i*numWorkItemsPerXForm, dataFormat); 
            kernelString += string("    }\n"); 
        } 
        else 
        { 
            kernelString += string("    ii = lId;\n"); 
            kernelString += string("    jj = 0;\n"); 
            kernelString += string("    offset =  mad24(groupId, ") + num2str(N) + string(", ii);\n"); 
            if(dataFormat == clFFT_InterleavedComplexFormat) 
            { 
                kernelString += string("        in += offset;\n"); 
                kernelString += string("        out += offset;\n"); 
            } 
            else 
            { 
                kernelString += string("        in_real += offset;\n"); 
                kernelString += string("        in_imag += offset;\n"); 
                kernelString += string("        out_real += offset;\n"); 
                kernelString += string("        out_imag += offset;\n"); 
            } 
            for(i = 0; i < R0; i++) 
                formattedLoad(kernelString, i, i*numWorkItemsPerXForm, dataFormat); 
        } 
    } 
    else if( N >= mem_coalesce_width ) 
    { 
        int numInnerIter = N / mem_coalesce_width; 
        int numOuterIter = numXFormsPerWG / ( groupSize / mem_coalesce_width ); 
         
        kernelString += string("    ii = lId & ") + num2str(mem_coalesce_width - 1) + string(";\n"); 
        kernelString += string("    jj = lId >> ") + num2str((int)log2(mem_coalesce_width)) + string(";\n"); 
        kernelString += string("    lMemStore = sMem + mad24( jj, ") + num2str(N + numWorkItemsPerXForm) + string(", ii );\n"); 
        kernelString += string("    offset = mad24( groupId, ") + num2str(numXFormsPerWG) + string(", jj);\n"); 
        kernelString += string("    offset = mad24( offset, ") + num2str(N) + string(", ii );\n"); 
        if(dataFormat == clFFT_InterleavedComplexFormat) 
        { 
            kernelString += string("        in += offset;\n"); 
            kernelString += string("        out += offset;\n"); 
        } 
        else 
        { 
            kernelString += string("        in_real += offset;\n"); 
            kernelString += string("        in_imag += offset;\n"); 
            kernelString += string("        out_real += offset;\n"); 
            kernelString += string("        out_imag += offset;\n"); 
        } 
         
        kernelString += string("if((groupId == get_num_groups(0)-1) && s) {\n"); 
        for(i = 0; i < numOuterIter; i++ ) 
        { 
            kernelString += string("    if( jj < s ) {\n"); 
            for(j = 0; j < numInnerIter; j++ )  
                formattedLoad(kernelString, i * numInnerIter + j, j * mem_coalesce_width + i * ( groupSize / mem_coalesce_width ) * N, dataFormat); 
            kernelString += string("    }\n");  
            if(i != numOuterIter - 1) 
                kernelString += string("    jj += ") + num2str(groupSize / mem_coalesce_width) + string(";\n");           
        } 
        kernelString += string("}\n "); 
        kernelString += string("else {\n"); 
        for(i = 0; i < numOuterIter; i++ ) 
        { 
            for(j = 0; j < numInnerIter; j++ )  
                formattedLoad(kernelString, i * numInnerIter + j, j * mem_coalesce_width + i * ( groupSize / mem_coalesce_width ) * N, dataFormat);          
        }        
        kernelString += string("}\n"); 
         
        kernelString += string("    ii = lId & ") + num2str(numWorkItemsPerXForm - 1) + string(";\n"); 
        kernelString += string("    jj = lId >> ") + num2str(log2NumWorkItemsPerXForm) + string(";\n"); 
        kernelString += string("    lMemLoad  = sMem + mad24( jj, ") + num2str(N + numWorkItemsPerXForm) + string(", ii);\n");   
         
        for( i = 0; i < numOuterIter; i++ ) 
        { 
            for( j = 0; j < numInnerIter; j++ ) 
            {    
                kernelString += string("    lMemStore[") + num2str(j * mem_coalesce_width + i * ( groupSize / mem_coalesce_width ) * (N + numWorkItemsPerXForm )) + string("] = a[") +  
                                num2str(i * numInnerIter + j) + string("].x;\n"); 
            } 
        }    
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n"); 
         
        for( i = 0; i < R0; i++ ) 
            kernelString += string("    a[") + num2str(i) + string("].x = lMemLoad[") + num2str(i * numWorkItemsPerXForm) + string("];\n");             
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");   
  
        for( i = 0; i < numOuterIter; i++ ) 
        { 
            for( j = 0; j < numInnerIter; j++ ) 
            {    
                kernelString += string("    lMemStore[") + num2str(j * mem_coalesce_width + i * ( groupSize / mem_coalesce_width ) * (N + numWorkItemsPerXForm )) + string("] = a[") +  
                                num2str(i * numInnerIter + j) + string("].y;\n"); 
            } 
        }    
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n"); 
                                                                                            
        for( i = 0; i < R0; i++ ) 
            kernelString += string("    a[") + num2str(i) + string("].y = lMemLoad[") + num2str(i * numWorkItemsPerXForm) + string("];\n");             
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");   
         
        lMemSize = (N + numWorkItemsPerXForm) * numXFormsPerWG; 
    }   
    else 
    { 
        kernelString += string("    offset = mad24( groupId,  ") + num2str(N * numXFormsPerWG) + string(", lId );\n"); 
        if(dataFormat == clFFT_InterleavedComplexFormat) 
        { 
            kernelString += string("        in += offset;\n"); 
            kernelString += string("        out += offset;\n"); 
        } 
        else 
        { 
            kernelString += string("        in_real += offset;\n"); 
            kernelString += string("        in_imag += offset;\n"); 
            kernelString += string("        out_real += offset;\n"); 
            kernelString += string("        out_imag += offset;\n"); 
        } 
         
        kernelString += string("    ii = lId & ") + num2str(N-1) + string(";\n"); 
        kernelString += string("    jj = lId >> ") + num2str((int)log2(N)) + string(";\n"); 
        kernelString += string("    lMemStore = sMem + mad24( jj, ") + num2str(N + numWorkItemsPerXForm) + string(", ii );\n"); 
         
        kernelString += string("if((groupId == get_num_groups(0)-1) && s) {\n"); 
        for( i = 0; i < R0; i++ ) 
        { 
            kernelString += string("    if(jj < s )\n"); 
            formattedLoad(kernelString, i, i*groupSize, dataFormat); 
            if(i != R0 - 1) 
                kernelString += string("    jj += ") + num2str(groupSize / N) + string(";\n"); 
        } 
        kernelString += string("}\n"); 
        kernelString += string("else {\n"); 
        for( i = 0; i < R0; i++ ) 
        { 
            formattedLoad(kernelString, i, i*groupSize, dataFormat); 
        }        
        kernelString += string("}\n"); 
         
        if(numWorkItemsPerXForm > 1) 
        { 
            kernelString += string("    ii = lId & ") + num2str(numWorkItemsPerXForm - 1) + string(";\n"); 
            kernelString += string("    jj = lId >> ") + num2str(log2NumWorkItemsPerXForm) + string(";\n"); 
            kernelString += string("    lMemLoad = sMem + mad24( jj, ") + num2str(N + numWorkItemsPerXForm) + string(", ii );\n");  
        } 
        else  
        { 
            kernelString += string("    ii = 0;\n"); 
            kernelString += string("    jj = lId;\n"); 
            kernelString += string("    lMemLoad = sMem + mul24( jj, ") + num2str(N + numWorkItemsPerXForm) + string(");\n");            
        } 
  
         
        for( i = 0; i < R0; i++ ) 
            kernelString += string("    lMemStore[") + num2str(i * ( groupSize / N ) * ( N + numWorkItemsPerXForm )) + string("] = a[") + num2str(i) + string("].x;\n");  
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");  
         
        for( i = 0; i < R0; i++ ) 
            kernelString += string("    a[") + num2str(i) + string("].x = lMemLoad[") + num2str(i * numWorkItemsPerXForm) + string("];\n"); 
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n"); 
         
        for( i = 0; i < R0; i++ ) 
            kernelString += string("    lMemStore[") + num2str(i * ( groupSize / N ) * ( N + numWorkItemsPerXForm )) + string("] = a[") + num2str(i) + string("].y;\n");  
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");  
         
        for( i = 0; i < R0; i++ ) 
            kernelString += string("    a[") + num2str(i) + string("].y = lMemLoad[") + num2str(i * numWorkItemsPerXForm) + string("];\n"); 
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n"); 
         
        lMemSize = (N + numWorkItemsPerXForm) * numXFormsPerWG; 
    } 
     
    return lMemSize; 
} 
  
static int 
insertGlobalStoresAndTranspose(string &kernelString, int N, int maxRadix, int Nr, int numWorkItemsPerXForm, int numXFormsPerWG, int mem_coalesce_width, clFFT_DataFormat dataFormat) 
{ 
    int groupSize = numWorkItemsPerXForm * numXFormsPerWG; 
    int i, j, k, ind; 
    int lMemSize = 0; 
    int numIter = maxRadix / Nr; 
    string indent = string(""); 
     
    if( numWorkItemsPerXForm >= mem_coalesce_width ) 
    {    
        if(numXFormsPerWG > 1) 
        { 
            kernelString += string("    if( !s || (groupId < get_num_groups(0)-1) || (jj < s) ) {\n"); 
            indent = string("    "); 
        }    
        for(i = 0; i < maxRadix; i++)  
        { 
            j = i % numIter; 
            k = i / numIter; 
            ind = j * Nr + k; 
            formattedStore(kernelString, ind, i*numWorkItemsPerXForm, dataFormat); 
        } 
        if(numXFormsPerWG > 1) 
            kernelString += string("    }\n"); 
    } 
    else if( N >= mem_coalesce_width ) 
    { 
        int numInnerIter = N / mem_coalesce_width; 
        int numOuterIter = numXFormsPerWG / ( groupSize / mem_coalesce_width ); 
         
        kernelString += string("    lMemLoad  = sMem + mad24( jj, ") + num2str(N + numWorkItemsPerXForm) + string(", ii );\n");   
        kernelString += string("    ii = lId & ") + num2str(mem_coalesce_width - 1) + string(";\n"); 
        kernelString += string("    jj = lId >> ") + num2str((int)log2(mem_coalesce_width)) + string(";\n"); 
        kernelString += string("    lMemStore = sMem + mad24( jj,") + num2str(N + numWorkItemsPerXForm) + string(", ii );\n"); 
         
        for( i = 0; i < maxRadix; i++ ) 
        { 
            j = i % numIter; 
            k = i / numIter; 
            ind = j * Nr + k; 
            kernelString += string("    lMemLoad[") + num2str(i*numWorkItemsPerXForm) + string("] = a[") + num2str(ind) + string("].x;\n");             
        }    
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");          
         
        for( i = 0; i < numOuterIter; i++ ) 
            for( j = 0; j < numInnerIter; j++ ) 
                kernelString += string("    a[") + num2str(i*numInnerIter + j) + string("].x = lMemStore[") + num2str(j*mem_coalesce_width + i*( groupSize / mem_coalesce_width )*(N + numWorkItemsPerXForm)) + string("];\n"); 
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n"); 
         
        for( i = 0; i < maxRadix; i++ ) 
        { 
            j = i % numIter; 
            k = i / numIter; 
            ind = j * Nr + k; 
            kernelString += string("    lMemLoad[") + num2str(i*numWorkItemsPerXForm) + string("] = a[") + num2str(ind) + string("].y;\n");             
        }    
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");          
         
        for( i = 0; i < numOuterIter; i++ ) 
            for( j = 0; j < numInnerIter; j++ ) 
                kernelString += string("    a[") + num2str(i*numInnerIter + j) + string("].y = lMemStore[") + num2str(j*mem_coalesce_width + i*( groupSize / mem_coalesce_width )*(N + numWorkItemsPerXForm)) + string("];\n"); 
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");  
         
        kernelString += string("if((groupId == get_num_groups(0)-1) && s) {\n"); 
        for(i = 0; i < numOuterIter; i++ ) 
        { 
            kernelString += string("    if( jj < s ) {\n"); 
            for(j = 0; j < numInnerIter; j++ )  
                formattedStore(kernelString, i*numInnerIter + j, j*mem_coalesce_width + i*(groupSize/mem_coalesce_width)*N, dataFormat);  
            kernelString += string("    }\n");  
            if(i != numOuterIter - 1) 
                kernelString += string("    jj += ") + num2str(groupSize / mem_coalesce_width) + string(";\n");           
        } 
        kernelString += string("}\n"); 
        kernelString += string("else {\n"); 
        for(i = 0; i < numOuterIter; i++ ) 
        { 
            for(j = 0; j < numInnerIter; j++ )  
                formattedStore(kernelString, i*numInnerIter + j, j*mem_coalesce_width + i*(groupSize/mem_coalesce_width)*N, dataFormat);  
        }        
        kernelString += string("}\n"); 
         
        lMemSize = (N + numWorkItemsPerXForm) * numXFormsPerWG; 
    }        
    else 
    {    
        kernelString += string("    lMemLoad  = sMem + mad24( jj,") + num2str(N + numWorkItemsPerXForm) + string(", ii );\n");   
         
        kernelString += string("    ii = lId & ") + num2str(N - 1) + string(";\n"); 
        kernelString += string("    jj = lId >> ") + num2str((int) log2(N)) + string(";\n"); 
        kernelString += string("    lMemStore = sMem + mad24( jj,") + num2str(N + numWorkItemsPerXForm) + string(", ii );\n"); 
         
        for( i = 0; i < maxRadix; i++ ) 
        { 
            j = i % numIter; 
            k = i / numIter; 
            ind = j * Nr + k; 
            kernelString += string("    lMemLoad[") + num2str(i*numWorkItemsPerXForm) + string("] = a[") + num2str(ind) + string("].x;\n"); 
        }    
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n"); 
         
        for( i = 0; i < maxRadix; i++ ) 
            kernelString += string("    a[") + num2str(i) + string("].x = lMemStore[") + num2str(i*( groupSize / N )*( N + numWorkItemsPerXForm )) + string("];\n");  
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");  
         
        for( i = 0; i < maxRadix; i++ ) 
        { 
            j = i % numIter; 
            k = i / numIter; 
            ind = j * Nr + k; 
            kernelString += string("    lMemLoad[") + num2str(i*numWorkItemsPerXForm) + string("] = a[") + num2str(ind) + string("].y;\n"); 
        }    
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n"); 
         
        for( i = 0; i < maxRadix; i++ ) 
            kernelString += string("    a[") + num2str(i) + string("].y = lMemStore[") + num2str(i*( groupSize / N )*( N + numWorkItemsPerXForm )) + string("];\n");  
        kernelString += string("    barrier( CLK_LOCAL_MEM_FENCE );\n");  
         
        kernelString += string("if((groupId == get_num_groups(0)-1) && s) {\n"); 
        for( i = 0; i < maxRadix; i++ ) 
        { 
            kernelString += string("    if(jj < s ) {\n"); 
            formattedStore(kernelString, i, i*groupSize, dataFormat); 
            kernelString += string("    }\n"); 
            if( i != maxRadix - 1) 
                kernelString += string("    jj +=") + num2str(groupSize / N) + string(";\n"); 
        }  
        kernelString += string("}\n"); 
        kernelString += string("else {\n"); 
        for( i = 0; i < maxRadix; i++ ) 
        { 
            formattedStore(kernelString, i, i*groupSize, dataFormat); 
        }        
        kernelString += string("}\n"); 
         
        lMemSize = (N + numWorkItemsPerXForm) * numXFormsPerWG; 
    } 
     
    return lMemSize; 
} 
  
static void  
insertfftKernel(string &kernelString, int Nr, int numIter) 
{ 
    int i; 
    for(i = 0; i < numIter; i++)  
    { 
        kernelString += string("    fftKernel") + num2str(Nr) + string("(a+") + num2str(i*Nr) + string(", dir);\n"); 
    } 
} 
  
static void 
insertTwiddleKernel(string &kernelString, int Nr, int numIter, int Nprev, int len, int numWorkItemsPerXForm) 
{ 
    int z, k; 
    int logNPrev = log2(Nprev); 
     
    for(z = 0; z < numIter; z++)  
    { 
        if(z == 0) 
        { 
            if(Nprev > 1) 
                kernelString += string("    angf = (float) (ii >> ") + num2str(logNPrev) + string(");\n"); 
            else 
                kernelString += string("    angf = (float) ii;\n"); 
        }    
        else 
        { 
            if(Nprev > 1) 
                kernelString += string("    angf = (float) ((") + num2str(z*numWorkItemsPerXForm) + string(" + ii) >>") + num2str(logNPrev) + string(");\n");  
            else 
                kernelString += string("    angf = (float) (") + num2str(z*numWorkItemsPerXForm) + string(" + ii);\n"); 
        }    
     
        for(k = 1; k < Nr; k++) { 
            int ind = z*Nr + k; 
            //float fac =  (float) (2.0 * M_PI * (double) k / (double) len); 
            kernelString += string("    ang = dir * ( 2.0f * M_PI * ") + num2str(k) + string(".0f / ") + num2str(len) + string(".0f )") + string(" * angf;\n"); 
            kernelString += string("    w = (float2)(native_cos(ang), native_sin(ang));\n"); 
            kernelString += string("    a[") + num2str(ind) + string("] = complexMul(a[") + num2str(ind) + string("], w);\n"); 
        } 
    } 
} 
  
static int 
getPadding(int numWorkItemsPerXForm, int Nprev, int numWorkItemsReq, int numXFormsPerWG, int Nr, int numBanks, int *offset, int *midPad) 
{ 
    if((numWorkItemsPerXForm <= Nprev) || (Nprev >= numBanks)) 
        *offset = 0; 
    else { 
        int numRowsReq = ((numWorkItemsPerXForm < numBanks) ? numWorkItemsPerXForm : numBanks) / Nprev; 
        int numColsReq = 1; 
        if(numRowsReq > Nr) 
            numColsReq = numRowsReq / Nr; 
        numColsReq = Nprev * numColsReq; 
        *offset = numColsReq; 
    } 
     
    if(numWorkItemsPerXForm >= numBanks || numXFormsPerWG == 1) 
        *midPad = 0; 
    else { 
        int bankNum = ( (numWorkItemsReq + *offset) * Nr ) & (numBanks - 1); 
        if( bankNum >= numWorkItemsPerXForm ) 
            *midPad = 0; 
        else 
            *midPad = numWorkItemsPerXForm - bankNum; 
    } 
     
    int lMemSize = ( numWorkItemsReq + *offset) * Nr * numXFormsPerWG + *midPad * (numXFormsPerWG - 1); 
    return lMemSize; 
} 
  
  
static void  
insertLocalStores(string &kernelString, int numIter, int Nr, int numWorkItemsPerXForm, int numWorkItemsReq, int offset, string &comp) 
{ 
    int z, k; 
  
    for(z = 0; z < numIter; z++) { 
        for(k = 0; k < Nr; k++) { 
            int index = k*(numWorkItemsReq + offset) + z*numWorkItemsPerXForm; 
            kernelString += string("    lMemStore[") + num2str(index) + string("] = a[") + num2str(z*Nr + k) + string("].") + comp + string(";\n"); 
        } 
    } 
    kernelString += string("    barrier(CLK_LOCAL_MEM_FENCE);\n"); 
} 
  
static void  
insertLocalLoads(string &kernelString, int n, int Nr, int Nrn, int Nprev, int Ncurr, int numWorkItemsPerXForm, int numWorkItemsReq, int offset, string &comp) 
{ 
    int numWorkItemsReqN = n / Nrn;                                      
    int interBlockHNum = max( Nprev / numWorkItemsPerXForm, 1 );             
    int interBlockHStride = numWorkItemsPerXForm;                            
    int vertWidth = max(numWorkItemsPerXForm / Nprev, 1);                    
    vertWidth = min( vertWidth, Nr);                                     
    int vertNum = Nr / vertWidth;                                        
    int vertStride = ( n / Nr + offset ) * vertWidth;                    
    int iter = max( numWorkItemsReqN / numWorkItemsPerXForm, 1); 
    int intraBlockHStride = (numWorkItemsPerXForm / (Nprev*Nr)) > 1 ? (numWorkItemsPerXForm / (Nprev*Nr)) : 1; 
    intraBlockHStride *= Nprev; 
     
    int stride = numWorkItemsReq / Nrn;                                  
    int i; 
    for(i = 0; i < iter; i++) { 
        int ii = i / (interBlockHNum * vertNum); 
        int zz = i % (interBlockHNum * vertNum); 
        int jj = zz % interBlockHNum; 
        int kk = zz / interBlockHNum; 
        int z; 
        for(z = 0; z < Nrn; z++) { 
            int st = kk * vertStride + jj * interBlockHStride + ii * intraBlockHStride + z * stride; 
            kernelString += string("    a[") + num2str(i*Nrn + z) + string("].") + comp + string(" = lMemLoad[") + num2str(st) + string("];\n"); 
        } 
    } 
    kernelString += string("    barrier(CLK_LOCAL_MEM_FENCE);\n"); 
} 
  
static void 
insertLocalLoadIndexArithmatic(string &kernelString, int Nprev, int Nr, int numWorkItemsReq, int numWorkItemsPerXForm, int numXFormsPerWG, int offset, int midPad) 
{    
    int Ncurr = Nprev * Nr; 
    int logNcurr = log2(Ncurr); 
    int logNprev = log2(Nprev); 
    int incr = (numWorkItemsReq + offset) * Nr + midPad; 
     
    if(Ncurr < numWorkItemsPerXForm)  
    { 
        if(Nprev == 1) 
            kernelString += string("    j = ii & ") + num2str(Ncurr - 1) + string(";\n"); 
        else 
            kernelString += string("    j = (ii & ") + num2str(Ncurr - 1) + string(") >> ") + num2str(logNprev) + string(";\n"); 
         
        if(Nprev == 1)  
            kernelString += string("    i = ii >> ") + num2str(logNcurr) + string(";\n"); 
        else  
            kernelString += string("    i = mad24(ii >> ") + num2str(logNcurr) + string(", ") + num2str(Nprev) + string(", ii & ") + num2str(Nprev - 1) + string(");\n");  
    }    
    else  
    { 
        if(Nprev == 1) 
            kernelString += string("    j = ii;\n"); 
        else 
            kernelString += string("    j = ii >> ") + num2str(logNprev) + string(";\n"); 
        if(Nprev == 1)  
            kernelString += string("    i = 0;\n");  
        else  
            kernelString += string("    i = ii & ") + num2str(Nprev - 1) + string(";\n"); 
    } 
  
    if(numXFormsPerWG > 1) 
        kernelString += string("    i = mad24(jj, ") + num2str(incr) + string(", i);\n");        
  
    kernelString += string("    lMemLoad = sMem + mad24(j, ") + num2str(numWorkItemsReq + offset) + string(", i);\n");  
} 
  
static void 
insertLocalStoreIndexArithmatic(string &kernelString, int numWorkItemsReq, int numXFormsPerWG, int Nr, int offset, int midPad) 
{ 
    if(numXFormsPerWG == 1) { 
        kernelString += string("    lMemStore = sMem + ii;\n");      
    } 
    else { 
        kernelString += string("    lMemStore = sMem + mad24(jj, ") + num2str((numWorkItemsReq + offset)*Nr + midPad) + string(", ii);\n");  
    } 
} 
  
  
static void 
createLocalMemfftKernelString(cl_fft_plan *plan) 
{ 
    unsigned int radixArray[10]; 
    unsigned int numRadix; 
      
    unsigned int n = plan->n.x; 
     
    assert(n <= plan->max_work_item_per_workgroup * plan->max_radix && "signal lenght too big for local mem fft\n"); 
     
    getRadixArray(n, radixArray, &numRadix, 0); 
    assert(numRadix > 0 && "no radix array supplied\n"); 
     
    if(n/radixArray[0] > plan->max_work_item_per_workgroup) 
        getRadixArray(n, radixArray, &numRadix, plan->max_radix); 
  
    assert(radixArray[0] <= plan->max_radix && "max radix choosen is greater than allowed\n"); 
    assert(n/radixArray[0] <= plan->max_work_item_per_workgroup && "required work items per xform greater than maximum work items allowed per work group for local mem fft\n"); 
     
    unsigned int tmpLen = 1; 
    unsigned int i; 
    for(i = 0; i < numRadix; i++) 
    {    
        assert( radixArray[i] && !( (radixArray[i] - 1) & radixArray[i] ) ); 
        tmpLen *= radixArray[i]; 
    } 
    assert(tmpLen == n && "product of radices choosen doesnt match the length of signal\n"); 
     
    int offset, midPad; 
    string localString(""), kernelName(""); 
     
    clFFT_DataFormat dataFormat = plan->format; 
    string *kernelString = plan->kernel_string; 
     
     
    cl_fft_kernel_info **kInfo = &plan->kernel_info; 
    int kCount = 0; 
     
    while(*kInfo) 
    { 
        kInfo = &(*kInfo)->next; 
        kCount++; 
    } 
     
    kernelName = string("fft") + num2str(kCount); 
     
    *kInfo = (cl_fft_kernel_info *) malloc(sizeof(cl_fft_kernel_info)); 
    (*kInfo)->kernel = 0; 
    (*kInfo)->lmem_size = 0; 
    (*kInfo)->num_workgroups = 0; 
    (*kInfo)->num_workitems_per_workgroup = 0; 
    (*kInfo)->dir = cl_fft_kernel_x; 
    (*kInfo)->in_place_possible = 1; 
    (*kInfo)->next = NULL; 
    (*kInfo)->kernel_name = (char *) malloc(sizeof(char)*(kernelName.size()+1)); 
    strcpy((*kInfo)->kernel_name, kernelName.c_str()); 
     
    unsigned int numWorkItemsPerXForm = n / radixArray[0]; 
    unsigned int numWorkItemsPerWG = numWorkItemsPerXForm <= 64 ? 64 : numWorkItemsPerXForm;  
    assert(numWorkItemsPerWG <= plan->max_work_item_per_workgroup); 
    int numXFormsPerWG = numWorkItemsPerWG / numWorkItemsPerXForm; 
    (*kInfo)->num_workgroups = 1; 
    (*kInfo)->num_xforms_per_workgroup = numXFormsPerWG; 
    (*kInfo)->num_workitems_per_workgroup = numWorkItemsPerWG; 
     
    unsigned int *N = radixArray; 
    unsigned int maxRadix = N[0]; 
    unsigned int lMemSize = 0; 
         
    insertVariables(localString, maxRadix); 
     
    lMemSize = insertGlobalLoadsAndTranspose(localString, n, numWorkItemsPerXForm, numXFormsPerWG, maxRadix, plan->min_mem_coalesce_width, dataFormat); 
    (*kInfo)->lmem_size = (lMemSize > (*kInfo)->lmem_size) ? lMemSize : (*kInfo)->lmem_size; 
     
    string xcomp = string("x"); 
    string ycomp = string("y"); 
     
    unsigned int Nprev = 1; 
    unsigned int len = n; 
    unsigned int r; 
    for(r = 0; r < numRadix; r++)  
    { 
        int numIter = N[0] / N[r]; 
        int numWorkItemsReq = n / N[r]; 
        int Ncurr = Nprev * N[r]; 
        insertfftKernel(localString, N[r], numIter); 
         
        if(r < (numRadix - 1)) { 
            insertTwiddleKernel(localString, N[r], numIter, Nprev, len, numWorkItemsPerXForm); 
            lMemSize = getPadding(numWorkItemsPerXForm, Nprev, numWorkItemsReq, numXFormsPerWG, N[r], plan->num_local_mem_banks, &offset, &midPad); 
            (*kInfo)->lmem_size = (lMemSize > (*kInfo)->lmem_size) ? lMemSize : (*kInfo)->lmem_size; 
            insertLocalStoreIndexArithmatic(localString, numWorkItemsReq, numXFormsPerWG, N[r], offset, midPad); 
            insertLocalLoadIndexArithmatic(localString, Nprev, N[r], numWorkItemsReq, numWorkItemsPerXForm, numXFormsPerWG, offset, midPad); 
            insertLocalStores(localString, numIter, N[r], numWorkItemsPerXForm, numWorkItemsReq, offset, xcomp); 
            insertLocalLoads(localString, n, N[r], N[r+1], Nprev, Ncurr, numWorkItemsPerXForm, numWorkItemsReq, offset, xcomp); 
            insertLocalStores(localString, numIter, N[r], numWorkItemsPerXForm, numWorkItemsReq, offset, ycomp); 
            insertLocalLoads(localString, n, N[r], N[r+1], Nprev, Ncurr, numWorkItemsPerXForm, numWorkItemsReq, offset, ycomp); 
            Nprev = Ncurr; 
            len = len / N[r]; 
        } 
    } 
     
    lMemSize = insertGlobalStoresAndTranspose(localString, n, maxRadix, N[numRadix - 1], numWorkItemsPerXForm, numXFormsPerWG, plan->min_mem_coalesce_width, dataFormat); 
    (*kInfo)->lmem_size = (lMemSize > (*kInfo)->lmem_size) ? lMemSize : (*kInfo)->lmem_size; 
     
    insertHeader(*kernelString, kernelName, dataFormat); 
    *kernelString += string("{\n"); 
    if((*kInfo)->lmem_size) 
        *kernelString += string("    __local float sMem[") + num2str((*kInfo)->lmem_size) + string("];\n"); 
    *kernelString += localString; 
    *kernelString += string("}\n"); 
} 
  
// For n larger than what can be computed using local memory fft, global transposes 
// multiple kernel launces is needed. For these sizes, n can be decomposed using 
// much larger base radices i.e. say n = 262144 = 128 x 64 x 32. Thus three kernel 
// launches will be needed, first computing 64 x 32, length 128 ffts, second computing 
// 128 x 32 length 64 ffts, and finally a kernel computing 128 x 64 length 32 ffts.  
// Each of these base radices can futher be divided into factors so that each of these  
// base ffts can be computed within one kernel launch using in-register ffts and local  
// memory transposes i.e for the first kernel above which computes 64 x 32 ffts on length  
// 128, 128 can be decomposed into 128 = 16 x 8 i.e. 8 work items can compute 8 length  
// 16 ffts followed by transpose using local memory followed by each of these eight  
// work items computing 2 length 8 ffts thus computing 16 length 8 ffts in total. This  
// means only 8 work items are needed for computing one length 128 fft. If we choose 
// work group size of say 64, we can compute 64/8 = 8 length 128 ffts within one 
// work group. Since we need to compute 64 x 32 length 128 ffts in first kernel, this  
// means we need to launch 64 x 32 / 8 = 256 work groups with 64 work items in each  
// work group where each work group is computing 8 length 128 ffts where each length 
// 128 fft is computed by 8 work items. Same logic can be applied to other two kernels 
// in this example. Users can play with difference base radices and difference  
// decompositions of base radices to generates different kernels and see which gives 
// best performance. Following function is just fixed to use 128 as base radix 
  
void 
getGlobalRadixInfo(int n, int *radix, int *R1, int *R2, int *numRadices) 
{ 
    int baseRadix = min(n, 128); 
     
    int numR = 0; 
    int N = n; 
    while(N > baseRadix)  
    { 
        N /= baseRadix; 
        numR++; 
    } 
     
    for(int i = 0; i < numR; i++) 
        radix[i] = baseRadix; 
     
    radix[numR] = N; 
    numR++; 
    *numRadices = numR; 
         
    for(int i = 0; i < numR; i++) 
    { 
        int B = radix[i]; 
        if(B <= 8) 
        { 
            R1[i] = B; 
            R2[i] = 1; 
            continue; 
        } 
         
        int r1 = 2;  
        int r2 = B / r1; 
        while(r2 > r1) 
        { 
           r1 *=2; 
           r2 = B / r1; 
        } 
        R1[i] = r1; 
        R2[i] = r2; 
    }    
} 
  
static void 
createGlobalFFTKernelString(cl_fft_plan *plan, int n, int BS, cl_fft_kernel_dir dir, int vertBS) 
{        
    int i, j, k, t; 
    int radixArr[10] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; 
    int R1Arr[10] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; 
    int R2Arr[10] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }; 
    int radix, R1, R2; 
    int numRadices; 
     
    int maxThreadsPerBlock = plan->max_work_item_per_workgroup; 
    int maxArrayLen = plan->max_radix; 
    int batchSize = plan->min_mem_coalesce_width;    
    clFFT_DataFormat dataFormat = plan->format; 
    int vertical = (dir == cl_fft_kernel_x) ? 0 : 1;     
     
    getGlobalRadixInfo(n, radixArr, R1Arr, R2Arr, &numRadices); 
         
    int numPasses = numRadices; 
     
    string localString(""), kernelName(""); 
    string *kernelString = plan->kernel_string; 
    cl_fft_kernel_info **kInfo = &plan->kernel_info;  
    int kCount = 0; 
     
    while(*kInfo) 
    { 
        kInfo = &(*kInfo)->next; 
        kCount++; 
    } 
     
    int N = n; 
    int m = (int)log2(n); 
    int Rinit = vertical ? BS : 1; 
    batchSize = vertical ? min(BS, batchSize) : batchSize; 
    int passNum; 
     
    for(passNum = 0; passNum < numPasses; passNum++)  
    { 
         
        localString.clear(); 
        kernelName.clear(); 
         
        radix = radixArr[passNum]; 
        R1 = R1Arr[passNum]; 
        R2 = R2Arr[passNum]; 
                 
        int strideI = Rinit; 
        for(i = 0; i < numPasses; i++) 
            if(i != passNum) 
                strideI *= radixArr[i]; 
         
        int strideO = Rinit; 
        for(i = 0; i < passNum; i++) 
            strideO *= radixArr[i]; 
         
        int threadsPerXForm = R2; 
        batchSize = R2 == 1 ? plan->max_work_item_per_workgroup : batchSize; 
        batchSize = min(batchSize, strideI); 
        int threadsPerBlock = batchSize * threadsPerXForm; 
        threadsPerBlock = min(threadsPerBlock, maxThreadsPerBlock); 
        batchSize = threadsPerBlock / threadsPerXForm; 
        assert(R2 <= R1); 
        assert(R1*R2 == radix); 
        assert(R1 <= maxArrayLen); 
        assert(threadsPerBlock <= maxThreadsPerBlock); 
         
        int numIter = R1 / R2; 
        int gInInc = threadsPerBlock / batchSize; 
         
         
        int lgStrideO = log2(strideO); 
        int numBlocksPerXForm = strideI / batchSize; 
        int numBlocks = numBlocksPerXForm; 
        if(!vertical) 
            numBlocks *= BS; 
        else 
            numBlocks *= vertBS; 
         
        kernelName = string("fft") + num2str(kCount); 
        *kInfo = (cl_fft_kernel_info *) malloc(sizeof(cl_fft_kernel_info)); 
        (*kInfo)->kernel = 0; 
        if(R2 == 1) 
            (*kInfo)->lmem_size = 0; 
        else 
        { 
            if(strideO == 1) 
                (*kInfo)->lmem_size = (radix + 1)*batchSize; 
            else 
                (*kInfo)->lmem_size = threadsPerBlock*R1; 
        } 
        (*kInfo)->num_workgroups = numBlocks; 
        (*kInfo)->num_xforms_per_workgroup = 1; 
        (*kInfo)->num_workitems_per_workgroup = threadsPerBlock; 
        (*kInfo)->dir = dir; 
        if( (passNum == (numPasses - 1)) && (numPasses & 1) ) 
            (*kInfo)->in_place_possible = 1; 
        else 
            (*kInfo)->in_place_possible = 0; 
        (*kInfo)->next = NULL; 
        (*kInfo)->kernel_name = (char *) malloc(sizeof(char)*(kernelName.size()+1)); 
        strcpy((*kInfo)->kernel_name, kernelName.c_str()); 
         
        insertVariables(localString, R1); 
                         
        if(vertical)  
        { 
            localString += string("xNum = groupId >> ") + num2str((int)log2(numBlocksPerXForm)) + string(";\n"); 
            localString += string("groupId = groupId & ") + num2str(numBlocksPerXForm - 1) + string(";\n"); 
            localString += string("indexIn = mad24(groupId, ") + num2str(batchSize) + string(", xNum << ") + num2str((int)log2(n*BS)) + string(");\n"); 
            localString += string("tid = mul24(groupId, ") + num2str(batchSize) + string(");\n"); 
            localString += string("i = tid >> ") + num2str(lgStrideO) + string(";\n"); 
            localString += string("j = tid & ") + num2str(strideO - 1) + string(";\n"); 
            int stride = radix*Rinit; 
            for(i = 0; i < passNum; i++) 
                stride *= radixArr[i]; 
            localString += string("indexOut = mad24(i, ") + num2str(stride) + string(", j + ") + string("(xNum << ") + num2str((int) log2(n*BS)) + string("));\n"); 
            localString += string("bNum = groupId;\n"); 
        } 
        else  
        { 
            int lgNumBlocksPerXForm = log2(numBlocksPerXForm); 
            localString += string("bNum = groupId & ") + num2str(numBlocksPerXForm - 1) + string(";\n"); 
            localString += string("xNum = groupId >> ") + num2str(lgNumBlocksPerXForm) + string(";\n"); 
            localString += string("indexIn = mul24(bNum, ") + num2str(batchSize) + string(");\n"); 
            localString += string("tid = indexIn;\n"); 
            localString += string("i = tid >> ") + num2str(lgStrideO) + string(";\n"); 
            localString += string("j = tid & ") + num2str(strideO - 1) + string(";\n");  
            int stride = radix*Rinit; 
            for(i = 0; i < passNum; i++) 
                stride *= radixArr[i]; 
            localString += string("indexOut = mad24(i, ") + num2str(stride) + string(", j);\n");             
            localString += string("indexIn += (xNum << ") + num2str(m) + string(");\n"); 
            localString += string("indexOut += (xNum << ") + num2str(m) + string(");\n");    
        } 
         
        // Load Data 
        int lgBatchSize = log2(batchSize); 
        localString += string("tid = lId;\n"); 
        localString += string("i = tid & ") + num2str(batchSize - 1) + string(";\n"); 
        localString += string("j = tid >> ") + num2str(lgBatchSize) + string(";\n");  
        localString += string("indexIn += mad24(j, ") + num2str(strideI) + string(", i);\n"); 
  
        if(dataFormat == clFFT_SplitComplexFormat)  
        { 
            localString += string("in_real += indexIn;\n"); 
            localString += string("in_imag += indexIn;\n");          
            for(j = 0; j < R1; j++) 
                localString += string("a[") + num2str(j) + string("].x = in_real[") + num2str(j*gInInc*strideI) + string("];\n"); 
            for(j = 0; j < R1; j++)  
                localString += string("a[") + num2str(j) + string("].y = in_imag[") + num2str(j*gInInc*strideI) + string("];\n"); 
        } 
        else  
        { 
            localString += string("in += indexIn;\n"); 
            for(j = 0; j < R1; j++) 
                localString += string("a[") + num2str(j) + string("] = in[") + num2str(j*gInInc*strideI) + string("];\n"); 
        } 
         
        localString += string("fftKernel") + num2str(R1) + string("(a, dir);\n");                              
         
        if(R2 > 1) 
        { 
            // twiddle 
            for(k = 1; k < R1; k++)  
            { 
                localString += string("ang = dir*(2.0f*M_PI*") + num2str(k) + string("/") + num2str(radix) + string(")*j;\n"); 
                localString += string("w = (float2)(native_cos(ang), native_sin(ang));\n"); 
                localString += string("a[") + num2str(k) + string("] = complexMul(a[") + num2str(k) + string("], w);\n");  
            } 
         
            // shuffle 
            numIter = R1 / R2;   
            localString += string("indexIn = mad24(j, ") + num2str(threadsPerBlock*numIter) + string(", i);\n"); 
            localString += string("lMemStore = sMem + tid;\n"); 
            localString += string("lMemLoad = sMem + indexIn;\n"); 
            for(k = 0; k < R1; k++)  
                localString += string("lMemStore[") + num2str(k*threadsPerBlock) + string("] = a[") + num2str(k) + string("].x;\n"); 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n");    
            for(k = 0; k < numIter; k++) 
                for(t = 0; t < R2; t++) 
                    localString += string("a[") + num2str(k*R2+t) + string("].x = lMemLoad[") + num2str(t*batchSize + k*threadsPerBlock) + string("];\n"); 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n"); 
            for(k = 0; k < R1; k++)  
                localString += string("lMemStore[") + num2str(k*threadsPerBlock) + string("] = a[") + num2str(k) + string("].y;\n"); 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n");    
            for(k = 0; k < numIter; k++) 
                for(t = 0; t < R2; t++) 
                    localString += string("a[") + num2str(k*R2+t) + string("].y = lMemLoad[") + num2str(t*batchSize + k*threadsPerBlock) + string("];\n"); 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n"); 
         
            for(j = 0; j < numIter; j++) 
                localString += string("fftKernel") + num2str(R2) + string("(a + ") + num2str(j*R2) + string(", dir);\n"); 
        } 
         
        // twiddle 
        if(passNum < (numPasses - 1))  
        { 
            localString += string("l = ((bNum << ") + num2str(lgBatchSize) + string(") + i) >> ") + num2str(lgStrideO) + string(";\n"); 
            localString += string("k = j << ") + num2str((int)log2(R1/R2)) + string(";\n");  
            localString += string("ang1 = dir*(2.0f*M_PI/") + num2str(N) + string(")*l;\n"); 
            for(t = 0; t < R1; t++)  
            { 
                localString += string("ang = ang1*(k + ") + num2str((t%R2)*R1 + (t/R2)) + string(");\n"); 
                localString += string("w = (float2)(native_cos(ang), native_sin(ang));\n"); 
                localString += string("a[") + num2str(t) + string("] = complexMul(a[") + num2str(t) + string("], w);\n"); 
            } 
        } 
         
        // Store Data 
        if(strideO == 1)  
        { 
             
            localString += string("lMemStore = sMem + mad24(i, ") + num2str(radix + 1) + string(", j << ") + num2str((int)log2(R1/R2)) + string(");\n"); 
            localString += string("lMemLoad = sMem + mad24(tid >> ") + num2str((int)log2(radix)) + string(", ") + num2str(radix+1) + string(", tid & ") + num2str(radix-1) + string(");\n"); 
             
            for(int i = 0; i < R1/R2; i++) 
                for(int j = 0; j < R2; j++) 
                    localString += string("lMemStore[ ") + num2str(i + j*R1) + string("] = a[") + num2str(i*R2+j) + string("].x;\n"); 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n"); 
            if(threadsPerBlock >= radix) 
            { 
                for(int i = 0; i < R1; i++) 
                localString += string("a[") + num2str(i) + string("].x = lMemLoad[") + num2str(i*(radix+1)*(threadsPerBlock/radix)) + string("];\n"); 
            } 
            else 
            { 
                int innerIter = radix/threadsPerBlock; 
                int outerIter = R1/innerIter; 
                for(int i = 0; i < outerIter; i++) 
                    for(int j = 0; j < innerIter; j++) 
                        localString += string("a[") + num2str(i*innerIter+j) + string("].x = lMemLoad[") + num2str(j*threadsPerBlock + i*(radix+1)) + string("];\n"); 
            } 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n"); 
             
            for(int i = 0; i < R1/R2; i++) 
                for(int j = 0; j < R2; j++) 
                    localString += string("lMemStore[ ") + num2str(i + j*R1) + string("] = a[") + num2str(i*R2+j) + string("].y;\n"); 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n"); 
            if(threadsPerBlock >= radix) 
            { 
                for(int i = 0; i < R1; i++) 
                    localString += string("a[") + num2str(i) + string("].y = lMemLoad[") + num2str(i*(radix+1)*(threadsPerBlock/radix)) + string("];\n"); 
            } 
            else 
            { 
                int innerIter = radix/threadsPerBlock; 
                int outerIter = R1/innerIter; 
                for(int i = 0; i < outerIter; i++) 
                    for(int j = 0; j < innerIter; j++) 
                        localString += string("a[") + num2str(i*innerIter+j) + string("].y = lMemLoad[") + num2str(j*threadsPerBlock + i*(radix+1)) + string("];\n"); 
            } 
            localString += string("barrier(CLK_LOCAL_MEM_FENCE);\n"); 
             
            localString += string("indexOut += tid;\n"); 
            if(dataFormat == clFFT_SplitComplexFormat) { 
                localString += string("out_real += indexOut;\n"); 
                localString += string("out_imag += indexOut;\n"); 
                for(k = 0; k < R1; k++) 
                    localString += string("out_real[") + num2str(k*threadsPerBlock) + string("] = a[") + num2str(k) + string("].x;\n"); 
                for(k = 0; k < R1; k++) 
                    localString += string("out_imag[") + num2str(k*threadsPerBlock) + string("] = a[") + num2str(k) + string("].y;\n"); 
            } 
            else { 
                localString += string("out += indexOut;\n"); 
                for(k = 0; k < R1; k++) 
                    localString += string("out[") + num2str(k*threadsPerBlock) + string("] = a[") + num2str(k) + string("];\n");                 
            } 
          
        } 
        else  
        { 
            localString += string("indexOut += mad24(j, ") + num2str(numIter*strideO) + string(", i);\n"); 
            if(dataFormat == clFFT_SplitComplexFormat) { 
                localString += string("out_real += indexOut;\n"); 
                localString += string("out_imag += indexOut;\n");            
                for(k = 0; k < R1; k++) 
                    localString += string("out_real[") + num2str(((k%R2)*R1 + (k/R2))*strideO) + string("] = a[") + num2str(k) + string("].x;\n"); 
                for(k = 0; k < R1; k++) 
                    localString += string("out_imag[") + num2str(((k%R2)*R1 + (k/R2))*strideO) + string("] = a[") + num2str(k) + string("].y;\n"); 
            } 
            else { 
                localString += string("out += indexOut;\n"); 
                for(k = 0; k < R1; k++) 
                    localString += string("out[") + num2str(((k%R2)*R1 + (k/R2))*strideO) + string("] = a[") + num2str(k) + string("];\n"); 
            } 
        } 
         
        insertHeader(*kernelString, kernelName, dataFormat); 
        *kernelString += string("{\n"); 
        if((*kInfo)->lmem_size) 
            *kernelString += string("    __local float sMem[") + num2str((*kInfo)->lmem_size) + string("];\n"); 
        *kernelString += localString; 
        *kernelString += string("}\n");      
         
        N /= radix; 
        kInfo = &(*kInfo)->next; 
        kCount++; 
    } 
} 
  
void FFT1D(cl_fft_plan *plan, cl_fft_kernel_dir dir) 
{    
    unsigned int radixArray[10]; 
    unsigned int numRadix; 
     
    switch(dir) 
    { 
        case cl_fft_kernel_x: 
            if(plan->n.x > plan->max_localmem_fft_size) 
            { 
                createGlobalFFTKernelString(plan, plan->n.x, 1, cl_fft_kernel_x, 1); 
            } 
            else if(plan->n.x > 1) 
            { 
                getRadixArray(plan->n.x, radixArray, &numRadix, 0); 
                if(plan->n.x / radixArray[0] <= plan->max_work_item_per_workgroup) 
                { 
                    createLocalMemfftKernelString(plan); 
                } 
                else 
                { 
                    getRadixArray(plan->n.x, radixArray, &numRadix, plan->max_radix); 
                    if(plan->n.x / radixArray[0] <= plan->max_work_item_per_workgroup) 
                        createLocalMemfftKernelString(plan); 
                    else 
                        createGlobalFFTKernelString(plan, plan->n.x, 1, cl_fft_kernel_x, 1); 
                } 
            } 
            break; 
             
        case cl_fft_kernel_y: 
            if(plan->n.y > 1) 
                createGlobalFFTKernelString(plan, plan->n.y, plan->n.x, cl_fft_kernel_y, 1); 
            break; 
             
        case cl_fft_kernel_z: 
            if(plan->n.z > 1) 
                createGlobalFFTKernelString(plan, plan->n.z, plan->n.x*plan->n.y, cl_fft_kernel_z, 1); 
        default: 
            return; 
    } 
}