// Version:    <1.0>

//

// Disclaimer: IMPORTANT:  This Apple software is supplied to you by Apple Inc. ("Apple")

//             in consideration of your agreement to the following terms, and your use,

//             installation, modification or redistribution of this Apple software

//             constitutes acceptance of these terms.  If you do not agree with these

//             terms, please do not use, install, modify or redistribute this Apple

//             software.

//

//             In consideration of your agreement to abide by the following terms, and

//             subject to these terms, Apple grants you a personal, non - exclusive

//             license, under Apple's copyrights in this original Apple software ( the

//             "Apple Software" ), to use, reproduce, modify and redistribute the Apple

//             Software, with or without modifications, in source and / or binary forms;

//             provided that if you redistribute the Apple Software in its entirety and

//             without modifications, you must retain this notice and the following text

//             and disclaimers in all such redistributions of the Apple Software. Neither

//             the name, trademarks, service marks or logos of Apple Inc. may be used to

//             endorse or promote products derived from the Apple Software without specific

//             prior written permission from Apple.  Except as expressly stated in this

//             notice, no other rights or licenses, express or implied, are granted by

//             Apple herein, including but not limited to any patent rights that may be

//             infringed by your derivative works or by other works in which the Apple

//             Software may be incorporated.

//

//             The Apple Software is provided by Apple on an "AS IS" basis.  APPLE MAKES NO

//             WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION THE IMPLIED

//             WARRANTIES OF NON - INFRINGEMENT, MERCHANTABILITY AND FITNESS FOR A

//             PARTICULAR PURPOSE, REGARDING THE APPLE SOFTWARE OR ITS USE AND OPERATION

//             ALONE OR IN COMBINATION WITH YOUR PRODUCTS.

//

//             IN NO EVENT SHALL APPLE BE LIABLE FOR ANY SPECIAL, INDIRECT, INCIDENTAL OR

//             CONSEQUENTIAL DAMAGES ( INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF

//             SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS

//             INTERRUPTION ) ARISING IN ANY WAY OUT OF THE USE, REPRODUCTION, MODIFICATION

//             AND / OR DISTRIBUTION OF THE APPLE SOFTWARE, HOWEVER CAUSED AND WHETHER

//             UNDER THEORY OF CONTRACT, TORT ( INCLUDING NEGLIGENCE ), STRICT LIABILITY OR

//             OTHERWISE, EVEN IF APPLE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

//

// Copyright ( C ) 2008 Apple Inc. All Rights Reserved.

//

////////////////////////////////////////////////////////////////////////////////////////////////////

#include <stdio.h>

#include <stdlib.h>

#include <math.h>

#include <iostream>

#include <sstream>

#include <string>

#include <assert.h>

#include "fft_internal.h"

#include "clFFT.h"

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 = 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], R1Arr[10], R2Arr[10];

    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_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");

            for(int i = 0; i < R1; i++)

                localString += string("a[") + num2str(i) + string("].x = lMemLoad[") + num2str(i*(radix+1)*(threadsPerBlock/radix)) + 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");

            for(int i = 0; i < R1; i++)

                localString += string("a[") + num2str(i) + string("].y = lMemLoad[") + num2str(i*(radix+1)*(threadsPerBlock/radix)) + 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;

    }

}