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fft_kernelstring.cpp

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  • Forked from einsteinathome / libclfft
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    fft_kernelstring.cpp 54.51 KiB
    
    //
    // File:       fft_kernelstring.cpp
    //
    // 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 <string.h>
    #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 = 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;
        }
    }