fft_kernelstring.cpp

//
// File:       fft_kernelstring.cpp
//
// Version:    <1.0>
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#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)