fft_base_kernels.h

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/*!
 * \file fft_base_kernels.h
 * \brief FFT base kernels for OpenCL
 *
 *
 * Version:    <1.0>
 *
 * Copyright ( C ) 2008 Apple Inc. All Rights Reserved.
 * SPDX-License-Identifier: LicenseRef-Apple-Permissive
 *
 */


#ifndef __CL_FFT_BASE_KERNELS_
#define __CL_FFT_BASE_KERNELS_

#include <string>

using namespace std;

static string baseKernels = string(
    "#ifndef M_PI\n"
    "#define M_PI 0x1.921fb54442d18p+1\n"
    "#endif\n"
    "#define complexMul(a,b) ((float2)(mad(-(a).y, (b).y, (a).x * (b).x), mad((a).y, (b).x, (a).x * (b).y)))\n"
    "#define conj(a) ((float2)((a).x, -(a).y))\n"
    "#define conjTransp(a) ((float2)(-(a).y, (a).x))\n"
    "\n"
    "#define fftKernel2(a,dir) \\\n"
    "{ \\\n"
    "    float2 c = (a)[0];    \\\n"
    "    (a)[0] = c + (a)[1];  \\\n"
    "    (a)[1] = c - (a)[1];  \\\n"
    "}\n"
    "\n"
    "#define fftKernel2S(d1,d2,dir) \\\n"
    "{ \\\n"
    "    float2 c = (d1);   \\\n"
    "    (d1) = c + (d2);   \\\n"
    "    (d2) = c - (d2);   \\\n"
    "}\n"
    "\n"
    "#define fftKernel4(a,dir) \\\n"
    "{ \\\n"
    "    fftKernel2S((a)[0], (a)[2], dir); \\\n"
    "    fftKernel2S((a)[1], (a)[3], dir); \\\n"
    "    fftKernel2S((a)[0], (a)[1], dir); \\\n"
    "    (a)[3] = (float2)(dir)*(conjTransp((a)[3])); \\\n"
    "    fftKernel2S((a)[2], (a)[3], dir); \\\n"
    "    float2 c = (a)[1]; \\\n"
    "    (a)[1] = (a)[2]; \\\n"
    "    (a)[2] = c; \\\n"
    "}\n"
    "\n"
    "#define fftKernel4s(a0,a1,a2,a3,dir) \\\n"
    "{ \\\n"
    "    fftKernel2S((a0), (a2), dir); \\\n"
    "    fftKernel2S((a1), (a3), dir); \\\n"
    "    fftKernel2S((a0), (a1), dir); \\\n"
    "    (a3) = (float2)(dir)*(conjTransp((a3))); \\\n"
    "    fftKernel2S((a2), (a3), dir); \\\n"
    "    float2 c = (a1); \\\n"
    "    (a1) = (a2); \\\n"
    "    (a2) = c; \\\n"
    "}\n"
    "\n"
    "#define bitreverse8(a) \\\n"
    "{ \\\n"
    "    float2 c; \\\n"
    "    c = (a)[1]; \\\n"
    "    (a)[1] = (a)[4]; \\\n"
    "    (a)[4] = c; \\\n"
    "    c = (a)[3]; \\\n"
    "    (a)[3] = (a)[6]; \\\n"
    "    (a)[6] = c; \\\n"
    "}\n"
    "\n"
    "#define fftKernel8(a,dir) \\\n"
    "{ \\\n"
    "   const float2 w1  = (float2)(0x1.6a09e6p-1f,  dir*0x1.6a09e6p-1f);  \\\n"
    "   const float2 w3  = (float2)(-0x1.6a09e6p-1f, dir*0x1.6a09e6p-1f);  \\\n"
    "   float2 c; \\\n"
    "   fftKernel2S((a)[0], (a)[4], dir); \\\n"
    "   fftKernel2S((a)[1], (a)[5], dir); \\\n"
    "   fftKernel2S((a)[2], (a)[6], dir); \\\n"
    "   fftKernel2S((a)[3], (a)[7], dir); \\\n"
    "   (a)[5] = complexMul(w1, (a)[5]); \\\n"
    "   (a)[6] = (float2)(dir)*(conjTransp((a)[6])); \\\n"
    "   (a)[7] = complexMul(w3, (a)[7]); \\\n"
    "   fftKernel2S((a)[0], (a)[2], dir); \\\n"
    "   fftKernel2S((a)[1], (a)[3], dir); \\\n"
    "   fftKernel2S((a)[4], (a)[6], dir); \\\n"
    "   fftKernel2S((a)[5], (a)[7], dir); \\\n"
    "   (a)[3] = (float2)(dir)*(conjTransp((a)[3])); \\\n"
    "   (a)[7] = (float2)(dir)*(conjTransp((a)[7])); \\\n"
    "   fftKernel2S((a)[0], (a)[1], dir); \\\n"
    "   fftKernel2S((a)[2], (a)[3], dir); \\\n"
    "   fftKernel2S((a)[4], (a)[5], dir); \\\n"
    "   fftKernel2S((a)[6], (a)[7], dir); \\\n"
    "   bitreverse8((a)); \\\n"
    "}\n"
    "\n"
    "#define bitreverse4x4(a) \\\n"
    "{ \\\n"
    "   float2 c; \\\n"
    "   c = (a)[1];  (a)[1]  = (a)[4];  (a)[4]  = c; \\\n"
    "   c = (a)[2];  (a)[2]  = (a)[8];  (a)[8]  = c; \\\n"
    "   c = (a)[3];  (a)[3]  = (a)[12]; (a)[12] = c; \\\n"
    "   c = (a)[6];  (a)[6]  = (a)[9];  (a)[9]  = c; \\\n"
    "   c = (a)[7];  (a)[7]  = (a)[13]; (a)[13] = c; \\\n"
    "   c = (a)[11]; (a)[11] = (a)[14]; (a)[14] = c; \\\n"
    "}\n"
    "\n"
    "#define fftKernel16(a,dir) \\\n"
    "{ \\\n"
    "    const float w0 = 0x1.d906bcp-1f; \\\n"
    "    const float w1 = 0x1.87de2ap-2f; \\\n"
    "    const float w2 = 0x1.6a09e6p-1f; \\\n"
    "    fftKernel4s((a)[0], (a)[4], (a)[8],  (a)[12], dir); \\\n"
    "    fftKernel4s((a)[1], (a)[5], (a)[9],  (a)[13], dir); \\\n"
    "    fftKernel4s((a)[2], (a)[6], (a)[10], (a)[14], dir); \\\n"
    "    fftKernel4s((a)[3], (a)[7], (a)[11], (a)[15], dir); \\\n"
    "    (a)[5]  = complexMul((a)[5], (float2)(w0, dir*w1)); \\\n"
    "    (a)[6]  = complexMul((a)[6], (float2)(w2, dir*w2)); \\\n"
    "    (a)[7]  = complexMul((a)[7], (float2)(w1, dir*w0)); \\\n"
    "    (a)[9]  = complexMul((a)[9], (float2)(w2, dir*w2)); \\\n"
    "    (a)[10] = (float2)(dir)*(conjTransp((a)[10])); \\\n"
    "    (a)[11] = complexMul((a)[11], (float2)(-w2, dir*w2)); \\\n"
    "    (a)[13] = complexMul((a)[13], (float2)(w1, dir*w0)); \\\n"
    "    (a)[14] = complexMul((a)[14], (float2)(-w2, dir*w2)); \\\n"
    "    (a)[15] = complexMul((a)[15], (float2)(-w0, dir*-w1)); \\\n"
    "    fftKernel4((a), dir); \\\n"
    "    fftKernel4((a) + 4, dir); \\\n"
    "    fftKernel4((a) + 8, dir); \\\n"
    "    fftKernel4((a) + 12, dir); \\\n"
    "    bitreverse4x4((a)); \\\n"
    "}\n"
    "\n"
    "#define bitreverse32(a) \\\n"
    "{ \\\n"
    "    float2 c1, c2; \\\n"
    "    c1 = (a)[2];   (a)[2] = (a)[1];   c2 = (a)[4];   (a)[4] = c1;   c1 = (a)[8];   (a)[8] = c2;    c2 = (a)[16];  (a)[16] = c1;   (a)[1] = c2; \\\n"
    "    c1 = (a)[6];   (a)[6] = (a)[3];   c2 = (a)[12];  (a)[12] = c1;  c1 = (a)[24];  (a)[24] = c2;   c2 = (a)[17];  (a)[17] = c1;   (a)[3] = c2; \\\n"
    "    c1 = (a)[10];  (a)[10] = (a)[5];  c2 = (a)[20];  (a)[20] = c1;  c1 = (a)[9];   (a)[9] = c2;    c2 = (a)[18];  (a)[18] = c1;   (a)[5] = c2; \\\n"
    "    c1 = (a)[14];  (a)[14] = (a)[7];  c2 = (a)[28];  (a)[28] = c1;  c1 = (a)[25];  (a)[25] = c2;   c2 = (a)[19];  (a)[19] = c1;   (a)[7] = c2; \\\n"
    "    c1 = (a)[22];  (a)[22] = (a)[11]; c2 = (a)[13];  (a)[13] = c1;  c1 = (a)[26];  (a)[26] = c2;   c2 = (a)[21];  (a)[21] = c1;   (a)[11] = c2; \\\n"
    "    c1 = (a)[30];  (a)[30] = (a)[15]; c2 = (a)[29];  (a)[29] = c1;  c1 = (a)[27];  (a)[27] = c2;   c2 = (a)[23];  (a)[23] = c1;   (a)[15] = c2; \\\n"
    "}\n"
    "\n"
    "#define fftKernel32(a,dir) \\\n"
    "{ \\\n"
    "    fftKernel2S((a)[0],  (a)[16], dir); \\\n"
    "    fftKernel2S((a)[1],  (a)[17], dir); \\\n"
    "    fftKernel2S((a)[2],  (a)[18], dir); \\\n"
    "    fftKernel2S((a)[3],  (a)[19], dir); \\\n"
    "    fftKernel2S((a)[4],  (a)[20], dir); \\\n"
    "    fftKernel2S((a)[5],  (a)[21], dir); \\\n"
    "    fftKernel2S((a)[6],  (a)[22], dir); \\\n"
    "    fftKernel2S((a)[7],  (a)[23], dir); \\\n"
    "    fftKernel2S((a)[8],  (a)[24], dir); \\\n"
    "    fftKernel2S((a)[9],  (a)[25], dir); \\\n"
    "    fftKernel2S((a)[10], (a)[26], dir); \\\n"
    "    fftKernel2S((a)[11], (a)[27], dir); \\\n"
    "    fftKernel2S((a)[12], (a)[28], dir); \\\n"
    "    fftKernel2S((a)[13], (a)[29], dir); \\\n"
    "    fftKernel2S((a)[14], (a)[30], dir); \\\n"
    "    fftKernel2S((a)[15], (a)[31], dir); \\\n"
    "    (a)[17] = complexMul((a)[17], (float2)(0x1.f6297cp-1f, dir*0x1.8f8b84p-3f)); \\\n"
    "    (a)[18] = complexMul((a)[18], (float2)(0x1.d906bcp-1f, dir*0x1.87de2ap-2f)); \\\n"
    "    (a)[19] = complexMul((a)[19], (float2)(0x1.a9b662p-1f, dir*0x1.1c73b4p-1f)); \\\n"
    "    (a)[20] = complexMul((a)[20], (float2)(0x1.6a09e6p-1f, dir*0x1.6a09e6p-1f)); \\\n"
    "    (a)[21] = complexMul((a)[21], (float2)(0x1.1c73b4p-1f, dir*0x1.a9b662p-1f)); \\\n"
    "    (a)[22] = complexMul((a)[22], (float2)(0x1.87de2ap-2f, dir*0x1.d906bcp-1f)); \\\n"
    "    (a)[23] = complexMul((a)[23], (float2)(0x1.8f8b84p-3f, dir*0x1.f6297cp-1f)); \\\n"
    "    (a)[24] = complexMul((a)[24], (float2)(0x0p+0f, dir*0x1p+0f)); \\\n"
    "    (a)[25] = complexMul((a)[25], (float2)(-0x1.8f8b84p-3f, dir*0x1.f6297cp-1f)); \\\n"
    "    (a)[26] = complexMul((a)[26], (float2)(-0x1.87de2ap-2f, dir*0x1.d906bcp-1f)); \\\n"
    "    (a)[27] = complexMul((a)[27], (float2)(-0x1.1c73b4p-1f, dir*0x1.a9b662p-1f)); \\\n"
    "    (a)[28] = complexMul((a)[28], (float2)(-0x1.6a09e6p-1f, dir*0x1.6a09e6p-1f)); \\\n"
    "    (a)[29] = complexMul((a)[29], (float2)(-0x1.a9b662p-1f, dir*0x1.1c73b4p-1f)); \\\n"
    "    (a)[30] = complexMul((a)[30], (float2)(-0x1.d906bcp-1f, dir*0x1.87de2ap-2f)); \\\n"
    "    (a)[31] = complexMul((a)[31], (float2)(-0x1.f6297cp-1f, dir*0x1.8f8b84p-3f)); \\\n"
    "    fftKernel16((a), dir); \\\n"
    "    fftKernel16((a) + 16, dir); \\\n"
    "    bitreverse32((a)); \\\n"
    "}\n\n");

static string twistKernelInterleaved = string(
    "__kernel void \\\n"
    "clFFT_1DTwistInterleaved(__global float2 *in, unsigned int startRow, unsigned int numCols, unsigned int N, unsigned int numRowsToProcess, int dir) \\\n"
    "{ \\\n"
    "   float2 a, w; \\\n"
    "   float ang; \\\n"
    "   unsigned int j; \\\n"
    "   unsigned int i = get_global_id(0); \\\n"
    "   unsigned int startIndex = i; \\\n"
    "    \\\n"
    "   if(i < numCols) \\\n"
    "   { \\\n"
    "       for(j = 0; j < numRowsToProcess; j++) \\\n"
    "       { \\\n"
    "           a = in[startIndex]; \\\n"
    "           ang = 2.0f * M_PI * dir * i * (startRow + j) / N; \\\n"
    "           w = (float2)(native_cos(ang), native_sin(ang)); \\\n"
    "           a = complexMul(a, w); \\\n"
    "           in[startIndex] = a; \\\n"
    "           startIndex += numCols; \\\n"
    "       } \\\n"
    "   }    \\\n"
    "} \\\n");

static string twistKernelPlannar = string(
    "__kernel void \\\n"
    "clFFT_1DTwistSplit(__global float *in_real, __global float *in_imag , unsigned int startRow, unsigned int numCols, unsigned int N, unsigned int numRowsToProcess, int dir) \\\n"
    "{ \\\n"
    "    float2 a, w; \\\n"
    "    float ang; \\\n"
    "    unsigned int j; \\\n"
    "   unsigned int i = get_global_id(0); \\\n"
    "   unsigned int startIndex = i; \\\n"
    "    \\\n"
    "   if(i < numCols) \\\n"
    "   { \\\n"
    "       for(j = 0; j < numRowsToProcess; j++) \\\n"
    "       { \\\n"
    "           a = (float2)(in_real[startIndex], in_imag[startIndex]); \\\n"
    "           ang = 2.0f * M_PI * dir * i * (startRow + j) / N; \\\n"
    "           w = (float2)(native_cos(ang), native_sin(ang)); \\\n"
    "           a = complexMul(a, w); \\\n"
    "           in_real[startIndex] = a.x; \\\n"
    "           in_imag[startIndex] = a.y; \\\n"
    "           startIndex += numCols; \\\n"
    "       } \\\n"
    "   }    \\\n"
    "} \\\n");


#endif