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feddischso |
/***************************************************************************
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* *
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* File : cordic_iterative.c *
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* Project : YAC (Yet Another CORDIC Core) *
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* Creation : Feb. 2014 *
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* Limitations : *
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* Platform : Linux, Mac, Windows *
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* Target : Octave, Matlab, Standalone-Application *
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* *
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* Author(s): : Christian Haettich *
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* Email : feddischson@opencores.org *
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* *
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* *
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** **
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* *
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* Description *
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* C-implementation of an interative cordic. *
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* General information about the CORDIC algorithm can be found *
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* here: - http://en.wikipedia.org/wiki/CORDIC *
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* - http://en.wikibooks.org/wiki/Digital_Circuits/CORDIC *
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* *
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* *
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** **
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* *
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* TODO *
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* Some documentation and function description *
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* *
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* *
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* *
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* *
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****************************************************************************
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* *
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* Copyright Notice *
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* *
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* This file is part of YAC - Yet Another CORDIC Core *
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* Copyright (c) 2014, Author(s), All rights reserved. *
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* *
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* YAC is free software; you can redistribute it and/or *
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* modify it under the terms of the GNU Lesser General Public *
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* License as published by the Free Software Foundation; either *
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* version 3.0 of the License, or (at your option) any later version. *
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* *
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* YAC is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
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* Lesser General Public License for more details. *
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* *
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* You should have received a copy of the GNU Lesser General Public *
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* License along with this library. If not, download it from *
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* http://www.gnu.org/licenses/lgpl *
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* *
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***************************************************************************/
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#include <stdio.h>
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#include <stdlib.h>
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#include <math.h>
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feddischso |
#ifndef OR32_TARGET
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#include "mex.h"
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#endif
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/* enable debug output */
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#define PRINT_DEBUG 0
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/* #define CORDIC_ROUNDING 0.5 */
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#define CORDIC_ROUNDING 0.0
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/* the supported modes */
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#define C_FLAG_VEC_ROT 0x08
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#define C_FLAG_ATAN_3 0x04
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#define C_MODE_MSK 0x03
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#define C_MODE_CIR 0x00
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#define C_MODE_LIN 0x01
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#define C_MODE_HYP 0x02
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#ifndef OR32_TARGET
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#define PRINT mexPrintf
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#endif
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void cordic_int( long long int x_i,
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long long int y_i,
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long long int a_i,
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long long int * x_o,
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long long int * y_o,
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long long int * a_o,
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int * it_o,
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int mode,
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int XY_WIDTH,
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int A_WIDTH,
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int GUARD_BITS,
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int RM_GAIN );
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void cordic_int_dbg ( long long int x,
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long long int y,
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long long int a,
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int mode,
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int it,
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char* msg );
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int cordic_int_init ( long long int *x,
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long long int *y,
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long long int *a,
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int mode,
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int A_WIDTH,
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int XY_WIDTH );
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void cordic_int_rm_gain( long long int *x,
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long long int *y,
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int mode,
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int rm_gain );
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int cordic_int_rotate( long long int * x,
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long long int * y,
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long long int * a,
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int mode,
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int A_WIDTH );
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long long int cordic_int_lut ( int mode,
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int it,
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int A_WIDTH );
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#ifndef OR32_TARGET
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void mexFunction(int nlhs, mxArray *plhs[],
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int nrhs, const mxArray *prhs[])
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{
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double *inx,*iny,*inz,*outx,*outy,*outz,*outi;
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double mode;
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double xy_width;
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double a_width;
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double guard_bits;
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double rm_gain;
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int mrowsx,ncolsx,mrowsy,ncolsy,mrowsz,ncolsz;
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int i;
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int it;
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if(nrhs!=8 )
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mexErrMsgTxt("8 input arguments required");
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if(nlhs!=4)
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mexErrMsgTxt("4 output arguments required");
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feddischso |
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if (!mxIsDouble(prhs[0]) || mxIsComplex(prhs[0]))
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mexErrMsgTxt("Input x must be double and non-complex");
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feddischso |
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if (!mxIsDouble(prhs[1]) || mxIsComplex(prhs[1]))
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mexErrMsgTxt("Input y must be double and non-complex");
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feddischso |
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if (!mxIsDouble(prhs[2]) || mxIsComplex(prhs[2]))
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mexErrMsgTxt("Input a must be double and non-complex");
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feddischso |
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feddischso |
mrowsx = mxGetM(prhs[0]);
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ncolsx = mxGetN(prhs[0]);
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mrowsy = mxGetM(prhs[1]);
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ncolsy = mxGetN(prhs[1]);
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mrowsz = mxGetM(prhs[2]);
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ncolsz = mxGetN(prhs[2]);
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if (mrowsx > 1 || mrowsy >1 || mrowsz > 1)
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mexErrMsgTxt("Input vector must have the size Nx1.");
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/* printf("%d %d %d\n", ncolsx, ncolsy, ncolsa); */
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feddischso |
if (ncolsx!=ncolsy || ncolsx!=ncolsz || ncolsy!=ncolsz)
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mexErrMsgTxt("Input vectors don't have the same length!");
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feddischso |
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feddischso |
plhs[0] = mxCreateDoubleMatrix(mrowsx,ncolsx,mxREAL);
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plhs[1] = mxCreateDoubleMatrix(mrowsy,ncolsy,mxREAL);
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plhs[2] = mxCreateDoubleMatrix(mrowsz,ncolsz,mxREAL);
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plhs[3] = mxCreateDoubleMatrix(mrowsz,ncolsz,mxREAL);
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feddischso |
inx = mxGetPr(prhs[0]);
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iny = mxGetPr(prhs[1]);
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inz = mxGetPr(prhs[2]);
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mode = mxGetScalar(prhs[3]);
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xy_width = mxGetScalar(prhs[4]);
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a_width = mxGetScalar(prhs[5]);
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guard_bits = mxGetScalar(prhs[6]);
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rm_gain = mxGetScalar(prhs[7]);
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outx= mxGetPr(plhs[0]);
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outy= mxGetPr(plhs[1]);
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outz= mxGetPr(plhs[2]);
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outi= mxGetPr(plhs[3]);
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for( i = 0; i < ncolsx; i++ )
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{
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long long int inx_i = inx[ i ];
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long long int iny_i = iny[ i ];
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long long int inz_i = inz[ i ];
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long long int outx_i = 0;
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long long int outy_i = 0;
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long long int outz_i = 0;
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/* PRINT("x: %lld, y: %lld, a: %lld\n", inx_i, iny_i, inz_i ); */
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cordic_int( inx_i, iny_i, inz_i,
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&outx_i, &outy_i, &outz_i,
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&it, mode,
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xy_width, a_width, guard_bits, rm_gain );
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outx[i] = outx_i;
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outy[i] = outy_i;
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outz[i] = outz_i;
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outi[i] = it;
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feddischso |
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2 |
feddischso |
}
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}
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7 |
feddischso |
#endif
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2 |
feddischso |
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void cordic_int( long long int x_i,
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long long int y_i,
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long long int a_i,
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long long int * x_o,
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long long int * y_o,
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long long int * a_o,
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int * it_o,
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int mode,
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int XY_WIDTH,
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int A_WIDTH,
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int GUARD_BITS,
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int RM_GAIN )
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{
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long long int x;
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long long int y;
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long long int a;
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long long int s;
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int ov;
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int it = 0;
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7 |
feddischso |
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2 |
feddischso |
/* total with, including guard bits */
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int XY_WIDTH_G = XY_WIDTH + GUARD_BITS;
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7 |
feddischso |
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2 |
feddischso |
cordic_int_dbg( x_i, y_i, a_i, mode, 0, "input" );
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if( !cordic_int_init( &x_i, &y_i, &a_i, mode, A_WIDTH, XY_WIDTH ) )
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{
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it = cordic_int_rotate( &x_i, &y_i, &a_i, mode, A_WIDTH );
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cordic_int_rm_gain( &x_i, &y_i, mode, RM_GAIN );
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}
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*x_o = x_i;
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*y_o = y_i;
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*a_o = a_i;
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*it_o = it;
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}
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| 267 |
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int cordic_int_init( long long int *x,
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long long int *y,
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long long int *a,
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int mode,
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int A_WIDTH,
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int XY_WIDTH )
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{
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| 275 |
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int already_done = 0;
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| 276 |
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| 277 |
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| 278 |
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long long int PI = ( long long int )( M_PI * pow( 2, A_WIDTH-1 ) + 0.5 );
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long long int PI_H = (long long int)( M_PI * pow( 2, A_WIDTH-2 ) + 0.5 );
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| 280 |
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4 |
feddischso |
long long int XY_MAX = pow( 2, XY_WIDTH-1 )-1;
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7 |
feddischso |
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4 |
feddischso |
cordic_int_dbg( *x, *y, *a, mode, 0, "before init" );
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| 286 |
7 |
feddischso |
if( 0 != ( mode & C_FLAG_VEC_ROT ) && *y == 0 )
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| 287 |
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{
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| 288 |
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already_done = 1;
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| 289 |
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*a = 0;
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| 290 |
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#if PRINT_DEBUG > 0
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| 291 |
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PRINT( "Zero input, skipping rotations \n" );
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| 292 |
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#endif
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| 293 |
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}
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| 294 |
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else if( 0 == ( mode & C_FLAG_VEC_ROT ) && *a == 0 )
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{
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| 296 |
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#if PRINT_DEBUG > 0
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| 297 |
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PRINT("zero angular input\n" );
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#endif
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already_done = 1;
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}
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2 |
feddischso |
/* Circular rotation mode */
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7 |
feddischso |
else if( 0 == ( mode & C_FLAG_VEC_ROT ) &&
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2 |
feddischso |
C_MODE_CIR == ( mode & C_MODE_MSK ) )
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{
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| 306 |
7 |
feddischso |
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| 307 |
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| 308 |
2 |
feddischso |
/* move from third quadrant to first
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| 309 |
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quadrant if necessary */
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| 310 |
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if( *a < - PI_H )
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| 311 |
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{
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| 312 |
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if( ! (mode & C_FLAG_ATAN_3) )
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| 313 |
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*a += PI;
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| 314 |
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*x = -*x;
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| 315 |
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*y = -*y;
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| 316 |
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#if PRINT_DEBUG > 0
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PRINT("move from third quadrand");
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#endif
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}
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| 320 |
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/* move from second quadrant to fourth
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| 321 |
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quadrant if necessary */
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| 322 |
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else if( *a > PI_H )
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| 323 |
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{
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| 324 |
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if( ! (mode & C_FLAG_ATAN_3) )
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| 325 |
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*a -= PI;
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*x = -*x;
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*y = -*y;
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| 328 |
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#if PRINT_DEBUG > 0
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PRINT("move from second quadrand\n" );
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#endif
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| 331 |
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}
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| 332 |
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}
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| 333 |
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| 334 |
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/* circular vector mode */
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| 335 |
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else if ( 0 != ( mode & C_FLAG_VEC_ROT ) &&
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| 336 |
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C_MODE_CIR == ( mode & C_MODE_MSK ) )
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| 337 |
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{
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| 338 |
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| 339 |
7 |
feddischso |
if( *x == XY_MAX && *y == XY_MAX )
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| 340 |
2 |
feddischso |
{
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| 341 |
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#if PRINT_DEBUG > 0
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| 342 |
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PRINT( "All max, skipping rotations 1\n" );
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| 343 |
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#endif
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| 344 |
7 |
feddischso |
*x = sqrt( 2 ) * pow( 2, XY_WIDTH-1 ) + 0.5;
|
| 345 |
|
|
*y = 0;
|
| 346 |
2 |
feddischso |
*a = cordic_int_lut( mode, 0, A_WIDTH );
|
| 347 |
|
|
already_done = 1;
|
| 348 |
|
|
}
|
| 349 |
|
|
else if( *x == -XY_MAX && *y == -XY_MAX )
|
| 350 |
|
|
{
|
| 351 |
|
|
#if PRINT_DEBUG > 0
|
| 352 |
|
|
PRINT( "All max, skipping rotations 2\n" );
|
| 353 |
|
|
#endif
|
| 354 |
7 |
feddischso |
*x = sqrt( 2 ) * pow( 2, XY_WIDTH-1 ) + 0.5;
|
| 355 |
|
|
*y = 0;
|
| 356 |
2 |
feddischso |
*a = cordic_int_lut( mode, 0, A_WIDTH ) - PI;
|
| 357 |
|
|
already_done = 1;
|
| 358 |
|
|
}
|
| 359 |
|
|
else if( *x == XY_MAX && *y == -XY_MAX )
|
| 360 |
|
|
{
|
| 361 |
|
|
#if PRINT_DEBUG > 0
|
| 362 |
|
|
PRINT( "All max, skipping rotations 3\n" );
|
| 363 |
|
|
#endif
|
| 364 |
7 |
feddischso |
*x = sqrt( 2 ) * pow( 2, XY_WIDTH-1 ) + 0.5;
|
| 365 |
|
|
*y = 0;
|
| 366 |
2 |
feddischso |
*a = -cordic_int_lut( mode, 0, A_WIDTH );
|
| 367 |
|
|
already_done = 1;
|
| 368 |
|
|
}
|
| 369 |
|
|
else if( *x == -XY_MAX && *y == XY_MAX )
|
| 370 |
|
|
{
|
| 371 |
|
|
#if PRINT_DEBUG > 0
|
| 372 |
|
|
PRINT( "All max, skipping rotations 4\n" );
|
| 373 |
|
|
#endif
|
| 374 |
7 |
feddischso |
*x = sqrt( 2 ) * pow( 2, XY_WIDTH-1 ) + 0.5;
|
| 375 |
|
|
*y = 0;
|
| 376 |
2 |
feddischso |
*a = PI - cordic_int_lut( mode, 0, A_WIDTH );
|
| 377 |
|
|
already_done = 1;
|
| 378 |
|
|
}
|
| 379 |
|
|
|
| 380 |
|
|
|
| 381 |
|
|
|
| 382 |
|
|
else if( *x == 0 && *y > 0 )
|
| 383 |
|
|
{
|
| 384 |
|
|
*a = PI_H;
|
| 385 |
|
|
*x = *y;
|
| 386 |
|
|
already_done = 1;
|
| 387 |
|
|
#if PRINT_DEBUG > 0
|
| 388 |
7 |
feddischso |
PRINT( "Fixed value of pi/2, skipping rotations\n" );
|
| 389 |
2 |
feddischso |
#endif
|
| 390 |
|
|
*y = 0;
|
| 391 |
|
|
}
|
| 392 |
|
|
else if( *x == 0 && *y < 0 )
|
| 393 |
|
|
{
|
| 394 |
|
|
*a = -PI_H;
|
| 395 |
|
|
*x = -*y;
|
| 396 |
|
|
*y = 0;
|
| 397 |
|
|
already_done = 1;
|
| 398 |
|
|
#if PRINT_DEBUG > 0
|
| 399 |
7 |
feddischso |
PRINT( "Fixed value of -pi/2, skipping rotations\n" );
|
| 400 |
2 |
feddischso |
#endif
|
| 401 |
|
|
}
|
| 402 |
|
|
else if( *x < 0 && *y >= 0 )
|
| 403 |
|
|
{
|
| 404 |
|
|
*x = -*x;
|
| 405 |
|
|
*y = -*y;
|
| 406 |
|
|
*a = PI;
|
| 407 |
|
|
#if PRINT_DEBUG > 0
|
| 408 |
|
|
PRINT("pre-rotation from second to the fourth quadrant\n" );
|
| 409 |
|
|
#endif
|
| 410 |
|
|
}
|
| 411 |
|
|
else if( *x < 0 && *y < 0 )
|
| 412 |
|
|
{
|
| 413 |
|
|
*x = -*x;
|
| 414 |
|
|
*y = -*y;
|
| 415 |
|
|
*a = -PI;
|
| 416 |
|
|
#if PRINT_DEBUG > 0
|
| 417 |
|
|
PRINT("pre-rotation from third to first quadrand\n" );
|
| 418 |
|
|
#endif
|
| 419 |
|
|
}
|
| 420 |
|
|
else
|
| 421 |
|
|
*a = 0;
|
| 422 |
|
|
}
|
| 423 |
|
|
/* linear vector mode */
|
| 424 |
|
|
else if ( 0 != ( mode & C_FLAG_VEC_ROT ) &&
|
| 425 |
|
|
C_MODE_LIN == ( mode & C_MODE_MSK ) )
|
| 426 |
|
|
{
|
| 427 |
|
|
if( *x < 0 )
|
| 428 |
|
|
{
|
| 429 |
|
|
*x = -*x;
|
| 430 |
|
|
*y = -*y;
|
| 431 |
|
|
}
|
| 432 |
|
|
*a = 0;
|
| 433 |
|
|
}
|
| 434 |
|
|
cordic_int_dbg( *x, *y, *a, mode, 0, "after init" );
|
| 435 |
|
|
return already_done;
|
| 436 |
|
|
}
|
| 437 |
|
|
|
| 438 |
|
|
|
| 439 |
|
|
|
| 440 |
11 |
feddischso |
void cordic_int_dbg( long long int x,
|
| 441 |
2 |
feddischso |
long long int y,
|
| 442 |
|
|
long long int a,
|
| 443 |
|
|
int mode,
|
| 444 |
|
|
int it,
|
| 445 |
|
|
char* msg )
|
| 446 |
|
|
{
|
| 447 |
|
|
#if PRINT_DEBUG > 0
|
| 448 |
|
|
PRINT( "%20s: mode = %d, iteration %d, x = % 10.lld, y = %10.lld, a = %10.lld \n",
|
| 449 |
|
|
msg,mode,it,x,y,a );
|
| 450 |
|
|
#endif
|
| 451 |
|
|
}
|
| 452 |
|
|
|
| 453 |
|
|
int cordic_int_repeat( iteration, mode )
|
| 454 |
|
|
{
|
| 455 |
|
|
int i = 4;
|
| 456 |
7 |
feddischso |
|
| 457 |
2 |
feddischso |
if( C_MODE_HYP != ( mode & C_MODE_MSK ) )
|
| 458 |
|
|
return 0;
|
| 459 |
7 |
feddischso |
|
| 460 |
|
|
|
| 461 |
2 |
feddischso |
while( 1 )
|
| 462 |
|
|
{
|
| 463 |
|
|
if( i == iteration )
|
| 464 |
|
|
return 1;
|
| 465 |
|
|
else if( i > iteration )
|
| 466 |
|
|
return 0;
|
| 467 |
|
|
i = i * 3 + 1;
|
| 468 |
|
|
}
|
| 469 |
|
|
}
|
| 470 |
|
|
|
| 471 |
|
|
|
| 472 |
|
|
|
| 473 |
|
|
|
| 474 |
|
|
int cordic_int_rotate( long long int * x,
|
| 475 |
|
|
long long int * y,
|
| 476 |
|
|
long long int * a,
|
| 477 |
|
|
int mode,
|
| 478 |
|
|
int A_WIDTH )
|
| 479 |
|
|
{
|
| 480 |
|
|
int it = 0;
|
| 481 |
|
|
long long int xsh, ysh;
|
| 482 |
|
|
long long int ylst, alst;
|
| 483 |
|
|
int sign;
|
| 484 |
|
|
int repeat = 0;
|
| 485 |
|
|
|
| 486 |
|
|
while( 1 )
|
| 487 |
|
|
{
|
| 488 |
|
|
/* get the sign */
|
| 489 |
|
|
if( 0 == ( mode & C_FLAG_VEC_ROT ) )
|
| 490 |
|
|
sign = ( *a >= 0 );
|
| 491 |
|
|
else
|
| 492 |
|
|
sign = !( *y >= 0 );
|
| 493 |
|
|
|
| 494 |
|
|
/* shift operation: hyperbolic case*/
|
| 495 |
|
|
if( C_MODE_HYP == ( mode & C_MODE_MSK ) )
|
| 496 |
|
|
{
|
| 497 |
|
|
xsh = *x >> (it+1);
|
| 498 |
|
|
ysh = *y >> (it+1);
|
| 499 |
|
|
}
|
| 500 |
|
|
/* shift operation: circular and linear case*/
|
| 501 |
|
|
else
|
| 502 |
|
|
{
|
| 503 |
|
|
xsh = *x >> it;
|
| 504 |
|
|
ysh = *y >> it;
|
| 505 |
|
|
}
|
| 506 |
|
|
|
| 507 |
|
|
if( sign == 1 )
|
| 508 |
|
|
{
|
| 509 |
|
|
*a -= cordic_int_lut( mode, it, A_WIDTH );
|
| 510 |
|
|
|
| 511 |
|
|
if( C_MODE_CIR == ( mode & C_MODE_MSK ) )
|
| 512 |
|
|
{
|
| 513 |
|
|
*x = *x - ysh;
|
| 514 |
|
|
*y = *y + xsh;
|
| 515 |
|
|
}
|
| 516 |
|
|
else
|
| 517 |
|
|
if( C_MODE_LIN == ( mode & C_MODE_MSK ) )
|
| 518 |
|
|
{
|
| 519 |
|
|
*x = *x;
|
| 520 |
|
|
*y = *y + xsh;
|
| 521 |
|
|
}
|
| 522 |
|
|
else
|
| 523 |
|
|
{
|
| 524 |
|
|
*x = *x + ysh;
|
| 525 |
|
|
*y = *y + xsh;
|
| 526 |
|
|
}
|
| 527 |
|
|
}
|
| 528 |
|
|
else
|
| 529 |
|
|
{
|
| 530 |
|
|
*a += cordic_int_lut( mode, it, A_WIDTH );
|
| 531 |
|
|
if( C_MODE_CIR == ( mode & C_MODE_MSK ) )
|
| 532 |
|
|
{
|
| 533 |
|
|
*x = *x + ysh;
|
| 534 |
|
|
*y = *y - xsh;
|
| 535 |
|
|
}
|
| 536 |
|
|
else
|
| 537 |
|
|
if( C_MODE_LIN == ( mode & C_MODE_MSK ) )
|
| 538 |
|
|
{
|
| 539 |
|
|
*x = *x;
|
| 540 |
|
|
*y = *y - xsh;
|
| 541 |
|
|
}
|
| 542 |
|
|
else
|
| 543 |
|
|
{
|
| 544 |
|
|
*x = *x - ysh;
|
| 545 |
|
|
*y = *y - xsh;
|
| 546 |
|
|
}
|
| 547 |
|
|
}
|
| 548 |
|
|
cordic_int_dbg( *x, *y, *a, mode, it, "after rotation" );
|
| 549 |
7 |
feddischso |
|
| 550 |
2 |
feddischso |
/* abort condition */
|
| 551 |
|
|
if( ( mode & C_FLAG_VEC_ROT ) == 0 &&
|
| 552 |
|
|
( *a == 0 /* || *a == -1 */ ) )
|
| 553 |
|
|
break;
|
| 554 |
|
|
if( ( mode & C_FLAG_VEC_ROT ) == 0 &&
|
| 555 |
|
|
( *a == alst ) )
|
| 556 |
|
|
break;
|
| 557 |
7 |
feddischso |
|
| 558 |
2 |
feddischso |
if( ( mode & C_FLAG_VEC_ROT ) != 0 &&
|
| 559 |
|
|
( *y == 0 /*|| *y == -1 */ ) )
|
| 560 |
|
|
break;
|
| 561 |
|
|
if( ( mode & C_FLAG_VEC_ROT ) != 0 &&
|
| 562 |
|
|
( *y == ylst ) )
|
| 563 |
|
|
break;
|
| 564 |
|
|
|
| 565 |
|
|
else if( it > 40 )
|
| 566 |
|
|
{
|
| 567 |
7 |
feddischso |
#if PRINT_DEBUG
|
| 568 |
2 |
feddischso |
PRINT( "ERROR: abort %lld %lld %lld %lld - %d - %d!\n", *a, alst, *y, ylst, mode, *y == ylst );
|
| 569 |
7 |
feddischso |
#endif
|
| 570 |
2 |
feddischso |
it = -1;
|
| 571 |
|
|
break;
|
| 572 |
|
|
}
|
| 573 |
|
|
|
| 574 |
|
|
|
| 575 |
|
|
ylst = *y;
|
| 576 |
|
|
alst = *a;
|
| 577 |
|
|
if( repeat == 0 && cordic_int_repeat( it, mode ) )
|
| 578 |
|
|
{
|
| 579 |
|
|
repeat = 1;
|
| 580 |
|
|
#if PRINT_DEBUG
|
| 581 |
|
|
mexPrintf( "repeat it %d\n" , it );
|
| 582 |
|
|
#endif
|
| 583 |
|
|
}
|
| 584 |
|
|
else
|
| 585 |
|
|
{
|
| 586 |
|
|
repeat = 0;
|
| 587 |
|
|
it++;
|
| 588 |
|
|
}
|
| 589 |
|
|
}
|
| 590 |
|
|
return it;
|
| 591 |
|
|
}
|
| 592 |
|
|
|
| 593 |
|
|
|
| 594 |
|
|
|
| 595 |
|
|
#define SCALE_VAL( _W_ )( (double)( (long long int) 1 << (long long int)( _W_ -1 ) ) )
|
| 596 |
|
|
|
| 597 |
|
|
long long int cordic_int_lut( int mode, int it, int A_WIDTH )
|
| 598 |
|
|
{
|
| 599 |
|
|
long long int lut_val;
|
| 600 |
|
|
if( C_MODE_CIR == ( mode & C_MODE_MSK ) )
|
| 601 |
|
|
{
|
| 602 |
|
|
if( it <= 10 )
|
| 603 |
|
|
lut_val = (long long int)( atan( pow( 2, -it ) ) * pow( 2, A_WIDTH-1 ) );
|
| 604 |
|
|
else
|
| 605 |
|
|
lut_val = pow( 2, A_WIDTH-1-it ); /* (long long int)( SCALE_VAL( A_WIDTH-it ) ); */
|
| 606 |
|
|
}
|
| 607 |
|
|
else
|
| 608 |
|
|
if( C_MODE_LIN == ( mode & C_MODE_MSK ) )
|
| 609 |
|
|
{
|
| 610 |
|
|
lut_val = (long long int)( 1.0 / (double)( ( long long int )1 << (long long int)it )
|
| 611 |
|
|
* SCALE_VAL( A_WIDTH ) -1 );
|
| 612 |
|
|
}
|
| 613 |
|
|
else
|
| 614 |
|
|
{
|
| 615 |
|
|
lut_val = (long long int)( atanh( 1.0 / (double)( (long long int)1 << ( long long int )(it+1) ) )
|
| 616 |
|
|
* SCALE_VAL( A_WIDTH ) );
|
| 617 |
|
|
}
|
| 618 |
|
|
return lut_val;
|
| 619 |
|
|
}
|
| 620 |
|
|
|
| 621 |
|
|
|
| 622 |
|
|
|
| 623 |
|
|
|
| 624 |
|
|
/**
|
| 625 |
|
|
*
|
| 626 |
|
|
* Cordic gain:
|
| 627 |
|
|
*
|
| 628 |
|
|
*
|
| 629 |
|
|
*
|
| 630 |
|
|
*/
|
| 631 |
|
|
void cordic_int_rm_gain( long long int *x,
|
| 632 |
|
|
long long int *y,
|
| 633 |
|
|
int mode,
|
| 634 |
|
|
int rm_gain )
|
| 635 |
|
|
{
|
| 636 |
|
|
/* for the non-linear case: remove cordic gain if RM_GAIN > 0 */
|
| 637 |
|
|
if( C_MODE_CIR == ( mode & C_MODE_MSK ) )
|
| 638 |
|
|
{
|
| 639 |
|
|
|
| 640 |
|
|
|
| 641 |
|
|
switch( rm_gain )
|
| 642 |
|
|
{
|
| 643 |
|
|
case 1: *x = + ( *x >> 1 ) ; break; /* error: 0.1072529350 */
|
| 644 |
|
|
case 2: *x = + ( *x >> 1 ) - ( *x >> 4 ) ; break; /* error: 0.1697529350 */
|
| 645 |
|
|
case 3: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 5 ) ; break; /* error: 0.0135029350 */
|
| 646 |
|
|
case 4: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 8 ) ; break; /* error: 0.0017841850 */
|
| 647 |
|
|
case 5: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 12 ) ; break; /* error: 0.0000752006 */
|
| 648 |
|
|
case 6: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 13 ) - ( *x >> 14 ) ; break; /* error: 0.0000141655 */
|
| 649 |
|
|
case 7: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 13 ) - ( *x >> 14 ) - ( *x >> 17 ) ; break; /* error: 0.0000217949 */
|
| 650 |
|
|
case 8: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 13 ) - ( *x >> 14 ) + ( *x >> 16 ) - ( *x >> 19 ) ; break; /* error: 0.0000008140 */
|
| 651 |
|
|
case 9: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 13 ) - ( *x >> 14 ) + ( *x >> 16 ) - ( *x >> 20 ) - ( *x >> 22 ) ; break; /* error: 0.0000000988 */
|
| 652 |
|
|
case 10: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 13 ) - ( *x >> 14 ) + ( *x >> 16 ) - ( *x >> 20 ) - ( *x >> 23 ) - ( *x >> 25 ) ; break; /* error: 0.0000000094 */
|
| 653 |
|
|
case 11: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 13 ) - ( *x >> 14 ) + ( *x >> 16 ) - ( *x >> 20 ) - ( *x >> 23 ) - ( *x >> 26 ) - ( *x >> 27 ) ; break; /* error: 0.0000000019 */
|
| 654 |
|
|
case 12: *x = + ( *x >> 1 ) + ( *x >> 3 ) - ( *x >> 6 ) - ( *x >> 9 ) - ( *x >> 13 ) - ( *x >> 14 ) + ( *x >> 16 ) - ( *x >> 20 ) - ( *x >> 23 ) - ( *x >> 26 ) - ( *x >> 28 ) - ( *x >> 29 ) ; break; /* error: 0.0000000001 */
|
| 655 |
|
|
default: *x = *x; break;
|
| 656 |
|
|
}
|
| 657 |
|
|
switch( rm_gain )
|
| 658 |
|
|
{
|
| 659 |
|
|
case 1: *y = + ( *y >> 1 ) ; break; /* error: 0.1072529350 */
|
| 660 |
|
|
case 2: *y = + ( *y >> 1 ) - ( *y >> 4 ) ; break; /* error: 0.1697529350 */
|
| 661 |
|
|
case 3: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 5 ) ; break; /* error: 0.0135029350 */
|
| 662 |
|
|
case 4: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 8 ) ; break; /* error: 0.0017841850 */
|
| 663 |
|
|
case 5: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 12 ) ; break; /* error: 0.0000752006 */
|
| 664 |
|
|
case 6: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 13 ) - ( *y >> 14 ) ; break; /* error: 0.0000141655 */
|
| 665 |
|
|
case 7: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 13 ) - ( *y >> 14 ) - ( *y >> 17 ) ; break; /* error: 0.0000217949 */
|
| 666 |
|
|
case 8: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 13 ) - ( *y >> 14 ) + ( *y >> 16 ) - ( *y >> 19 ) ; break; /* error: 0.0000008140 */
|
| 667 |
|
|
case 9: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 13 ) - ( *y >> 14 ) + ( *y >> 16 ) - ( *y >> 20 ) - ( *y >> 22 ) ; break; /* error: 0.0000000988 */
|
| 668 |
|
|
case 10: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 13 ) - ( *y >> 14 ) + ( *y >> 16 ) - ( *y >> 20 ) - ( *y >> 23 ) - ( *y >> 25 ) ; break; /* error: 0.0000000094 */
|
| 669 |
|
|
case 11: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 13 ) - ( *y >> 14 ) + ( *y >> 16 ) - ( *y >> 20 ) - ( *y >> 23 ) - ( *y >> 26 ) - ( *y >> 27 ) ; break; /* error: 0.0000000019 */
|
| 670 |
|
|
case 12: *y = + ( *y >> 1 ) + ( *y >> 3 ) - ( *y >> 6 ) - ( *y >> 9 ) - ( *y >> 13 ) - ( *y >> 14 ) + ( *y >> 16 ) - ( *y >> 20 ) - ( *y >> 23 ) - ( *y >> 26 ) - ( *y >> 28 ) - ( *y >> 29 ) ; break; /* error: 0.0000000001 */
|
| 671 |
|
|
default: *x = *y; break;
|
| 672 |
|
|
}
|
| 673 |
|
|
|
| 674 |
|
|
}
|
| 675 |
|
|
else
|
| 676 |
|
|
if( C_MODE_HYP == ( mode & C_MODE_MSK ) )
|
| 677 |
|
|
{
|
| 678 |
|
|
switch( rm_gain )
|
| 679 |
|
|
{
|
| 680 |
|
|
case 1: *x = *x - ( *x >> 3 ) ; break; /* error: 0.3324970678 */
|
| 681 |
|
|
case 2: *x = *x + ( *x >> 2 ) - ( *x >> 4 ) ; break; /* error: 0.0199970678 */
|
| 682 |
|
|
case 3: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 6 ) ; break; /* error: 0.0043720678 */
|
| 683 |
|
|
case 4: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) ; break; /* error: 0.0004658178 */
|
| 684 |
|
|
case 5: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) - ( *x >> 12 ) ; break; /* error: 0.0007099584 */
|
| 685 |
|
|
case 6: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) + ( *x >> 11 ) - ( *x >> 15 ) ; break; /* error: 0.0000080541 */
|
| 686 |
|
|
case 7: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) + ( *x >> 11 ) - ( *x >> 16 ) - ( *x >> 17 ) ; break; /* error: 0.0000004247 */
|
| 687 |
|
|
case 8: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) + ( *x >> 11 ) - ( *x >> 16 ) - ( *x >> 17 ) - ( *x >> 22 ) ; break; /* error: 0.0000006631 */
|
| 688 |
|
|
case 9: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) + ( *x >> 11 ) - ( *x >> 16 ) - ( *x >> 17 ) + ( *x >> 21 ) - ( *x >> 24 ) ; break; /* error: 0.0000000075 */
|
| 689 |
|
|
case 10: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) + ( *x >> 11 ) - ( *x >> 16 ) - ( *x >> 17 ) + ( *x >> 21 ) - ( *x >> 24 ) + ( *x >> 27 ) ; break; /* error: 0.0000000000 */
|
| 690 |
|
|
case 11: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) + ( *x >> 11 ) - ( *x >> 16 ) - ( *x >> 17 ) + ( *x >> 21 ) - ( *x >> 24 ) + ( *x >> 27 ) - ( *x >> 37 ) ; break; /* error: 0.0000000000 */
|
| 691 |
|
|
case 12: *x = *x + ( *x >> 2 ) - ( *x >> 5 ) - ( *x >> 7 ) - ( *x >> 8 ) + ( *x >> 11 ) - ( *x >> 16 ) - ( *x >> 17 ) + ( *x >> 21 ) - ( *x >> 24 ) + ( *x >> 27 ) + ( *x >> 36 ) - ( *x >> 39 ) ; break; /* error: 0.0000000000 */
|
| 692 |
|
|
}
|
| 693 |
|
|
switch( rm_gain )
|
| 694 |
|
|
{
|
| 695 |
|
|
case 1: *y = *y - ( *y >> 3 ) ; break; /* error: 0.3324970678 */
|
| 696 |
|
|
case 2: *y = *y + ( *y >> 2 ) - ( *y >> 4 ) ; break; /* error: 0.0199970678 */
|
| 697 |
|
|
case 3: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 6 ) ; break; /* error: 0.0043720678 */
|
| 698 |
|
|
case 4: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) ; break; /* error: 0.0004658178 */
|
| 699 |
|
|
case 5: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) - ( *y >> 12 ) ; break; /* error: 0.0007099584 */
|
| 700 |
|
|
case 6: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) + ( *y >> 11 ) - ( *y >> 15 ) ; break; /* error: 0.0000080541 */
|
| 701 |
|
|
case 7: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) + ( *y >> 11 ) - ( *y >> 16 ) - ( *y >> 17 ) ; break; /* error: 0.0000004247 */
|
| 702 |
|
|
case 8: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) + ( *y >> 11 ) - ( *y >> 16 ) - ( *y >> 17 ) - ( *y >> 22 ) ; break; /* error: 0.0000006631 */
|
| 703 |
|
|
case 9: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) + ( *y >> 11 ) - ( *y >> 16 ) - ( *y >> 17 ) + ( *y >> 21 ) - ( *y >> 24 ) ; break; /* error: 0.0000000075 */
|
| 704 |
|
|
case 10: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) + ( *y >> 11 ) - ( *y >> 16 ) - ( *y >> 17 ) + ( *y >> 21 ) - ( *y >> 24 ) + ( *y >> 27 ) ; break; /* error: 0.0000000000 */
|
| 705 |
|
|
case 11: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) + ( *y >> 11 ) - ( *y >> 16 ) - ( *y >> 17 ) + ( *y >> 21 ) - ( *y >> 24 ) + ( *y >> 27 ) - ( *y >> 37 ) ; break; /* error: 0.0000000000 */
|
| 706 |
|
|
case 12: *y = *y + ( *y >> 2 ) - ( *y >> 5 ) - ( *y >> 7 ) - ( *y >> 8 ) + ( *y >> 11 ) - ( *y >> 16 ) - ( *y >> 17 ) + ( *y >> 21 ) - ( *y >> 24 ) + ( *y >> 27 ) + ( *y >> 36 ) - ( *y >> 39 ) ; break; /* error: 0.0000000000 */
|
| 707 |
|
|
}
|
| 708 |
|
|
}
|
| 709 |
|
|
}
|
| 710 |
|
|
|
