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509 lines
20 KiB
C++
509 lines
20 KiB
C++
/******************************************************************************
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*
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* MATLAB (R) is a trademark of The Mathworks (R) Corporation
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*
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* Function: halfprecision
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* Filename: halfprecision.c
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* Programmer: James Tursa
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* Version: 1.0
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* Date: March 3, 2009
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* Copyright: (c) 2009 by James Tursa, All Rights Reserved
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*
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* This code uses the BSD License:
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are
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* met:
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*
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* * Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the distribution
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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* halfprecision converts the input argument to/from a half precision floating
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* point bit pattern corresponding to IEEE 754r. The bit pattern is stored in a
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* uint16 class variable. Please note that halfprecision is *not* a class. That
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* is, you cannot do any arithmetic with the half precision bit patterns.
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* halfprecision is simply a function that converts the IEEE 754r half precision
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* bit pattern to/from other numeric MATLAB variables. You can, however, take
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* the half precision bit patterns, convert them to single or double, do the
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* operation, and then convert the result back manually.
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*
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* 1 bit sign bit
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* 5 bits exponent, biased by 15
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* 10 bits mantissa, hidden leading bit, normalized to 1.0
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*
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* Special floating point bit patterns recognized and supported:
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*
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* All exponent bits zero:
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* - If all mantissa bits are zero, then number is zero (possibly signed)
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* - Otherwise, number is a denormalized bit pattern
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*
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* All exponent bits set to 1:
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* - If all mantissa bits are zero, then number is +Infinity or -Infinity
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* - Otherwise, number is NaN (Not a Number)
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*
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* Building:
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*
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* halfprecision requires that a mex routine be built (one time only). This
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* process is typically self-building the first time you call the function
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* as long as you have the files halfprecision.m and halfprecision.c in the
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* same directory somewhere on the MATLAB path. If you need to manually build
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* the mex function, here are the commands:
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*
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* >> mex -setup
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* (then follow instructions to select a C / C++ compiler of your choice)
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* >> mex halfprecision.c
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*
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* If you have an older version of MATLAB, you may need to use this command:
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*
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* >> mex -DDEFINEMWSIZE halfprecision.c
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*
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* Syntax
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*
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* B = halfprecision(A)
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* C = halfprecision(B,S)
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* halfprecision(B,'disp')
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*
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* Description
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*
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* A = a MATLAB numeric array, char array, or logical array.
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*
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* B = the variable A converted into half precision floating point bit pattern.
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* The bit pattern will be returned as a uint16 class variable. The values
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* displayed are simply the bit pattern interpreted as if it were an unsigned
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* 16-bit integer. To see the halfprecision values, use the 'disp' option, which
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* simply converts the bit patterns into a single class and then displays them.
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*
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* C = the half precision floating point bit pattern in B converted into class S.
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* B must be a uint16 or int16 class variable.
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*
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* S = char string naming the desired class (e.g., 'single', 'int32', etc.)
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* If S = 'disp', then the floating point bit values are simply displayed.
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*
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* Examples
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*
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* >> a = [-inf -1e30 -1.2 NaN 1.2 1e30 inf]
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* a =
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* 1.0e+030 *
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* -Inf -1.0000 -0.0000 NaN 0.0000 1.0000 Inf
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*
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* >> b = halfprecision(a)
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* b =
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* 64512 64512 48333 65024 15565 31744 31744
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*
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* >> halfprecision(b,'disp')
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* -Inf -Inf -1.2002 NaN 1.2002 Inf Inf
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*
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* >> halfprecision(b,'double')
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* ans =
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* -Inf -Inf -1.2002 NaN 1.2002 Inf Inf
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*
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* >> 2^(-24)
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* ans =
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* 5.9605e-008
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*
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* >> halfprecision(ans)
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* ans =
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* 1
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*
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* >> halfprecision(ans,'disp')
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* 5.9605e-008
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*
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* >> 2^(-25)
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* ans =
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* 2.9802e-008
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*
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* >> halfprecision(ans)
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* ans =
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* 1
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*
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* >> halfprecision(ans,'disp')
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* 5.9605e-008
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*
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* >> 2^(-26)
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* ans =
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* 1.4901e-008
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*
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* >> halfprecision(ans)
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* ans =
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* 0
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*
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* >> halfprecision(ans,'disp')
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* 0
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*
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* Note that the special cases of -Inf, +Inf, and NaN are handled correctly.
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* Also, note that the -1e30 and 1e30 values overflow the half precision format
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* and are converted into half precision -Inf and +Inf values, and stay that
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* way when they are converted back into doubles.
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*
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* For the denormalized cases, note that 2^(-24) is the smallest number that can
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* be represented in half precision exactly. 2^(-25) will convert to 2^(-24)
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* because of the rounding algorithm used, and 2^(-26) is too small and underflows
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* to zero.
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*
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********************************************************************************/
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// Includes -------------------------------------------------------------------
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// #include "matlab_overload.h"
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#include <math.h>
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#include <stdio.h>
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#include <stdint.h>
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#include <string.h>
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#include "mex.h"
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#include <omp.h>
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// Macros ---------------------------------------------------------------------
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// Needed for older MATLAB versions that do not have mwSize
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#ifdef DEFINEMWSIZE
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#define mwSize int
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#endif
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#define INT16_TYPE int16_t
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#define UINT16_TYPE uint16_t
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#define INT32_TYPE int32_t
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#define UINT32_TYPE uint32_t
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#define THREADS 28
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// Global ---------------------------------------------------------------------
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int next; // Little Endian adjustment
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int checkieee = 1; // Flag to check for IEEE754, Endian, and word size
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// Prototypes -----------------------------------------------------------------
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template <typename dtype_out,typename dtype_in >
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void singles2halfp(mxArray *target[], const mxArray *source[], const mwSize numel);
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template <typename dtype_out,typename dtype_in >
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void halfp2singles( mxArray *target[], const mxArray *source[], const mwSize numel);
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// overload the GetData function for each of the possible data type + select the correct matlab get function
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inline void GetData(const mxArray *in, const mxComplexSingle *& out) { out = mxGetComplexSingles(in); return;};
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inline void GetData(const mxArray *in, const mxComplexUint16 *& out) { out = mxGetComplexUint16s(in); return;};
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inline void GetData(const mxArray *in, const mxSingle *& out) { out = mxGetSingles(in); return;};
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inline void GetData(const mxArray *in, const mxUint16 *& out) { out = mxGetUint16s(in); return;};
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inline void GetData(const mxArray *in, mxComplexSingle *& out) { out = mxGetComplexSingles(in); return;};
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inline void GetData(const mxArray *in, mxComplexUint16 *& out) { out = mxGetComplexUint16s(in); return;};
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inline void GetData(const mxArray *in, mxSingle *& out) { out = mxGetSingles(in); return;};
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inline void GetData(const mxArray *in, mxUint16 *& out) { out = mxGetUint16s(in); return;};
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// Gateway Function -----------------------------------------------------------
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void mexFunction(int nlhs, mxArray *plhs[],int nrhs, const mxArray *prhs[])
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{
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mwSize ndim; // Number of dimensions of input
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mwSize numel; // Number of elements of input
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const mwSize *dims; // Pointer to dimensions array
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mxClassID classid; // Class id of input or desired output
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mxComplexity complexity; // Complexity of input
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mxArray *rhs[2], *lhs[1], *currentformat[1]; // Used for callbacks into MATLAB
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char *classname; // Class name of desired output
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int disp = 0; // Display flag
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double one = 1.0; // Used for checking IEEE754 floating point format
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UINT32_TYPE *ip; // Used for checking IEEE754 floating point format
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if( checkieee ) { // 1st call, so check for IEEE754, Endian, and word size
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ip = (UINT32_TYPE *) &one;
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if( *ip ) { // If Big Endian, then no adjustment
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next = 0;
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} else { // If Little Endian, then adjustment will be necessary
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next = 1;
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ip++;
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}
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if( *ip != 0x3FF00000u ) { // Check for exact IEEE 754 bit pattern of 1.0
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mexErrMsgTxt("Floating point bit pattern is not IEEE 754");
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}
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if( sizeof(INT16_TYPE) != 2 || sizeof(INT32_TYPE) != 4 ) {
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mexErrMsgTxt("Internal error. short is not 16-bits, or long is not 32-bits.");
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}
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checkieee = 0; // Everything checks out OK
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}
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// Check input arguments for number and type
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if( nlhs > 1 ) {
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mexErrMsgTxt("Too many output arguments.");
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}
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if( nrhs != 1 && nrhs != 2 ) {
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mexErrMsgTxt("Need one or two input arguments.");
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}
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if( mxIsSparse(prhs[0]) ) {
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mexErrMsgTxt("Sparse matrices not supported.");
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}
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if( nrhs == 2 ) {
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if( !mxIsChar(prhs[1]) )
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mexErrMsgTxt("2nd input argument must be char string naming desired class, or 'disp'.");
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if( !mxIsInt16(prhs[0]) && !mxIsUint16(prhs[0]) )
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mexErrMsgTxt("1st input argument must be uint16 or int16 class.");
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classname = mxArrayToString(prhs[1]);
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if( strcmp(classname,"double") == 0 ) { // Check 2nd input for proper class name string
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classid = mxDOUBLE_CLASS;
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} else if( strcmp(classname,"single") == 0 ) {
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classid = mxSINGLE_CLASS;
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} else if( strcmp(classname,"int8") == 0 ) {
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classid = mxINT8_CLASS;
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} else if( strcmp(classname,"uint8") == 0 ) {
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classid = mxUINT8_CLASS;
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} else if( strcmp(classname,"int16") == 0 ) {
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classid = mxINT16_CLASS;
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} else if( strcmp(classname,"uint16") == 0 ) {
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classid = mxUINT16_CLASS;
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} else if( strcmp(classname,"int32") == 0 ) {
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classid = mxINT32_CLASS;
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} else if( strcmp(classname,"uint32") == 0 ) {
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classid = mxUINT32_CLASS;
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} else if( strcmp(classname,"int64") == 0 ) {
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classid = mxINT64_CLASS;
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} else if( strcmp(classname,"uint64") == 0 ) {
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classid = mxUINT64_CLASS;
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} else if( strcmp(classname,"char") == 0 ) {
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classid = mxCHAR_CLASS;
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} else if( strcmp(classname,"logical") == 0 ) {
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classid = mxLOGICAL_CLASS;
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} else if( strcmp(classname,"disp") == 0 ) {
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disp = 1;
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} else {
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mexErrMsgTxt("2nd input argument must be char string naming desired class, or 'disp'.");
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}
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}
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if( nrhs == 1 ) { // Convert from input MATLAB variable to halfprecision ---------------------
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classid = mxGetClassID(prhs[0]); // Check for supported class
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switch( classid ) {
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case mxDOUBLE_CLASS:
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case mxSINGLE_CLASS:
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case mxUINT64_CLASS:
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case mxINT64_CLASS:
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case mxUINT32_CLASS:
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case mxINT32_CLASS:
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case mxUINT16_CLASS:
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case mxINT16_CLASS:
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case mxUINT8_CLASS:
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case mxINT8_CLASS:
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case mxLOGICAL_CLASS:
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case mxCHAR_CLASS:
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break;
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default:
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mexErrMsgTxt("Unable to convert input argument to halfprecision.");
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}
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complexity = mxIsComplex(prhs[0]) ? mxCOMPLEX : mxREAL; // Get stats of input variable
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numel = mxGetNumberOfElements(prhs[0]);
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ndim = mxGetNumberOfDimensions(prhs[0]);
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dims = mxGetDimensions(prhs[0]);
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plhs[0] = mxCreateNumericArray(ndim, dims, mxUINT16_CLASS, complexity); // halfprecision stored as uint16
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switch( classid ) {
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case mxDOUBLE_CLASS: // Custom code for double class
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mexErrMsgTxt("Use single precision output");
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break;
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case mxSINGLE_CLASS: // Custom code for single class
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if (mxIsComplex(prhs[0]))
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singles2halfp<mxComplexUint16,mxComplexSingle>(plhs,prhs,2*numel);
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else
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singles2halfp<mxUint16,mxSingle>(plhs,prhs,numel);
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break;
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case mxUINT64_CLASS:
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case mxINT64_CLASS:
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case mxUINT32_CLASS:
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case mxINT32_CLASS:
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case mxUINT16_CLASS:
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case mxINT16_CLASS:
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case mxUINT8_CLASS:
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case mxINT8_CLASS:
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case mxLOGICAL_CLASS:
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case mxCHAR_CLASS: // All other classes get converted to single first
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mexErrMsgTxt("Use single precision output");
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}
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} else { // Convert halfprecision to desired class ----------------------------------
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complexity = mxIsComplex(prhs[0]) ? mxCOMPLEX : mxREAL; // Get stats of input variable
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numel = mxGetNumberOfElements(prhs[0]);
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ndim = mxGetNumberOfDimensions(prhs[0]);
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dims = mxGetDimensions(prhs[0]);
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switch( classid ) {
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case mxDOUBLE_CLASS: // Custom code for double class
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mexErrMsgTxt("Use single precision input");
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break;
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case mxSINGLE_CLASS: // Custom code for single class
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plhs[0] = mxCreateNumericArray(ndim, dims, mxSINGLE_CLASS, complexity);
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// Convert input to single
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if (mxIsComplex(prhs[0]))
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halfp2singles<mxComplexSingle, mxComplexUint16>(plhs,prhs,2*numel);
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else
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halfp2singles<mxSingle, mxUint16>(plhs,prhs,numel);
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break;
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case mxUINT64_CLASS:
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case mxINT64_CLASS:
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case mxUINT32_CLASS:
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case mxINT32_CLASS:
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case mxUINT16_CLASS:
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case mxINT16_CLASS:
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case mxUINT8_CLASS:
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case mxINT8_CLASS:
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case mxLOGICAL_CLASS:
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case mxCHAR_CLASS: // All other classes get converted to single first
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mexErrMsgTxt("Use single precision input");
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break;
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default:
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mexErrMsgTxt("Unable to convert input argument to halfprecision.");
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}
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mxFree(classname);
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}
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}
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//-----------------------------------------------------------------------------
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template <typename dtype_out,typename dtype_in >
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void singles2halfp( mxArray *target[], const mxArray *source[], const mwSize numel)
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{
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dtype_in const * source_array;
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GetData(source[0], source_array);
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dtype_out * target_array;
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GetData(target[0], target_array);
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UINT16_TYPE *hp = (UINT16_TYPE *) target_array; // Type pun output as an unsigned 16-bit int
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UINT32_TYPE const *xp = (UINT32_TYPE *) source_array; // Type pun input as an unsigned 32-bit int
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UINT16_TYPE hs, he, hm;
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UINT32_TYPE x, xs, xe, xm;
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int hes;
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mwSize i;
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if( source == NULL || target == NULL ) { // Nothing to convert (e.g., imag part of pure real)
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return;
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}
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#pragma omp parallel for schedule(static) num_threads(THREADS) private(i,x,xs,xe,xm,hs,he,hm,hes)
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for( i = 0; i < numel; i++)
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{
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x = xp[i];
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if( (x & 0x7FFFFFFFu) == 0 ) { // Signed zero
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hp[i] = (UINT16_TYPE) (x >> 16); // Return the signed zero
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} else { // Not zero
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xs = x & 0x80000000u; // Pick off sign bit
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xe = x & 0x7F800000u; // Pick off exponent bits
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xm = x & 0x007FFFFFu; // Pick off mantissa bits
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if( xe == 0 ) { // Denormal will underflow, return a signed zero
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hp[i] = (UINT16_TYPE) (xs >> 16);
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} else if( xe == 0x7F800000u ) { // Inf or NaN (all the exponent bits are set)
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if( xm == 0 ) { // If mantissa is zero ...
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hp[i] = (UINT16_TYPE) ((xs >> 16) | 0x7C00u); // Signed Inf
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} else {
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hp[i] = (UINT16_TYPE) 0xFE00u; // NaN, only 1st mantissa bit set
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}
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} else { // Normalized number
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hs = (UINT16_TYPE) (xs >> 16); // Sign bit
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hes = ((int)(xe >> 23)) - 127 + 15; // Exponent unbias the single, then bias the halfp
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if( hes >= 0x1F ) { // Overflow
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hp[i] = (UINT16_TYPE) ((xs >> 16) | 0x7C00u); // Signed Inf
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} else if( hes <= 0 ) { // Underflow
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if( (14 - hes) > 24 ) { // Mantissa shifted all the way off & no rounding possibility
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hm = (UINT16_TYPE) 0u; // Set mantissa to zero
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} else {
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xm |= 0x00800000u; // Add the hidden leading bit
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hm = (UINT16_TYPE) (xm >> (14 - hes)); // Mantissa
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if( (xm >> (13 - hes)) & 0x00000001u ) // Check for rounding
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hm += (UINT16_TYPE) 1u; // Round, might overflow into exp bit, but this is OK
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}
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hp[i] = (hs | hm); // Combine sign bit and mantissa bits, biased exponent is zero
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} else {
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he = (UINT16_TYPE) (hes << 10); // Exponent
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hm = (UINT16_TYPE) (xm >> 13); // Mantissa
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if( xm & 0x00001000u ) // Check for rounding
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hp[i] = (hs | he | hm) + (UINT16_TYPE) 1u; // Round, might overflow to inf, this is OK
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else
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hp[i] = (hs | he | hm); // No rounding
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}
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}
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}
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}
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}
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template <typename dtype_out,typename dtype_in>
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void halfp2singles( mxArray *target[], const mxArray *source[], const mwSize numel)
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{
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dtype_in * source_array;
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GetData(source[0], source_array);
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dtype_out const * target_array;
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GetData(target[0], target_array);
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UINT16_TYPE const *hp = (UINT16_TYPE *) source_array; // Type pun output as an unsigned 16-bit int
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UINT32_TYPE *xp = (UINT32_TYPE *) target_array; // Type pun input as an unsigned 32-bit int
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UINT16_TYPE h, hs, he, hm;
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UINT32_TYPE xs, xe, xm;
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INT32_TYPE xes;
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int e;
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mwSize i;
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if( source == NULL || target == NULL ) // Nothing to convert (e.g., imag part of pure real)
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return;
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#pragma omp parallel for schedule(static) num_threads(THREADS) private(i,e,xs,xe,xm,h,hs,he,hm,xes)
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for( i = 0; i < numel; i++)
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{
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h = hp[i];
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if( (h & 0x7FFFu) == 0 ) { // Signed zero
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xp[i] = ((UINT32_TYPE) h) << 16; // Return the signed zero
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} else { // Not zero
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hs = h & 0x8000u; // Pick off sign bit
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he = h & 0x7C00u; // Pick off exponent bits
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hm = h & 0x03FFu; // Pick off mantissa bits
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if( he == 0 ) { // Denormal will convert to normalized
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e = -1; // The following loop figures out how much extra to adjust the exponent
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do {
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e++;
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hm <<= 1;
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} while( (hm & 0x0400u) == 0 ); // Shift until leading bit overflows into exponent bit
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xs = ((UINT32_TYPE) hs) << 16; // Sign bit
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xes = ((INT32_TYPE) (he >> 10)) - 15 + 127 - e; // Exponent unbias the halfp, then bias the single
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xe = (UINT32_TYPE) (xes << 23); // Exponent
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xm = ((UINT32_TYPE) (hm & 0x03FFu)) << 13; // Mantissa
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xp[i] = (xs | xe | xm); // Combine sign bit, exponent bits, and mantissa bits
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} else if( he == 0x7C00u ) { // Inf or NaN (all the exponent bits are set)
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if( hm == 0 ) { // If mantissa is zero ...
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xp[i] = (((UINT32_TYPE) hs) << 16) | ((UINT32_TYPE) 0x7F800000u); // Signed Inf
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} else {
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xp[i] = (UINT32_TYPE) 0xFFC00000u; // NaN, only 1st mantissa bit set
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}
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} else { // Normalized number
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xs = ((UINT32_TYPE) hs) << 16; // Sign bit
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xes = ((INT32_TYPE) (he >> 10)) - 15 + 127; // Exponent unbias the halfp, then bias the single
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xe = (UINT32_TYPE) (xes << 23); // Exponent
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xm = ((UINT32_TYPE) hm) << 13; // Mantissa
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xp[i] = (xs | xe | xm); // Combine sign bit, exponent bits, and mantissa bits
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}
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}
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}
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}
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