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