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## IEEE 754r Half Precision floating point converter

version 2.0 (33.2 KB) by
Converts MATLAB or C variables to/from IEEE 754r Half Precision floating point bit pattern.

Updated 18 May 2020

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, and performs various tests on the bit patterns (isinf, isnan, eps, etc.).

The half precision bit pattern is as follows:

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 (leading bit is present)

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)

More details of this floating point format can be found here:

http://en.wikipedia.org/wiki/Half_precision

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, see the documentation in halfprecision.m for instructions on building the mex routine.

Syntax

B = halfprecision(A)
C = halfprecision(B,classname or function)
L = halfprecision(directive)
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.

classname = char string naming the desired class (e.g., 'single', 'int32', etc.)

function = char string giving one of the following functions:
'isinf' = returns a logical variable, true where B is inf
'isnan' = returns a logical variable, true where B is nan
'isnormal' = returns a logical variable, true where B is normalized
'isdenormal' = returns a logical variable, true where B is denormalized
'eps' = returns eps of the half precision values

directive = char string giving one of the following directives:
'openmp' = returns a logical variable, true when compiled with OpenMP
'realmax' = returns max half precision value
'realmin' = returns min half precision normalized value
'realmindenormal' = returns min half precision denormalized value
'version' = returns a string with compilation memory model

'disp' = 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.

Caveat: I have only tested this code on a PC, which is Little Endian. I put in code to handle Big Endian machines, but I do not have a way to test it, so I can't say for sure that it will work properly. Let me know if you have problems.

### Cite As

James Tursa (2021). IEEE 754r Half Precision floating point converter (https://www.mathworks.com/matlabcentral/fileexchange/23173-ieee-754r-half-precision-floating-point-converter), MATLAB Central File Exchange. Retrieved .

Hsiu-Wei Hsu

I want to read the 16bit floating points number by MatLAB. I have found the way for a long time.
I want to ask how can I read the 16bit floating points number data by the subroutine.
I can convert the number from half-precision to double or from double to half-precision , but I don't know how to read the 16bit floating binary data by it.
Thanks!!!!!

Jia Xi

QAQ want to know how to do arithmetic operations and functions directly on the variables

Richard Crozier

I had additional issues building on Linux, fist of all gcc assumes files ending in.c are C files, and throws an error because comments are C++ comments. Fixed by changing the file extension to .cpp

Also get a compile error from gcc which can be fixed by calling as:

mex -v CXXFLAGS='\$CXXFLAGS -fpermissive' halfprecision.cpp

The problem is with the call to mexCallMATLAB on line 320 which expects the fourth arg (prhs) to be const.

Nick L

+1 @james.tursa's help:
On my 64-bit Linux machine, I was getting the "not IEEE 754" error until I added #include <stdint.h> and the four #define macros to halfprecision.c. The re-compiled halfprecision() seems to work as advertised after that.

David Young

Michael

Hello,

when i run
mex halfprecision.c
halfprecision.c: In function ‘mexFunction’:
halfprecision.c:314: warning: passing argument 4 of ‘mexCallMATLAB’ from incompatible pointer type

Any help is much appreciated, because halfprecision(a) (see example) results in: 'Floating point bit pattern is not IEEE 754'

Thanks,
michael

Sebastiaan

Thanks, works perfectly! Actually looking forward for TMW to include half and quadruple precision.

James Tursa

Also this:

#include <stdint.h>

James Tursa

I just got a report from a 64-bit linux user that the ieehalfprecision.c code did not work as posted, but he did get it to work by changing some types as follows:

#define INT16_TYPE int16_t
#define UINT16_TYPE uint16_t
#define INT32_TYPE int32_t
#define UINT32_TYPE uint32_t

I do not have a 64-bit system to test with, but I would assume this works as long as your compiler supports the int16_t etc types.

##### MATLAB Release Compatibility
Created with R2007a
Compatible with any release
##### Platform Compatibility
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