Controlling FPU rounding modes with Python

Hey folks! In the previous post I talked a little about the theory behind the floating-point arithmetic and rounding methods. This time I’ll try a more practical approach showing how to control the rounding modes that FPUs (Floating-Point Units) employ to perform their operations. For that I’ll use Python. But, first let me introduce the <fenv.h> header of the ANSI C99 standard.

The ANSI C99 standard establishes the <fenv.h> header to control the floating-point environment of the machine. A lot of functions and constants allowing to configure the properties of the floating-point system (including rounding modes) are defined in this header. In our case, the important definitions are:

Functions

• int fegetround() – Returns the current rounding mode
• int fesetround(int mode) – Sets the rounding mode returning 0 if all went ok and some other value otherwise

Constants

• FE_TOWARDZERO – Flag for round to zero
• FE_DOWNWARD – Flag for round toward minus infinity
• FE_UPWARD – Flag for round toward plus infinity
• FE_TONEAREST – Flag for round to nearest

Unfortunately, not all compilers fully implement the ANSI C99 standard. Therefore, there is no guarantee on the portability of code that uses the <fenv.h> header. Considering this caveat, the GCC compiler supports it, which makes it possible to build a Python extension wrapping the features of <fenv.h>. However, this is not a smart way to reach our goal since it would require forcing users to compile the source code of the extension. An alternative is to use the ctypes Python module to instantiate the libm (part of the standard C library used by GCC, typically glibc, that implements <fenv.h>):

from ctypes import cdll
from ctypes.util import find_library
libm = cdll.LoadLibrary(find_library('m'))

The constants that identify the rounding modes are usually defined as macros in <fenv.h> and, therefore, are not accessible via ctypes. We need to redefine them in Python. The problem is that they vary according the processor so that it is necessary to establish some logic on the result of the function platform.processor(). Right now, however, I just have a x86 processor to test, so I will use the constants for it only:

FE_TOWARDZERO = 0xc00
FE_DOWNWARD = 0x400
FE_UPWARD = 0x800
FE_TONEAREST = 0

Now, just call the appropriate functions:

>>> back_rounding_mode = libm.fegetround()
>>> libm.fesetround(FE_DOWNWARD)
0
>>> 1.0/10.0
0.099999999999999992
>>> libm.fesetround(FE_UPWARD)
0
>>> 1.0/10.0
0.10000000000000001
>>> libm.fesetround(back_rounding_mode)

But, what about the MS Visual Studio? Well… the standard C library of this compiler, msvcrt (MS Visual Studio C Run-Time Library), does not support <fenv.h>. Nonetheless, MS Visual Studio implements a set of non-standard (quite typical…) constants and functions specialized in manipulating the properties of the machine FPU. These constants and functions are defined in the <float.h> header distributed with that compiler. The following definitions are of particular interest to us:

Functions

• unsigned int _controlfp(unsigned int new, unsigned int mask) – Sets/gets the control vector of the floating-point system (more information here)

Constants

• _MCW_RC = 0x300 – Control vector mask for information about rounding modes
• _RC_CHOP = 0x300 – Control vector value for round to zero mode
• _RC_UP = 0x200 – Control vector value for round toward plus infinity mode
• _RC_DOWN = 0x100 – Control vector value for round toward minus infinity mode
• _RC_NEAR = 0 – Control vector value for round to nearest mode

Analogous to the previous case:

>>> _MCW_RC = 0x300
>>> _RC_UP = 0x200
>>> _RC_DOWN = 0x100
>>> from ctypes import cdll
>>> msvcrt = cdll.msvcrt
>>> back_rounding_mode = msvcrt._controlfp(0, 0)
>>> msvcrt._controlfp(_RC_DOWN, _MCW_RC)
590111
>>> 1.0/10.0
0.099999999999999992
>>> msvcrt._controlfp(_RC_UP, _MCW_RC)
590367
>>> 1.0/10.0
0.10000000000000001
>>> msvcrt._controlfp(back_rounding_mode, _MCW_RC)
589855

For sure, it is not convenient to type all this every time you want to change the rounding mode. Nor it is appropriate to guess the standard C library of the system. But you can always create functions encapsulating this behavior. Something like this:

def _start_libm():
    global TO_ZERO, TOWARD_MINUS_INF, TOWARD_PLUS_INF, TO_NEAREST
    global set_rounding, get_rounding
    from ctypes import cdll
    from ctypes.util import find_library
    libm = cdll.LoadLibrary(find_library('m'))
    set_rounding, get_rounding = libm.fesetround, libm.fegetround
    # x86
    TO_ZERO = 0xc00
    TOWARD_MINUS_INF = 0x400
    TOWARD_PLUS_INF = 0x800
    TO_NEAREST = 0

def _start_msvcrt():
    global TO_ZERO, TOWARD_MINUS_INF, TOWARD_PLUS_INF, TO_NEAREST
    global set_rounding, get_rounding
    from ctypes import cdll
    msvcrt = cdll.msvcrt
    set_rounding = lambda mode: msvcrt._controlfp(mode, 0x300)
    get_rounding = lambda: msvcrt._controlfp(0, 0)
    TO_ZERO = 0x300
    TOWARD_MINUS_INF = 0x100
    TOWARD_PLUS_INF = 0x200
    TO_NEAREST = 0

for _start_rounding in _start_libm, _start_msvcrt:
    try:
        _start_rounding()
        break
    except:
        pass
else:
    print "ERROR: You couldn't start the FPU module"

In this case, the constants and functions to be called, as well as the standard C library instantiated, are abstracted. Just use the constants TO_ZERO, TOWARD_MINUS_INF, TOWARD_PLUS_INF, TO_NEAREST and the functions set_rounding, get_rounding.

So, that’s it… I hope this has been useful to you somehow (I doubt it… :P) or, at least, that it was interesting… Until next time…