How Can I Efficiently Change the Rounding Mode for IEEE 754 Floating-Point Numbers in C?

Changing Rounding Mode for IEEE 754 Floating-Point Numbers

In the realm of numerical computing, maintaining precision and controlling rounding errors are crucial. IEEE 754 floating-point numbers provide standardized mechanisms for representing and manipulating real numbers while offering various rounding modes to cater to different precision requirements.

This question delves into the most efficient approach to change the rounding mode of IEEE 754 floating-point numbers. The primary focus is on portable C solutions, although assembly solutions for x86 platforms are also explored.

C-Based Solutions:

For portable C code, the standard solution involves leveraging the library and utilizes the fesetround() function. This function allows programmers to set the desired rounding mode (e.g., towards nearest, towards zero, or towards positive/negative infinity).

#include <fenv.h>
#pragma STDC FENV_ACCESS ON

// Store the original rounding mode
const int originalRounding = fegetround();
// Establish the desired rounding mode
fesetround(FE_TOWARDZERO);
// Perform desired operations...
// ...
// Restore the original mode afterwards
fesetround(originalRounding);</fenv.h>

Assembly-Based Solutions:

For older platforms lacking C99 support, assembly solutions might be necessary. In such scenarios, adjusting the rounding mode typically involves modifying the control bits for both the x87 unit via the fldcw instruction and the SSE unit via the ldmxcsr instruction.

MSVC-Specific Solution:

For Microsoft Visual C (MSVC), a non-standard but convenient option is available. The _controlfp() function can be utilized to manipulate the rounding mode.

unsigned int originalRounding = _controlfp(0, 0);
_controlfp(_RC_CHOP, _MCW_RC);
// Perform desired operations...
// ...
_controlfp(originalRounding, _MCW_RC);

Rounding Mode Decoding:

For reference, the different rounding modes and their corresponding C and MSVC names are listed below:

Rounding Mode	C Name	MSVC Name
To nearest	FE_TONEAREST	_RC_NEAR
Toward zero	FE_TOWARDZERO	_RC_CHOP
To infinity	FE_UPWARD	_RC_UP
To -infinity	FE_DOWNWARD	_RC_DOWN

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