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Operating System

Handling FP errors

Linux
Solaris 10
Mac OS X 10.5
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C99 FP functions - These functions are declared in fenv.h [2]
]]></ac:plain-text-body></ac:structured-macro>
Before fenv.h based functions were standardized; an alternative to using these C99/fenv function is using ieee_flags and ieee_handler  

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Windows

Structured Exception Handling - user defined handler _fpieee_flt [3]
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Non-Compliant Code Example

In this NCCE, floating point operations are carried out and there is no observation for errors during floating point operations. Please note the range check on various operands for the operations has been intentionally ignored, since our intention is capture the errors during a floating point operation.

Code Block
bgColor#FFCCCC
fpOper_noErrorChecking()
 {
	...
	double a = 1e-40, b, c = 0.1;
	float x = 0, y;
	// inexact and underflows
	y = a;
	// divide by zero operation
	b = y / x;
	// inexact (loss of precision)
	c = sin(30) * a;
	...
}

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Windows OS nor the libraries with MS Visual studio support C99 functions, instead Structured Exception Handling is used to handle for FP operation.   Windows also provides an alternative method to get the FP exception code - using _statusfp/_statusfp2.

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Using the SEH allows the programmer to change the results of the FP operation that caused the error condition. Using SEH also provides more information about the error condition

Code Block
&nbsp;fp_usingSEH()
{
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {
  /* ...
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; */
  double a = 1e-40, b, c = 0.1;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  float x = 0, y;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  unsigned int rv ;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; unmask_fp();

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \_try
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // Store into y is inexact and underflows:
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; y = a;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // divide by zero operation
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b = y / x;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // inexact
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; c = sin(30) * a;
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; }

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \_except (_fpieee_flt (GetExceptionCode(), GetExceptionInformation(), fpieee_handler))
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; {
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; printf ("fpieee_handler: EXCEPTION_EXECUTE_HANDLER");
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; }

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; ...
}

void unmask_fpsr(void)
{
&nbsp;&nbsp;&nbsp;&nbsp; unsigned int u;
&nbsp;&nbsp;&nbsp;&nbsp; unsigned int control_word;
&nbsp;&nbsp;&nbsp;&nbsp; \_controlfp_s(&control_word, 0, 0);
&nbsp;&nbsp;&nbsp;&nbsp; u = control_word & \~(_EM_INVALID \| \_EM_DENORMAL \| \_EM_ZERODIVIDE
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \| \_EM_OVERFLOW \| \_EM_UNDERFLOW \| \_EM_INEXACT);
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; \_controlfp_s( &control_word, u, \_MCW_EM);
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; return ;
}

int fpieee_handler (_FPIEEE_RECORD \*ieee)
{
&nbsp;&nbsp;&nbsp; // ...

&nbsp;&nbsp;&nbsp; switch(ieee->RoundingMode)
&nbsp;&nbsp;&nbsp; {
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; case \_FpRoundNearest:
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // ....
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; break;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /\* Other RMs include \_FpRoundMinusInfinity, \_FpRoundPlusInfinity, \_FpRoundChopped \*/
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // ....
&nbsp;&nbsp;&nbsp; }

&nbsp;&nbsp;&nbsp; switch(ieee->Precision)
&nbsp;&nbsp;&nbsp; {
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; case \_FpPrecision24:
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // ....
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; break;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /\* Other Ps include \_FpPrecision53*/
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // ....
&nbsp;&nbsp; }

&nbsp;&nbsp; switch(ieee->Operation)
&nbsp;&nbsp; {
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; case \_FpCodeAdd:
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // ...
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; break;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; /\* Other Ops include \_FpCodeSubtract, \_FpCodeMultiply, \_FpCodeDivide, \_FpCodeSquareRoot, \_FpCodeCompare, \_FpCodeConvert, \_FpCodeConvertTrunc \*/
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; // ....

&nbsp;&nbsp; }

&nbsp;&nbsp; // process the bitmap ieee->Cause
&nbsp;&nbsp; // process the bitmap ieee->Enable
&nbsp;&nbsp; // process the bitmap ieee->Status
&nbsp;&nbsp; // process the Operand ieee->Operand1, evaluate format and Value
&nbsp;&nbsp; // process the Operand ieee->Operand2, evaluate format and Value
&nbsp;&nbsp; // process the Result ieee->Result, evaluate format and Value
&nbsp;&nbsp; // the result should be set according to the operation specified in ieee->Cause and the result format as specified in ieee->Result
&nbsp;&nbsp; // the Result set is based on the
&nbsp;&nbsp; ...
}\\

Risk Assessment

The Floating point exceptions if they go undetected will cause one or more of these conditions - security vulnerability, lower program efficiency and generate inaccurate results. Most processors stall for significant duration (sometimes upto a second or even more on 32bit desktop processors) when an operation incur a NaN.

References

Wiki Markup
\[1\] IEEE standard for binary floating-point arithmetic

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