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Errors during floating-point operations are often neglected by applications; instead, the greatest effort is usually in validating the programmers who instead focus on validating operands before an operation. Errors occurring that occur during floating-point operations are admittedly difficult to determine and diagnose, but the benefits of understanding how to check for these errors and employing the process of doing so may often outweigh the costs. This recommendation suggests ways to capture errors during floating-point operations.

Consider the The following code exhibits undefined behavior:

int j = 0;
int iResult = 1 / j;

Running the code above results in undefined behavior. On most implementations, integer division by zero is a terminal error, commonly printing a diagnostic message and aborting the program.:

double x = 0.0;
double dResult = 1 / x;

Though the code above Floating-point division by zero also results in undefined behavior, although most implementations do not view floating point division by zero treat it as a terminal error. If extra steps additional precautions are not taken, the operation happens "silently." it results in a silent error.

The most portable way to determine if a floating-point exceptional condition has occurred is to use the floating-point exception facilities provided by C in fenv.h Wiki MarkupThe most portable way of determining a floating point exceptional condition has occurred is to make use of the floating point exception faculties provided by C99 in {{fenv.h}} \[[ISO/IEC 9899:1999|AA. C References#ISO/IEC 9899-1999]\].

However, the C99 C floating-point exception functions are not without problems. The following caveats exist regarding the interaction between floating-point exceptions and conversions:

• Conversion from floating-point to integer may cause an "invalid" floating-point exception. If this occurs, the value of that integer is undefined and should not be used.
• Most implementations fail to raise "invalid" for conversions from any negative or "large" positive FP floating-point values to unsigned integer types or to signed char. (see See tflt2int.c.).
• When a nonnoninteger floating-integer floating point value is converted into to an integer, the "inexact" floating-point exception is raised.

For information regarding floating-point number conversions, see FLP34-C. Ensure that floating-point conversions are within range of the new type.

Though the notion of floating point exceptions guaranteed by C99, floating point exceptions generally only exist on architectures utilizing IEEE-754. Despite thisThe C Standard does not require all implementations to support floating-point exceptions. Each exception macro in fenv.h is defined if, and only if, the corresponding exception is supported. Only implementations that use IEC 60559 (formerly IEEE-754) floating-point arithmetic are required to support all five exceptions defined by C (see the C Standard, subclause 7.6.2 [ISO/IEC 9899:2011]). Nevertheless, these functions are the only somewhat most portable solution to for handling floating-point exceptions.

A less portable , but sometimes more intuitive and/or more informative, potentially more secure solution is to make use of the faculties capabilities provided by the underlying implementation. If this approach is taken, the caveats of that system need to must be well understood. The following table can serve as  The following table provides a starting point for some common architecturesoperating systems:

Non-Compliant Code Example

In the following non-compliant code, floating point operations are carried out and there is no observation for errors during floating point operations. Please note that the range check on various operands for the operations has been intentionally ignored because we intend to capture the errors during a floating point operation.

Noncompliant Code Example

In this noncompliant code example, floating-point operations are performed without checking for errors. Note that range checking has been intentionally omitted because the intent is to detect errors following the floating-point operation.

void fpOper_noErrorChecking(void) {
  /* ... */
  double a = 1e-40, b, c = 0.1;
  float x = 0, y;
  /* Inexact and underflows */
  y = a;
  /* Divide-by-zero operation */
  b = y / x

fpOper_noErrorChecking(void) {
  /* ... */
  double a = 1e-40, b, c = 0.1;
  float x = 0, y;
  /* inexact and underflowsInexact (loss of precision) */
  yc = sin(30) * a;
  /* divide by zero operation ... */
  b = y / x;
  /* inexact (loss of precision) */
  c = sin(30) * a;
  /* ... */
}

However, as the comments indicate, various exceptional conditions occur that may lead to unexpected arithmetic results.

Compliant Solution 1

}

However, exceptional conditions (as indicated by the comments) occur that may lead to unexpected arithmetic results.

Compliant Solution (C)

This compliant solution uses C Standard functions to handle floating-point errors:This compliant solution uses C99 standard functions to handle floating point errors.

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

void fpOper_fenv(void) {
  double a = 1e-40, b, c = 0.1;
  float x = 0, y;
  int fpeRaised;
  /* ... */

  feclearexcept(FE_ALL_EXCEPT);
  /* Store a into y is inexact and underflows: */
  y = a;
  fpeRaised = fetestexcept(FE_ALL_EXCEPT);
  /* fpeRaised  has FE_INEXACT and FE_UNDERFLOW */

  feclearexcept(FE_ALL_EXCEPT);

  /* divide Divide-by -zero operation */
  b = y / x;
  fpeRaised = fetestexcept(FE_ALL_EXCEPT);
  /* fpeRaised has FE_DIVBYZERO */

  feclearexcept(FE_ALL_EXCEPT);

  c = sin(30) * a;
  fpeRaised = fetestexcept(FE_ALL_EXCEPT);
  /* fpeRaised has FE_INEXACT */

  feclearexcept(FE_ALL_EXCEPT);
  /* ... */
}

Compliant Solution

...

(Windows)

MS Microsoft Visual Studio 2008 and earlier does versions do not support C99 C functions to handle floating-point errors. Windows provides an alternative method to get floating point exception code using _statusfp(), _statusfp2(), and _clearfp().

void 
fpOper_usingStatus(void) {
  /* ... */
  double a = 1e-40, b, c;
  float x = 0, y;
  unsigned int rv = _clearfp();

  /* Store into y is inexact and underflows: */
  y = a;
  rv = _clearfp();  /* rv has _SW_INEXACT and _SW_UNDERFLOW */

  /* zeroZero-divide */
  b = y / x; rv = _clearfp(); /* rv has _SW_ZERODIVIDE */

  /* inexactInexact */
  c = sin(30) * a; rv = _clearfp(); /* rv has _SW_INEXACT */
  /* ... */
}

Compliant Solution

...

(Windows SEH)

MS Microsoft Visual Studio 2008 also uses structured exception handling (SEH) to handle floating-point operation. Using the SEH operations. SEH provides more information about the error and allows the programmer to change the results of the floating-point operation that caused the error condition. Using SEH also provides more information about the error condition.

void 

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

  unmask_fpfpsr();

  _try {
    /* Store into y is inexact and underflows: */
    y = a;

    /* divide Divide-by -zero operation */
    b = y / x;

    /* inexactInexact */
    c = sin(30) * a;
  }

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

  /* ... */
}

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

int fpieee_handler(_FPIEEE_RECORD *ieee) {
  /* ... */

  switch (ieee->RoundingMode) {
    case _FpRoundNearest:
      /* ... */
      break;

      /*
       * Other RMs include _FpRoundMinusInfinity, 
       * _FpRoundPlusInfinity, _FpRoundChopped */.
    
   */

      /* ... */
    }

  switch (ieee->Precision) {
    case _FpPrecision24:
      /* ... */
      break;

      /* Other Ps include _FpPrecision53 */
      /* ... */
    }

   switch (ieee->Operation) {
     case _FpCodeAdd:
       /* ... */
       break;

       /* 
        * Other Ops include _FpCodeSubtract, _FpCodeMultiply, 
        * _FpCodeDivide, _FpCodeSquareRoot, _FpCodeCompare, 
        * _FpCodeConvert, _FpCodeConvertTrunc.
        */
       /* ... */
    }

  /* 
   * processProcess the bitmap ieee->Cause.
 */
  /* processProcess the bitmap ieee->Enable.
 */
  /* processProcess the bitmap ieee->Status */
  /.
   * processProcess the Operand ieee->Operand1, 
   * evaluate format and Value.
 */
  /* processProcess the Operand ieee->Operand2, 
   * evaluate format and Value.
 */
  /* processProcess the Result ieee->Result, 
   * evaluate format and Value.
 */
  /* The result should be set according to the operation 
   * specified in ieee->Cause and the result formatformatted as 
   * specified in ieee->Result.
   */

  /* ... */
}

Risk Assessment

If Undetected floating point exceptions go undetected, they will cause one or more of these conditions: a security vulnerability, lower program efficiency, and inaccurate results-point errors may result in lower program efficiency, inaccurate results, or software vulnerabilities. Most processors stall for a significant duration (sometimes up to a second or even more on 32-bit desktop processors) when an operation incurs a NaN (not a number) value.

Automated Detection

...

Tool	Version	Checker	Description
Astrée	Include Page Astrée_V Astrée_V	float-division-by-zero	Partially checked
Compass/ROSE			Could detect violations of this rule

...

by ensuring that floating-point operations are surrounded by feclearexcept() and fetestexcept(). It would need to look for type conversions to float or double, divisions (by a number not known to be nonzero), and multiplication. It may be wisest to apply this to all floating-point operations in general

...

Related Vulnerabilities

Search for vulnerabilities resulting from the violation of this rule on the CERT website.

References

\[[IEEE 754|AA. C References#IEEE 754 2006]\]
\[[Intel 01|AA. C References#Intel 01]\]
\[[Keil 08|AA. C References#Keil 08]\]
\[[MSDN|AA. C References#MSDN]\] "[fpieee_flt (CRT)|http://msdn.microsoft.com/en-us/library/te2k2f2t(VS.80).aspx]"
\[[Open Group 04|AA. C References#Open Group 04]\] "[fenv.h - Floating point environment|http://www.opengroup.org/onlinepubs/009695399/basedefs/fenv.h.html]"
\[[SecurityFocus 07|AA. C References#SecurityFocus 07]\] 

Related Vulnerabilities

Search for vulnerabilities resulting from the violation of this recommendation on the CERT website.

Related Guidelines

Bibliography

...

Image Added Image Added Image AddedFLP02-A. Consider avoiding floating point numbers when precise computation is needed      05. Floating Point (FLP)       FLP30-C. Do not use floating point variables as loop counters