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Errors during floating-point operations are often neglected by 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 doing so often outweigh the costs. This recommendation suggests ways to capture errors during floating-point operations.

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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;

Floating-point division by zero also results in undefined behavior, although most implementations do not treat it as a terminal error. If additional precautions are not taken, it results in a silent error.

The most portable way of determining to determine if a floating-point exceptional condition has occurred is to use the floating-point exception facilities provided by C in fenv.h [ISO/IEC 9899:2011].

However, the 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 floating-point values to unsigned integer types or to signed char. (See tflt2int.c.)
• When a noninteger floating-point value is converted 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.

The C standard does 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 Section the C Standard, subclause 7.6.2 [ISO/IEC 9899:2011]). Nevertheless, these functions are the most portable solution for handling floating-point exceptions.

A less portable but potentially more secure solution is to use the 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 provides a starting point for some common operating systems:

Noncompliant Code Example

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

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

Compliant Solution (

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C)

This compliant solution uses C standard 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);
  /* ... */
}

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Microsoft Visual Studio 2008 and earlier versions do not support C functions to handle floating-point errors. Windows provides an alternative method for handling floating-point errors using 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 */
  /* ... */
}

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Microsoft Visual Studio 2008 also uses structured exception handling (SEH) to handle floating-point operationoperations. 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.

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

  unmask_fpsr();

  _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.
   */

  /* ... */
}

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Undetected floating-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

Related Vulnerabilities

Related Vulnerabilities

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

Related Guidelines

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Bibliography

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MITRE CWE: CWE-369, "Divide by zero"

Bibliography

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