Handling overflow when casting doubles to integers in C

Solution 1:

When casting floats to integers, overflow causes undefined behavior. From the C99 spec, section 6.3.1.4 Real floating and integer:

When a finite value of real floating type is converted to an integer type other than _Bool, the fractional part is discarded (i.e., the value is truncated toward zero). If the value of the integral part cannot be represented by the integer type, the behavior is undefined.

You have to check the range manually, but don't use code like:

// DON'T use code like this!
if (my_double > INT_MAX || my_double < INT_MIN)
    printf("Overflow!");

INT_MAX is an integer constant that may not have an exact floating-point representation. When comparing to a float, it may be rounded to the nearest higher or nearest lower representable floating point value (this is implementation-defined). With 64-bit integers, for example, INT_MAX is 2^63 - 1 which will typically be rounded to 2^63, so the check essentially becomes my_double > INT_MAX + 1. This won't detect an overflow if my_double equals 2^63.

For example with gcc 4.9.1 on Linux, the following program

#include <math.h>
#include <stdint.h>
#include <stdio.h>

int main() {
    double  d = pow(2, 63);
    int64_t i = INT64_MAX;
    printf("%f > %lld is %s\n", d, i, d > i ? "true" : "false");
    return 0;
}

prints

9223372036854775808.000000 > 9223372036854775807 is false

It's hard to get this right if you don't know the limits and internal representation of the integer and double types beforehand. But if you convert from double to int64_t, for example, you can use floating point constants that are exact doubles (assuming two's complement and IEEE doubles):

if (!(my_double >= -9223372036854775808.0   // -2^63
   && my_double <   9223372036854775808.0)  // 2^63
) {
    // Handle overflow.
}

The construct !(A && B)also handles NaNs correctly. A portable, safe, but slighty inaccurate version for ints is:

if (!(my_double > INT_MIN && my_double < INT_MAX)) {
    // Handle overflow.
}

This errs on the side of caution and will falsely reject values that equal INT_MIN or INT_MAX. But for most applications, this should be fine.

Solution 2:

limits.h has constants for max and min possible values for integer data types, you can check your double variable before casting, like

if (my_double > nextafter(INT_MAX, 0) || my_double < nextafter(INT_MIN, 0))
    printf("Overflow!");
else
    my_int = (int)my_double;

EDIT: nextafter() will solve the problem mentioned by nwellnhof

Solution 3:

To answer your question: The behaviour when you cast out of range floats is undefined or implementation specific.

Speaking from experience: I've worked on a MIPS64 system that didn't implemented these kind of casts at all. Instead of doing something deterministic the CPU threw a CPU exception. The exception handler that ought to emulate the cast returned without doing anything to the result.

I've ended up with random integers. Guess how long it took to trace back a bug to this cause. :-)

You'll better do the range check yourself if you aren't sure that the number can't get out of the valid range.

Solution 4:

A portable way for C++ is to use the SafeInt class:

http://www.codeplex.com/SafeInt

The implementation will allow for normal addition/subtract/etc on a C++ number type including casts. It will throw an exception whenever and overflow scenario is detected.

SafeInt<int> s1 = INT_MAX;
SafeInt<int> s2 = 42;
SafeInt<int> s3 = s1 + s2;  // throws

I highly advise using this class in any place where overflow is an important scenario. It makes it very difficult to avoid silently overflowing. In cases where there is a recovery scenario for an overflow, simply catch the SafeIntException and recover as appropriate.

SafeInt now works on GCC as well as Visual Studio

Solution 5:

What is the best way to detect this under/overflow?

Compare the truncated double to exact limits near INT_MIN,INT_MAX.

The trick is to exactly convert limits based on INT_MIN,INT_MAX into double values. A double may not exactly represent INT_MAX as the number of bits in an int may exceed that floating point's precision.^*1 In that case, the conversion of INT_MAX to double suffers from rounding. The number after INT_MAX is a power-of-2 and is certainly representable as a double. 2.0*(INT_MAX/2 + 1) generates the whole number one greater than INT_MAX.

The same applies to INT_MIN on non-2s-complement machines.

INT_MAX is always a power-of-2 - 1.
INT_MIN is always:
-INT_MAX (not 2's complement) or
-INT_MAX-1 (2's complement)

int double_to_int(double x) {
  x = trunc(x);
  if (x >= 2.0*(INT_MAX/2 + 1)) Handle_Overflow();
  #if -INT_MAX == INT_MIN
  if (x <= 2.0*(INT_MIN/2 - 1)) Handle_Underflow();
  #else

  // Fixed 2022
  // if (x < INT_MIN) Handle_Underflow();
  if (x - INT_MIN < -1.0) Handle_Underflow();

  #endif
  return (int) x;
}

To detect NaN and not use trunc()

#define DBL_INT_MAXP1 (2.0*(INT_MAX/2+1)) 
#define DBL_INT_MINM1 (2.0*(INT_MIN/2-1)) 

int double_to_int(double x) {
  if (x < DBL_INT_MAXP1) {
    #if -INT_MAX == INT_MIN
    if (x > DBL_INT_MINM1) {
      return (int) x;
    }
    #else
    if (ceil(x) >= INT_MIN) {
      return (int) x;
    }
    #endif 
    Handle_Underflow();
  } else if (x > 0) {
    Handle_Overflow();
  } else {
    Handle_NaN();
  }
}

[Edit 2022] Corner error corrected after 6 years.

double values in the range (INT_MIN - 1.0 ... INT_MIN) (non-inclusive end-points) convert well to int. Prior code failed those.

^*1 This applies too to INT_MIN - 1 when int precision is more than double. Although this is rare, the issues readily applies to long long. Consider the difference between:

  if (x < LLONG_MIN - 1.0) Handle_Underflow(); // Bad
  if (x - LLONG_MIN < -1.0) Handle_Underflow();// Good

With 2's complement, some_int_type_MIN is a (negative) power-of-2 and exactly converts to a double. Thus x - LLONG_MIN is exact in the range of concern while LLONG_MIN - 1.0 may suffer precision loss in the subtraction.