How to get the lowest representable floating point value in C++

Question

I have a program where I need to set a variable to the lowest representable (non infinite) double-precision floating point number in C++. How am I able to set a variable to the lowest double-precision floating point value?

I tried using std::numeric_limits. I am not using C++11 so I am unable to try to use the lowest() function. I tried to use max(), but when I tried it, it returned infinity. I also tried subtracting a value from max() in the hope that I would then get a representable number.

double max_value = std::numeric_limits<double>::max();
cout << "Test 1: " << max_value << endl;    
max_value = max_value - 1;
cout << "Test 2: " << max_value << endl;
double low_value = - std::numeric_limits<double>::max();
cout << "Test 3: " << low_value << endl;
cout << "Test 4: " << low_value + 1 << endl;

Output:

Test 1: inf
Test 2: inf
Test 3: -inf
Test 4: -inf

How can I set low_value in the example above to the lowest representable double?

Answer 1

Once you have -inf (you got it), you can get the lowest finite value with the nextafter function on (-inf,0).

EDIT: Depending on the context, this may be better than -DBL_MAX in case DBL_MAX is represented in decimal (thus in an inexact way). However the C standard requires that floating constants be evaluated in the default rounding mode (ie to nearest). In the particular case of GCC, DBL_MAX is a long double value cast to double; however the long double value seems to have enough digits so that, once converted from decimal to long double, the value is exactly representable in as double, so that the cast is exact and the active rounding mode doesn't affect it. As you can see, this is rather tricky, and one may want to check on various platforms that it is correct under any context. In a similar way, I have serious doubts on the correctness of the definition DBL_EPSILON by GCC on PowerPC (where the long double type is implemented as a double-double arithmetic ) since there are many long double values extremely close to a power of two.

Answer 2

The standard library <cfloat> / <float.h> provides macros defining floating point implementation parameters.

The question is somewhat ambiguous - it is not clear whether you mean the smallest magnitude representable non-zero value (which would be DBL_MIN ) or the lowest representable value (given by -DBL_MAX ). Either way - take your pick as necessary.

Answer 3

It turned out that there was a bug in the iostream that I was using to print the values. I switched to using cstdio instead of iostream. The values were then printed as expected.

double low_value = - std::numeric_limits<double>::max();
cout <<"cout: " << low_value << endl;
printf("printf: %f\n",low_value);

Output:

cout: inf
printf: 179769...