minimum double value in C/C++

Question

Is there a standard and/or portable way to represent the smallest negative value (e.g. to use negative infinity) in a C(++) program?

DBL_MIN in float.h is the smallest positive number.

Answer 1

Floating point numbers (IEEE 754) are symmetrical, so if you can represent the greatest value (DBL_MAX or numeric_limits<double>::max()), just prepend a minus sign.

And then is the cool way:

double f;
(*((uint64_t*)&f))= ~(1LL<<52);

Answer 2

If you do not have float exceptions enabled (which you shouldn't imho), you can simply say:

double neg_inf = -1/0.0;

This yields negative infinity. If you need a float, you can either cast the result

float neg_inf = (float)-1/0.0;

or use single precision arithmetic

float neg_inf = -1.0f/0.0f;

The result is always the same, there is exactly one representation of negative infinity in both single and double precision, and they convert to each other as you would expect.

Answer 3

Is there a standard and/or portable way to represent the smallest negative value (e.g. to use negative infinity) in a C(++) program?

C approach.

Many implementations support +/- infinities, so the most negative double value is -INFINITY.

#include <math.h>
double most_negative = -INFINITY;

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Is there a standard and/or portable way ....?

Now we need to also consider other cases:

• No infinities

Simply -DBL_MAX.

• Only an unsigned infinity.

I'd expect in this case, OP would prefer -DBL_MAX.

• De-normal values greater in magnitude than DBL_MAX.

This is an unusual case, likely outside OP's concern. When double is encoded as a pair of a floating points to achieve desired range/precession, (see double-double) there exist a maximum normal double and perhaps a greater de-normal one. I have seen debate if DBL_MAX should refer to the greatest normal, of the greatest of both.

Fortunately this paired approach usually includes an -infinity, so the most negative value remains -INFINITY.

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For more portability, code can go down the route

// HUGE_VAL is designed to be infinity or DBL_MAX (when infinites are not implemented)
// .. yet is problematic with unsigned infinity.
double most_negative1 = -HUGE_VAL;  

// Fairly portable, unless system does not understand "INF"
double most_negative2 = strtod("-INF", (char **) NULL);

// Pragmatic
double most_negative3 = strtod("-1.0e999999999", (char **) NULL);

// Somewhat time-consuming
double most_negative4 = pow(-DBL_MAX, 0xFFFF /* odd value */);

// My suggestion
double most_negative5 = (-DBL_MAX)*DBL_MAX;

Answer 4

Are you looking for actual infinity or the minimal finite value? If the former, use

-numeric_limits<double>::infinity()

which only works if

numeric_limits<double>::has_infinity

Otherwise, you should use

numeric_limits<double>::lowest()

which was introduces in C++11.

If lowest() is not available, you can fall back to

-numeric_limits<double>::max()

which may differ from lowest() in principle, but normally doesn't in practice.

Answer 5

A truly portable C++ solution

As from C++11 you can use numeric_limits<double>::lowest(). According to the standard, it returns exactly what you're looking for:

A finite value x such that there is no other finite value y where y < x.
Meaningful for all specializations in which is_bounded != false.

Online demo

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Lots of non portable C++ answers here !

There are many answers going for -std::numeric_limits<double>::max().

Fortunately, they will work well in most of the cases. Floating point encoding schemes decompose a number in a mantissa and an exponent and most of them (e.g. the popular IEEE-754) use a distinct sign bit, which doesn't belong to the mantissa. This allows to transform the largest positive in the smallest negative just by flipping the sign:

Why aren't these portable ?

The standard doesn't impose any floating point standard.

I agree that my argument is a little bit theoretic, but suppose that some excentric compiler maker would use a revolutionary encoding scheme with a mantissa encoded in some variations of a two's complement. Two's complement encoding are not symmetric. for example for a signed 8 bit char the maximum positive is 127, but the minimum negative is -128. So we could imagine some floating point encoding show similar asymmetric behavior.

I'm not aware of any encoding scheme like that, but the point is that the standard doesn't guarantee that the sign flipping yields the intended result. So this popular answer (sorry guys !) can't be considered as fully portable standard solution ! /* at least not if you didn't assert that numeric_limits<double>::is_iec559 is true */

Answer 6

The original question concerns infinity. So, why not use

#define Infinity  ((double)(42 / 0.0))

according to the IEEE definition? You can negate that of course.

Answer 7

In C, use

#include <float.h>

const double lowest_double = -DBL_MAX;

In C++pre-11, use

#include <limits>

const double lowest_double = -std::numeric_limits<double>::max();

In C++11 and onwards, use

#include <limits>

constexpr double lowest_double = std::numeric_limits<double>::lowest();

Answer 8

-DBL_MAX in ANSI C, which is defined in float.h.

Answer 9

- std::numeric_limits<double>::max()

should work just fine

Numeric limits

Answer 10

Try this:

-1 * numeric_limits<double>::max()

Reference: numeric_limits

This class is specialized for each of the fundamental types, with its members returning or set to the different values that define the properties that type has in the specific platform in which it compiles.