[numeric.limits.members] (original) (raw)

17 Language support library [support]

17.3 Implementation properties [support.limits]

17.3.5 Class template numeric_limits [numeric.limits]

17.3.5.2 numeric_limits members [numeric.limits.members]

Each member function defined in this subclause is signal-safe ([support.signal]).

[Note 1:

The arithmetic specification described in ISO/IEC 10967-1:2012 is commonly termed LIA-1.

— _end note_]

static constexpr T min() noexcept;

For floating-point types with subnormal numbers, returns the minimum positive normalized value.

Meaningful for all specializations in whichis_bounded != false, oris_bounded == false && is_signed == false.

static constexpr T max() noexcept;

Meaningful for all specializations in whichis_bounded != false.

static constexpr T lowest() noexcept;

A finite value x such that there is no other finite value y where y < x.163

Meaningful for all specializations in which is_bounded != false.

static constexpr int digits;

Number ofradixdigits that can be represented without change.

For integer types, the number of non-sign bits in the representation.

For floating-point types, the number of radix digits in the significand.164

static constexpr int digits10;

Number of base 10 digits that can be represented without change.165

Meaningful for all specializations in whichis_bounded != false.

static constexpr int max_digits10;

Number of base 10 digits required to ensure that values which differ are always differentiated.

Meaningful for all floating-point types.

static constexpr bool is_signed;

true if the type is signed.

Meaningful for all specializations.

static constexpr bool is_integer;

true if the type is integer.

Meaningful for all specializations.

static constexpr bool is_exact;

true if the type uses an exact representation.

All integer types are exact, but not all exact types are integer.

For example, rational and fixed-exponent representations are exact but not integer.

Meaningful for all specializations.

static constexpr int radix;

For floating-point types, specifies the base or radix of the exponent representation (often 2).166

For integer types, specifies the base of the representation.167

Meaningful for all specializations.

static constexpr T epsilon() noexcept;

Machine epsilon: the difference between 1 and the least value greater than 1 that is representable.168

Meaningful for all floating-point types.

static constexpr T round_error() noexcept;

Measure of the maximum rounding error.169

static constexpr int min_exponent;

Minimum negative integer such thatradixraised to the power of one less than that integer is a normalized floating-point number.170

Meaningful for all floating-point types.

static constexpr int min_exponent10;

Minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers.171

Meaningful for all floating-point types.

static constexpr int max_exponent;

Maximum positive integer such thatradixraised to the power one less than that integer is a representable finite floating-point number.172

Meaningful for all floating-point types.

static constexpr int max_exponent10;

Maximum positive integer such that 10 raised to that power is in the range of representable finite floating-point numbers.173

Meaningful for all floating-point types.

static constexpr bool has_infinity;

true if the type has a representation for positive infinity.

Meaningful for all floating-point types.

Shall betruefor all specializations in whichis_iec559 != false.

static constexpr bool has_quiet_NaN;

true if the type has a representation for a quiet (non-signaling) “Not a Number”.174

Meaningful for all floating-point types.

Shall betruefor all specializations in whichis_iec559 != false.

static constexpr bool has_signaling_NaN;

true if the type has a representation for a signaling “Not a Number”.175

Meaningful for all floating-point types.

Shall betruefor all specializations in whichis_iec559 != false.

static constexpr T infinity() noexcept;

Representation of positive infinity, if available.176

Meaningful for all specializations for whichhas_infinity != false.

Required in specializations for whichis_iec559 != false.

static constexpr T quiet_NaN() noexcept;

Representation of a quiet “Not a Number”, if available.177

Meaningful for all specializations for whichhas_quiet_NaN != false.

Required in specializations for whichis_iec559 != false.

static constexpr T signaling_NaN() noexcept;

Representation of a signaling “Not a Number”, if available.178

Meaningful for all specializations for whichhas_signaling_NaN != false.

Required in specializations for whichis_iec559 != false.

static constexpr T denorm_min() noexcept;

Minimum positive subnormal value, if available.179

Otherwise, minimum positive normalized value.

Meaningful for all floating-point types.

static constexpr bool is_iec559;

true if and only if the type adheres to ISO/IEC 60559.180

[Note 2:

The value is true for any of the typesfloat16_t, float32_t, float64_t, or float128_t, if present ([basic.extended.fp]).

— _end note_]

Meaningful for all floating-point types.

static constexpr bool is_bounded;

true if the set of values representable by the type is finite.181

[Note 3:

This member would be false for arbitrary precision types.

— _end note_]

Meaningful for all specializations.

static constexpr bool is_modulo;

true if the type is modulo.182

A type is modulo if, for any operation involving +, -, or* on values of that type whose result would fall outside the range [min(), max()], the value returned differs from the true value by an integer multiple of max() - min() + 1.

[Example 1:

is_modulo is false for signed integer types ([basic.fundamental]) unless an implementation, as an extension to this document, defines signed integer overflow to wrap.

— _end example_]

Meaningful for all specializations.

static constexpr bool traps;

trueif, at the start of the program, there exists a value of the type that would cause an arithmetic operation using that value to trap.183

Meaningful for all specializations.

static constexpr bool tinyness_before;

trueif tinyness is detected before rounding.184

Meaningful for all floating-point types.

static constexpr float_round_style round_style;

The rounding style for the type.185

Meaningful for all floating-point types.

Specializations for integer types shall returnround_toward_zero.