[support.limits] (original) (raw)

17.3.5.1 General [numeric.limits.general]

Thenumeric_limitsclass template provides a C++ program with information about various properties of the implementation's representation of the arithmetic types.

namespace std { template<class T> class numeric_limits { public: static constexpr bool is_specialized = false;static constexpr T min() noexcept { return T(); } static constexpr T max() noexcept { return T(); } static constexpr T lowest() noexcept { return T(); } static constexpr int digits = 0;static constexpr int digits10 = 0;static constexpr int max_digits10 = 0;static constexpr bool is_signed = false;static constexpr bool is_integer = false;static constexpr bool is_exact = false;static constexpr int radix = 0;static constexpr T epsilon() noexcept { return T(); } static constexpr T round_error() noexcept { return T(); } static constexpr int min_exponent = 0;static constexpr int min_exponent10 = 0;static constexpr int max_exponent = 0;static constexpr int max_exponent10 = 0;static constexpr bool has_infinity = false;static constexpr bool has_quiet_NaN = false;static constexpr bool has_signaling_NaN = false;static constexpr T infinity() noexcept { return T(); } static constexpr T quiet_NaN() noexcept { return T(); } static constexpr T signaling_NaN() noexcept { return T(); } static constexpr T denorm_min() noexcept { return T(); } static constexpr bool is_iec559 = false;static constexpr bool is_bounded = false;static constexpr bool is_modulo = false;static constexpr bool traps = false;static constexpr bool tinyness_before = false;static constexpr float_round_style round_style = round_toward_zero;};}

For all members declaredstatic constexprin thenumeric_limitstemplate, specializations shall define these values in such a way that they are usable as constant expressions.

For thenumeric_limitsprimary template, all data members are value-initialized and all member functions return a value-initialized object.

[Note 1:

This means all members have zero or false values unless numeric_limits is specialized for a type.

— _end note_]

Specializations shall be provided for each arithmetic type, both floating-point and integer, includingbool.

The memberis_specializedshall betruefor all such specializations ofnumeric_limits.

The value of each member of a specialization ofnumeric_limits on a cv-qualified typecv T shall be equal to the value of the corresponding member of the specialization on the unqualified type T.

Non-arithmetic standard types, such ascomplex, shall not have specializations.

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.

17.3.5.3 numeric_limits specializations [numeric.special]

All members shall be provided for all specializations.

However, many values are only required to be meaningful under certain conditions (for example,epsilon()is only meaningful ifis_integerisfalse).

Any value that is not “meaningful” shall be set to 0 orfalse.

[Example 1: namespace std { template<> class numeric_limits<float> { public: static constexpr bool is_specialized = true;static constexpr float min() noexcept { return 1.17549435E-38F; } static constexpr float max() noexcept { return 3.40282347E+38F; } static constexpr float lowest() noexcept { return -3.40282347E+38F; } static constexpr int digits = 24;static constexpr int digits10 = 6;static constexpr int max_digits10 = 9;static constexpr bool is_signed = true;static constexpr bool is_integer = false;static constexpr bool is_exact = false;static constexpr int radix = 2;static constexpr float epsilon() noexcept { return 1.19209290E-07F; } static constexpr float round_error() noexcept { return 0.5F; } static constexpr int min_exponent = -125;static constexpr int min_exponent10 = - 37;static constexpr int max_exponent = +128;static constexpr int max_exponent10 = + 38;static constexpr bool has_infinity = true;static constexpr bool has_quiet_NaN = true;static constexpr bool has_signaling_NaN = true;static constexpr float infinity() noexcept { return value; } static constexpr float quiet_NaN() noexcept { return value; } static constexpr float signaling_NaN() noexcept { return value; } static constexpr float denorm_min() noexcept { return min(); } static constexpr bool is_iec559 = true;static constexpr bool is_bounded = true;static constexpr bool is_modulo = false;static constexpr bool traps = true;static constexpr bool tinyness_before = true;static constexpr float_round_style round_style = round_to_nearest;};} — _end example_]

The specialization forboolshall be provided as follows:namespace std { template<> class numeric_limits<bool> { public: static constexpr bool is_specialized = true;static constexpr bool min() noexcept { return false; } static constexpr bool max() noexcept { return true; } static constexpr bool lowest() noexcept { return false; } static constexpr int digits = 1;static constexpr int digits10 = 0;static constexpr int max_digits10 = 0;static constexpr bool is_signed = false;static constexpr bool is_integer = true;static constexpr bool is_exact = true;static constexpr int radix = 2;static constexpr bool epsilon() noexcept { return 0; } static constexpr bool round_error() noexcept { return 0; } static constexpr int min_exponent = 0;static constexpr int min_exponent10 = 0;static constexpr int max_exponent = 0;static constexpr int max_exponent10 = 0;static constexpr bool has_infinity = false;static constexpr bool has_quiet_NaN = false;static constexpr bool has_signaling_NaN = false;static constexpr bool infinity() noexcept { return 0; } static constexpr bool quiet_NaN() noexcept { return 0; } static constexpr bool signaling_NaN() noexcept { return 0; } static constexpr bool denorm_min() noexcept { return 0; } static constexpr bool is_iec559 = false;static constexpr bool is_bounded = true;static constexpr bool is_modulo = false;static constexpr bool traps = false;static constexpr bool tinyness_before = false;static constexpr float_round_style round_style = round_toward_zero;};}