17 Language support library [support]

17.3 Implementation properties [support.limits]

17.3.5 Class template numeric_limits [numeric.limits]

17.3.5.1 General [numeric.limits.general]

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

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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 declared static constexpr in the numeric_limits template, specializations shall define these values in such a way that they are usable as constant expressions.

For the numeric_limits primary 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, including bool.

The member is_specialized shall be true for all such specializations of numeric_limits.

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

Non-arithmetic standard types, such as complex<T>, shall not have specializations.

17.3.5.2 numeric_limits members [numeric.limits.members]

Each member function defined in this subclause is signal-safe .

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static constexpr T min() noexcept;

Minimum finite value.169

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

Meaningful for all specializations in which is_bounded != false, or is_bounded == false && is_signed == false.

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static constexpr T max() noexcept;

Maximum finite value.170

Meaningful for all specializations in which is_bounded != false.

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static constexpr T lowest() noexcept;

A finite value x such that there is no other finite value y where y < x.171

Meaningful for all specializations in which is_bounded != false.

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static constexpr int digits;

Number of radix digits 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.172

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static constexpr int digits10;

Number of base 10 digits that can be represented without change.173

Meaningful for all specializations in which is_bounded != false.

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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.

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static constexpr bool is_signed;

true if the type is signed.

Meaningful for all specializations.

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static constexpr bool is_integer;

true if the type is integer.

Meaningful for all specializations.

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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.

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static constexpr int radix;

For floating-point types, specifies the base or radix of the exponent representation (often 2).174

For integer types, specifies the base of the representation.175

Meaningful for all specializations.

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static constexpr T epsilon() noexcept;

Machine epsilon: the difference between 1 and the least value greater than 1 that is representable.176

Meaningful for all floating-point types.

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static constexpr T round_error() noexcept;

Measure of the maximum rounding error.177

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static constexpr int  min_exponent;

Minimum negative integer such that radix raised to the power of one less than that integer is a normalized floating-point number.178

Meaningful for all floating-point types.

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static constexpr int  min_exponent10;

Minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers.179

Meaningful for all floating-point types.

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static constexpr int  max_exponent;

Maximum positive integer such that radix raised to the power one less than that integer is a representable finite floating-point number.180

Meaningful for all floating-point types.

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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.181

Meaningful for all floating-point types.

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static constexpr bool has_infinity;

true if the type has a representation for positive infinity.

Meaningful for all floating-point types.

Shall be true for all specializations in which is_iec559 != false.

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static constexpr bool has_quiet_NaN;

true if the type has a representation for a quiet (non-signaling) “Not a Number”.182

Meaningful for all floating-point types.

Shall be true for all specializations in which is_iec559 != false.

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static constexpr bool has_signaling_NaN;

true if the type has a representation for a signaling “Not a Number”.183

Meaningful for all floating-point types.

Shall be true for all specializations in which is_iec559 != false.

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static constexpr T infinity() noexcept;

Representation of positive infinity, if available.184

Meaningful for all specializations for which has_infinity != false.

Required in specializations for which is_iec559 != false.

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static constexpr T quiet_NaN() noexcept;

Representation of a quiet “Not a Number”, if available.185

Meaningful for all specializations for which has_quiet_NaN != false.

Required in specializations for which is_iec559 != false.

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static constexpr T signaling_NaN() noexcept;

Representation of a signaling “Not a Number”, if available.186

Meaningful for all specializations for which has_signaling_NaN != false.

Required in specializations for which is_iec559 != false.

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static constexpr T denorm_min() noexcept;

Minimum positive subnormal value, if available.187

Otherwise, minimum positive normalized value.

Meaningful for all floating-point types.

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static constexpr bool is_iec559;

true if and only if the type adheres to ISO/IEC/IEEE 60559.188

[Note 1:

The value is true for any of the types float16_t, float32_t, float64_t, or float128_t, if present ([basic.extended.fp]).

— end note]

Meaningful for all floating-point types.

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static constexpr bool is_bounded;

true if the set of values representable by the type is finite.189

[Note 2:

All fundamental types ([basic.fundamental]) are bounded.

This member would be false for arbitrary precision types.

— end note]

Meaningful for all specializations.

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static constexpr bool is_modulo;

true if the type is modulo.190

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.

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static constexpr bool traps;

true if, at the start of the program, there exists a value of the type that would cause an arithmetic operation using that value to trap.191

Meaningful for all specializations.

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static constexpr bool tinyness_before;

true if tinyness is detected before rounding.192

Meaningful for all floating-point types.

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static constexpr float_round_style round_style;

The rounding style for the type.193

Meaningful for all floating-point types.

Specializations for integer types shall return round_toward_zero.

169)169)

Equivalent to CHAR_MIN, SHRT_MIN, FLT_MIN, DBL_MIN, etc.

170)170)

Equivalent to CHAR_MAX, SHRT_MAX, FLT_MAX, DBL_MAX, etc.

171)171)

lowest() is necessary because not all floating-point representations have a smallest (most negative) value that is the negative of the largest (most positive) finite value.

172)172)

Equivalent to FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG.

173)173)

Equivalent to FLT_DIG, DBL_DIG, LDBL_DIG.

174)174)

Equivalent to FLT_RADIX.

175)175)

Distinguishes types with bases other than 2 (e.g., BCD).

176)176)

Equivalent to FLT_EPSILON, DBL_EPSILON, LDBL_EPSILON.

177)177)

Rounding error is described in LIA-1 Section 5.2.4 and Annex C Rationale Section C.5.2.4 — Rounding and rounding constants.

178)178)

Equivalent to FLT_MIN_EXP, DBL_MIN_EXP, LDBL_MIN_EXP.

179)179)

Equivalent to FLT_MIN_10_EXP, DBL_MIN_10_EXP, LDBL_MIN_10_EXP.

180)180)

Equivalent to FLT_MAX_EXP, DBL_MAX_EXP, LDBL_MAX_EXP.

181)181)

Equivalent to FLT_MAX_10_EXP, DBL_MAX_10_EXP, LDBL_MAX_10_EXP.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

ISO/IEC/IEEE 60559:2020 is the same as IEEE 754-2019.

Required by LIA-1.

Required by LIA-1.

Required by LIA-1.

Refer to ISO/IEC/IEEE 60559.

Required by LIA-1.

193)193)

Equivalent to FLT_ROUNDS.

Required by LIA-1.

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 if is_integer is false).

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

[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 for bool shall be provided as follows:

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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; }; }