The numeric_limits class 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 float_denorm_style has_denorm = denorm_absent; static constexpr bool has_denorm_loss = 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; }; template<class T> class numeric_limits<const T>; template<class T> class numeric_limits<volatile T>; template<class T> class numeric_limits<const volatile T>; }
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.
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.
static constexpr T min() noexcept;
Meaningful for all specializations in which is_bounded != false, or is_bounded == false && is_signed == false.
static constexpr T max() noexcept;
static constexpr T lowest() noexcept;
static constexpr int digits;
static constexpr int digits10;
static constexpr int max_digits10;
static constexpr bool is_signed;
static constexpr bool is_integer;
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.
static constexpr int radix;
static constexpr T epsilon() noexcept;
static constexpr T round_error() noexcept;
static constexpr int min_exponent;
static constexpr int min_exponent10;
static constexpr int max_exponent;
static constexpr int max_exponent10;
static constexpr bool has_infinity;
static constexpr bool has_quiet_NaN;
static constexpr bool has_signaling_NaN;
static constexpr float_denorm_style has_denorm;
static constexpr bool has_denorm_loss;
static constexpr T infinity() noexcept;
Meaningful for all specializations for which has_infinity != false. Required in specializations for which is_iec559 != false.
static constexpr T quiet_NaN() noexcept;
Meaningful for all specializations for which has_quiet_NaN != false. Required in specializations for which is_iec559 != false.
static constexpr T signaling_NaN() noexcept;
Meaningful for all specializations for which has_signaling_NaN != false. Required in specializations for which is_iec559 != false.
static constexpr T denorm_min() noexcept;
In specializations for which has_denorm == false, returns the minimum positive normalized value.
static constexpr bool is_iec559;
static constexpr bool is_bounded;
true if the set of values representable by the type is finite.210 [ Note: All fundamental types ([basic.fundamental]) are bounded. This member would be false for arbitrary precision types. — end note ]
static constexpr bool is_modulo;
[ Example: is_modulo is false for signed integer types ([basic.fundamental]) unless an implementation, as an extension to this International Standard, defines signed integer overflow to wrap. — end example ]
static constexpr bool traps;
static constexpr bool tinyness_before;
static constexpr float_round_style round_style;
Meaningful for all floating-point types. Specializations for integer types shall return round_toward_zero.
Equivalent to CHAR_MIN, SHRT_MIN, FLT_MIN, DBL_MIN, etc.
Equivalent to CHAR_MAX, SHRT_MAX, FLT_MAX, DBL_MAX, etc.
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.
Equivalent to FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG.
Equivalent to FLT_DIG, DBL_DIG, LDBL_DIG.
Equivalent to FLT_RADIX.
Distinguishes types with bases other than 2 (e.g. BCD).
Equivalent to FLT_EPSILON, DBL_EPSILON, LDBL_EPSILON.
Rounding error is described in LIA-1 Section 5.2.4 and Annex C Rationale Section C.5.2.4 — Rounding and rounding constants.
Equivalent to FLT_MIN_EXP, DBL_MIN_EXP, LDBL_MIN_EXP.
Equivalent to FLT_MIN_10_EXP, DBL_MIN_10_EXP, LDBL_MIN_10_EXP.
Equivalent to FLT_MAX_EXP, DBL_MAX_EXP, LDBL_MAX_EXP.
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.
See ISO/IEC/IEEE 60559.
Required by LIA-1.
Required by LIA-1.
Required by LIA-1.
Required by LIA-1.
ISO/IEC/IEEE 60559:2011 is the same as IEEE 754-2008.
Required by LIA-1.
Required by LIA-1.
Required by LIA-1.
Refer to ISO/IEC/IEEE 60559. Required by LIA-1.
Equivalent to FLT_ROUNDS. Required by LIA-1.
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:
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_denorm_style has_denorm = denorm_absent; static constexpr bool has_denorm_loss = false; 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:
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 float_denorm_style has_denorm = denorm_absent; static constexpr bool has_denorm_loss = 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; }; }