18 Language support library [language.support]

18.3 Implementation properties [support.limits]

18.3.2 Numeric limits [limits]

18.3.2.4 numeric_limits members [numeric.limits.members]

static constexpr T min() noexcept;

Minimum finite value.189

For floating types with denormalization, returns the minimum positive normalized value.

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

static constexpr T max() noexcept;

Maximum finite value.190

Meaningful for all specializations in which is_bounded != false.

static constexpr T lowest() noexcept;

A finite value x such that there is no other finite value y where y < x.191

Meaningful for all specializations in which is_bounded != false.

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 mantissa.192

static constexpr int digits10;

Number of base 10 digits that can be represented without change.193

Meaningful for all specializations in which is_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 types, specifies the base or radix of the exponent representation (often 2).194

For integer types, specifies the base of the representation.195

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.196

Meaningful for all floating-point types.

static constexpr T round_error() noexcept;

Measure of the maximum rounding error.197

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.198

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.199

Meaningful for all floating-point types.

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.200

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.201

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

static constexpr bool has_quiet_NaN;

True if the type has a representation for a quiet (non-signaling) “Not a Number.”202

Meaningful for all floating-point types.

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

static constexpr bool has_signaling_NaN;

True if the type has a representation for a signaling “Not a Number.”203

Meaningful for all floating-point types.

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

static constexpr float_denorm_style has_denorm;

denorm_present if the type allows denormalized values (variable number of exponent bits)204, denorm_absent if the type does not allow denormalized values, and denorm_indeterminate if it is indeterminate at compile time whether the type allows denormalized values.

Meaningful for all floating-point types.

static constexpr bool has_denorm_loss;

True if loss of accuracy is detected as a denormalization loss, rather than as an inexact result.205

static constexpr T infinity() noexcept;

Representation of positive infinity, if available.206

Meaningful for all specializations for which has_infinity != false. Required in specializations for which is_iec559 != false.

static constexpr T quiet_NaN() noexcept;

Representation of a quiet “Not a Number,” if available.207

Meaningful for all specializations for which has_quiet_NaN != false. Required in specializations for which is_iec559 != false.

static constexpr T signaling_NaN() noexcept;

Representation of a signaling “Not a Number,” if available.208

Meaningful for all specializations for which has_signaling_NaN != false. Required in specializations for which is_iec559 != false.

static constexpr T denorm_min() noexcept;

Minimum positive denormalized value.209

Meaningful for all floating-point types.

In specializations for which has_denorm == false, returns the minimum positive normalized value.

static constexpr bool is_iec559;

True if and only if the type adheres to ISO/IEC/IEEE 60559.210

Meaningful for all floating-point types.

static constexpr bool is_bounded;

True if the set of values representable by the type is finite.211Note: All fundamental types ([basic.fundamental]) are bounded. 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.212 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: 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 ]

Meaningful for all specializations.

static constexpr bool traps;

true if, at program startup, there exists a value of the type that would cause an arithmetic operation using that value to trap.213

Meaningful for all specializations.

static constexpr bool tinyness_before;

true if tinyness is detected before rounding.214

Meaningful for all floating-point types.

static constexpr float_round_style round_style;

The rounding style for the type.215

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 ISO/IEC 10967-1 Language independent arithmetic - Part 1 Section 5.2.8 and Annex A Rationale Section A.5.2.8 - 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.