static constexpr T min() noexcept;
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;
Meaningful for all specializations in which is_bounded != false.
static constexpr T lowest() noexcept;
Meaningful for all specializations in which is_bounded != false.
Number of radix digits that can be represented without change.
For integer types, the number of non-sign bits in the representation.
static constexpr int digits10;
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.
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;
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;
Meaningful for all floating-point types.
Shall be true for all specializations in which is_iec559 != false.
static constexpr bool has_signaling_NaN;
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;
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;
Meaningful for all floating-point types.
In specializations for which has_denorm == false, returns the minimum positive normalized value.
static constexpr bool is_iec559;
Meaningful for all floating-point types.
static constexpr bool is_bounded;
True if the set of values representable by the type is finite.211 [ Note: 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.
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;
Meaningful for all floating-point types.
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 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.