17 Language support library [support]

17.3 Implementation properties [support.limits]

17.3.5 Class template numeric_limits [numeric.limits]

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.
β€” end note]
static constexpr T min() noexcept;
Minimum finite value.165
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.
static constexpr T max() noexcept;
Maximum finite value.166
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.167
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 significand.168
static constexpr int digits10;
Number of base 10 digits that can be represented without change.169
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-point types, specifies the base or radix of the exponent representation (often 2).170
For integer types, specifies the base of the representation.171
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.172
Meaningful for all floating-point types.
static constexpr T round_error() noexcept;
Measure of the maximum rounding error.173
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.174
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.175
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.176
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.177
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) β€œNot a Number”.178
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 β€œNot a Number”.179
Meaningful for all floating-point types.
Shall be true for all specializations in which is_iec559 != false.
static constexpr T infinity() noexcept;
Representation of positive infinity, if available.180
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 β€œNot a Number”, if available.181
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 β€œNot a Number”, if available.182
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 subnormal value, if available.183
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 60559.184
[Note 2: 
The value is true for any of the types float16_t, float32_t, float64_t, or float128_t, if present ([basic.extended.fp]).
β€” 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.185
[Note 3: 
All fundamental types ([basic.fundamental]) are bounded.
This member would be false for arbitrary precision types.
β€” end note]
Meaningful for all specializations.
static constexpr bool is_modulo;
true if the type is modulo.186
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.
β€” end example]
Meaningful for all specializations.
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.187
Meaningful for all specializations.
static constexpr bool tinyness_before;
true if tinyness is detected before rounding.188
Meaningful for all floating-point types.
static constexpr float_round_style round_style;
The rounding style for the type.189
Meaningful for all floating-point types.
Specializations for integer types shall return round_toward_zero.
165)165)
Equivalent to CHAR_MIN, SHRT_MIN, FLT_MIN, DBL_MIN, etc.
166)166)
Equivalent to CHAR_MAX, SHRT_MAX, FLT_MAX, DBL_MAX, etc.
167)167)
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.
168)168)
Equivalent to FLT_MANT_DIG, DBL_MANT_DIG, LDBL_MANT_DIG.
169)169)
Equivalent to FLT_DIG, DBL_DIG, LDBL_DIG.
170)170)
Equivalent to FLT_RADIX.
171)171)
Distinguishes types with bases other than 2 (e.g., BCD).
172)172)
Equivalent to FLT_EPSILON, DBL_EPSILON, LDBL_EPSILON.
173)173)
Rounding error is described in ISO/IEC 10967-1:2012 Section 5.2.4 and Annex C Rationale Section C.5.2.4 β€” Rounding and rounding constants.
174)174)
Equivalent to FLT_MIN_EXP, DBL_MIN_EXP, LDBL_MIN_EXP.
175)175)
Equivalent to FLT_MIN_10_EXP, DBL_MIN_10_EXP, LDBL_MIN_10_EXP.
176)176)
Equivalent to FLT_MAX_EXP, DBL_MAX_EXP, LDBL_MAX_EXP.
177)177)
Equivalent to FLT_MAX_10_EXP, DBL_MAX_10_EXP, LDBL_MAX_10_EXP.
178)178)
Required by ISO/IEC 10967-1:2012.
179)179)
Required by ISO/IEC 10967-1:2012.
180)180)
Required by ISO/IEC 10967-1:2012.
181)181)
Required by ISO/IEC 10967-1:2012.
182)182)
Required by ISO/IEC 10967-1:2012.
183)183)
Required by ISO/IEC 10967-1:2012.
184)184)
ISO/IEC 60559:2020 is the same as IEEE 754-2019.
185)185)
Required by ISO/IEC 10967-1:2012.
186)186)
Required by ISO/IEC 10967-1:2012.
187)187)
Required by ISO/IEC 10967-1:2012.
188)188)
Refer to ISO/IEC 60559.
Required by ISO/IEC 10967-1:2012.
189)189)
Equivalent to FLT_ROUNDS.
Required by ISO/IEC 10967-1:2012.