cppdraft_translate/cppdraft/numeric/limits/members.md

[numeric.limits.members]

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]

1

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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.

— end note]

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static constexpr T min() noexcept;

2

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Minimum finite value.161

3

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

4

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Meaningful for all specializations in whichis_bounded != false, oris_bounded == false && is_signed == false.

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static constexpr T max() noexcept;

5

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Maximum finite value.162

6

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Meaningful for all specializations in whichis_bounded != false.

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static constexpr T lowest() noexcept;

7

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A finite value x such that there is no other finite value y where y < x.163

8

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Meaningful for all specializations in which is_bounded != false.

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static constexpr int digits;

9

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Number ofradix digits that can be represented without change.

10

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For integer types, the number of non-sign bits in the representation.

11

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For floating-point types, the number of radix digits in the significand.164

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static constexpr int digits10;

12

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Number of base 10 digits that can be represented without change.165

13

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Meaningful for all specializations in whichis_bounded != false.

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static constexpr int max_digits10;

14

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Number of base 10 digits required to ensure that values which differ are always differentiated.

15

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Meaningful for all floating-point types.

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static constexpr bool is_signed;

16

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true if the type is signed.

17

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Meaningful for all specializations.

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static constexpr bool is_integer;

18

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true if the type is integer.

19

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Meaningful for all specializations.

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static constexpr bool is_exact;

20

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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.

21

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Meaningful for all specializations.

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static constexpr int radix;

22

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For floating-point types, specifies the base or radix of the exponent representation (often 2).166

23

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For integer types, specifies the base of the representation.167

24

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Meaningful for all specializations.

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static constexpr T epsilon() noexcept;

25

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Machine epsilon: the difference between 1 and the least value greater than 1 that is representable.168

26

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Meaningful for all floating-point types.

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static constexpr T round_error() noexcept;

27

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Measure of the maximum rounding error.169

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static constexpr int min_exponent;

28

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Minimum negative integer such thatradix raised to the power of one less than that integer is a normalized floating-point number.170

29

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Meaningful for all floating-point types.

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static constexpr int min_exponent10;

30

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Minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers.171

31

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Meaningful for all floating-point types.

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static constexpr int max_exponent;

32

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Maximum positive integer such thatradix raised to the power one less than that integer is a representable finite floating-point number.172

33

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Meaningful for all floating-point types.

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static constexpr int max_exponent10;

34

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Maximum positive integer such that 10 raised to that power is in the range of representable finite floating-point numbers.173

35

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Meaningful for all floating-point types.

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static constexpr bool has_infinity;

36

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true if the type has a representation for positive infinity.

37

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Meaningful for all floating-point types.

38

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Shall betrue for all specializations in whichis_iec559 != false.

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static constexpr bool has_quiet_NaN;

39

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true if the type has a representation for a quiet (non-signaling) “Not a Number”.174

40

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Meaningful for all floating-point types.

41

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Shall betrue for all specializations in whichis_iec559 != false.

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static constexpr bool has_signaling_NaN;

42

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true if the type has a representation for a signaling “Not a Number”.175

43

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Meaningful for all floating-point types.

44

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Shall betrue for all specializations in whichis_iec559 != false.

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static constexpr T infinity() noexcept;

45

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Representation of positive infinity, if available.176

46

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Meaningful for all specializations for whichhas_infinity != false.

Required in specializations for whichis_iec559 != false.

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static constexpr T quiet_NaN() noexcept;

47

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Representation of a quiet “Not a Number”, if available.177

48

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Meaningful for all specializations for whichhas_quiet_NaN != false.

Required in specializations for whichis_iec559 != false.

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static constexpr T signaling_NaN() noexcept;

49

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Representation of a signaling “Not a Number”, if available.178

50

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Meaningful for all specializations for whichhas_signaling_NaN != false.

Required in specializations for whichis_iec559 != false.

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static constexpr T denorm_min() noexcept;

51

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Minimum positive subnormal value, if available.179

Otherwise, minimum positive normalized value.

52

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Meaningful for all floating-point types.

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static constexpr bool is_iec559;

53

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true if and only if the type adheres to ISO/IEC 60559.180

[Note 2:

The value is true for any of the typesfloat16_t, float32_t, float64_t, or float128_t, if present ([basic.extended.fp]).

— end note]

54

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Meaningful for all floating-point types.

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static constexpr bool is_bounded;

55

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true if the set of values representable by the type is finite.181

[Note 3:

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

This member would be false for arbitrary precision types.

— end note]

56

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Meaningful for all specializations.

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static constexpr bool is_modulo;

57

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true if the type is modulo.182

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.

58

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[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]

59

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Meaningful for all specializations.

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static constexpr bool traps;

60

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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.183

61

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Meaningful for all specializations.

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static constexpr bool tinyness_before;

62

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true if tinyness is detected before rounding.184

63

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Meaningful for all floating-point types.

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static constexpr float_round_style round_style;

64

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The rounding style for the type.185

65

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Meaningful for all floating-point types.

Specializations for integer types shall returnround_toward_zero.

161)161)

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

162)162)

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

163)163)

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.

164)164)

Equivalent to FLT_MANT_DIG, DBL_MANT_DIG,LDBL_MANT_DIG.

165)165)

Equivalent to FLT_DIG, DBL_DIG,LDBL_DIG.

166)166)

Equivalent to FLT_RADIX.

167)167)

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

168)168)

Equivalent to FLT_EPSILON, DBL_EPSILON, LDBL_EPSILON.

169)169)

Rounding error is described in ISO/IEC 10967-1:2012 Section 5.2.4 and Annex C Rationale Section C.5.2.4 — Rounding and rounding constants.

170)170)

Equivalent to FLT_MIN_EXP, DBL_MIN_EXP,LDBL_MIN_EXP.

171)171)

Equivalent toFLT_MIN_10_EXP, DBL_MIN_10_EXP, LDBL_MIN_10_EXP.

172)172)

Equivalent to FLT_MAX_EXP,DBL_MAX_EXP, LDBL_MAX_EXP.

173)173)

Equivalent toFLT_MAX_10_EXP, DBL_MAX_10_EXP, LDBL_MAX_10_EXP.

174)174)

Required by ISO/IEC 10967-1:2012.

175)175)

Required by ISO/IEC 10967-1:2012.

176)176)

Required by ISO/IEC 10967-1:2012.

177)177)

Required by ISO/IEC 10967-1:2012.

178)178)

Required by ISO/IEC 10967-1:2012.

179)179)

Required by ISO/IEC 10967-1:2012.

180)180)

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

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)

Refer to ISO/IEC 60559.

Required by ISO/IEC 10967-1:2012.

185)185)

Equivalent to FLT_ROUNDS.

Required by ISO/IEC 10967-1:2012.