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
#
Each member function defined in this subclause is signal-safe.
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static constexpr T min() noexcept;
2
#
Minimum finite value.189
3
#
For floating-point types with subnormal numbers, returns the minimum positive normalized value.
4
#
Meaningful for all specializations in which is_­bounded != false, or is_­bounded == false && is_­signed == false.
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static constexpr T max() noexcept;
5
#
Maximum finite value.190
6
#
Meaningful for all specializations in which is_­bounded != false.
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static constexpr T lowest() noexcept;
7
#
A finite value x such that there is no other finite value y where y < x.191
8
#
Meaningful for all specializations in which is_­bounded != false.
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static constexpr int digits;
9
#
Number of radix digits that can be represented without change.
10
#
For integer types, the number of non-sign bits in the representation.
11
#
For floating-point types, the number of radix digits in the mantissa.192
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static constexpr int digits10;
12
#
Number of base 10 digits that can be represented without change.193
13
#
Meaningful for all specializations in which is_­bounded != false.
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static constexpr int max_digits10;
14
#
Number of base 10 digits required to ensure that values which differ are always differentiated.
15
#
Meaningful for all floating-point types.
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static constexpr bool is_signed;
16
#
true if the type is signed.
17
#
Meaningful for all specializations.
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static constexpr bool is_integer;
18
#
true if the type is integer.
19
#
Meaningful for all specializations.
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static constexpr bool is_exact;
20
#
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
#
Meaningful for all specializations.
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static constexpr int radix;
22
#
For floating-point types, specifies the base or radix of the exponent representation (often 2).194
23
#
For integer types, specifies the base of the representation.195
24
#
Meaningful for all specializations.
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static constexpr T epsilon() noexcept;
25
#
Machine epsilon: the difference between 1 and the least value greater than 1 that is representable.196
26
#
Meaningful for all floating-point types.
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static constexpr T round_error() noexcept;
27
#
Measure of the maximum rounding error.197
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static constexpr int min_exponent;
28
#
Minimum negative integer such that radix raised to the power of one less than that integer is a normalized floating-point number.198
29
#
Meaningful for all floating-point types.
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static constexpr int min_exponent10;
30
#
Minimum negative integer such that 10 raised to that power is in the range of normalized floating-point numbers.199
31
#
Meaningful for all floating-point types.
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static constexpr int max_exponent;
32
#
Maximum positive integer such that radix raised to the power one less than that integer is a representable finite floating-point number.200
33
#
Meaningful for all floating-point types.
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static constexpr int max_exponent10;
34
#
Maximum positive integer such that 10 raised to that power is in the range of representable finite floating-point numbers.201
35
#
Meaningful for all floating-point types.
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static constexpr bool has_infinity;
36
#
true if the type has a representation for positive infinity.
37
#
Meaningful for all floating-point types.
38
#
Shall be true for all specializations in which is_­iec559 != false.
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static constexpr bool has_quiet_NaN;
39
#
true if the type has a representation for a quiet (non-signaling) “Not a Number”.202
40
#
Meaningful for all floating-point types.
41
#
Shall be true for all specializations in which is_­iec559 != false.
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static constexpr bool has_signaling_NaN;
42
#
true if the type has a representation for a signaling “Not a Number”.203
43
#
Meaningful for all floating-point types.
44
#
Shall be true for all specializations in which is_­iec559 != false.
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static constexpr float_denorm_style has_denorm;
45
#
denorm_­present if the type allows subnormal values (variable number of exponent bits)204, denorm_­absent if the type does not allow subnormal values, and denorm_­indeterminate if it is indeterminate at compile time whether the type allows subnormal values.
46
#
Meaningful for all floating-point types.
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static constexpr bool has_denorm_loss;
47
#
true if loss of accuracy is detected as a denormalization loss, rather than as an inexact result.205
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static constexpr T infinity() noexcept;
48
#
Representation of positive infinity, if available.206
49
#
Meaningful for all specializations for which has_­infinity != false.
Required in specializations for which is_­iec559 != false.
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static constexpr T quiet_NaN() noexcept;
50
#
Representation of a quiet “Not a Number”, if available.207
51
#
Meaningful for all specializations for which has_­quiet_­NaN != false.
Required in specializations for which is_­iec559 != false.
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static constexpr T signaling_NaN() noexcept;
52
#
Representation of a signaling “Not a Number”, if available.208
53
#
Meaningful for all specializations for which has_­signaling_­NaN != false.
Required in specializations for which is_­iec559 != false.
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static constexpr T denorm_min() noexcept;
54
#
Minimum positive subnormal value.209
55
#
Meaningful for all floating-point types.
56
#
In specializations for which has_­denorm == false, returns the minimum positive normalized value.
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static constexpr bool is_iec559;
57
#
true if and only if the type adheres to ISO/IEC/IEEE 60559.210
58
#
Meaningful for all floating-point types.
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static constexpr bool is_bounded;
59
#
true if the set of values representable by the type is finite.211
[Note 1:
All fundamental types ([basic.fundamental]) are bounded.
This member would be false for arbitrary precision types.
— end note]
60
#
Meaningful for all specializations.
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static constexpr bool is_modulo;
61
#
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.
62
#
[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]
63
#
Meaningful for all specializations.
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static constexpr bool traps;
64
#
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.213
65
#
Meaningful for all specializations.
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static constexpr bool tinyness_before;
66
#
true if tinyness is detected before rounding.214
67
#
Meaningful for all floating-point types.
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static constexpr float_round_style round_style;
68
#
The rounding style for the type.215
69
#
Meaningful for all floating-point types.
Specializations for integer types shall return round_­toward_­zero.
189)
Equivalent to CHAR_­MIN, SHRT_­MIN, FLT_­MIN, DBL_­MIN, etc.
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190)
Equivalent to CHAR_­MAX, SHRT_­MAX, FLT_­MAX, DBL_­MAX, etc.
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191)
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.
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192)
Equivalent to FLT_­MANT_­DIG, DBL_­MANT_­DIG, LDBL_­MANT_­DIG.
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193)
Equivalent to FLT_­DIG, DBL_­DIG, LDBL_­DIG.
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194)
Equivalent to FLT_­RADIX.
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195)
Distinguishes types with bases other than 2 (e.g. BCD).
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196)
Equivalent to FLT_­EPSILON, DBL_­EPSILON, LDBL_­EPSILON.
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197)
Rounding error is described in LIA-1 Section 5.2.4 and Annex C Rationale Section C.5.2.4 — Rounding and rounding constants.
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198)
Equivalent to FLT_­MIN_­EXP, DBL_­MIN_­EXP, LDBL_­MIN_­EXP.
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199)
Equivalent to FLT_­MIN_­10_­EXP, DBL_­MIN_­10_­EXP, LDBL_­MIN_­10_­EXP.
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200)
Equivalent to FLT_­MAX_­EXP, DBL_­MAX_­EXP, LDBL_­MAX_­EXP.
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201)
Equivalent to FLT_­MAX_­10_­EXP, DBL_­MAX_­10_­EXP, LDBL_­MAX_­10_­EXP.
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202)
Required by LIA-1.
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203)
Required by LIA-1.
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204)
Required by LIA-1.
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205)
See ISO/IEC/IEEE 60559.
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206)
Required by LIA-1.
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207)
Required by LIA-1.
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208)
Required by LIA-1.
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209)
Required by LIA-1.
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210)
ISO/IEC/IEEE 60559:2011 is the same as IEEE 754-2008.
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211)
Required by LIA-1.
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212)
Required by LIA-1.
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213)
Required by LIA-1.
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214)
Refer to ISO/IEC/IEEE 60559.
Required by LIA-1.
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215)
Equivalent to FLT_­ROUNDS.
Required by LIA-1.
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