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| Static constants | ||||
numeric_limits::digits10 | ||||
(C++11) | ||||
| Static member functions | ||||
(C++11) | ||||
| Helper types | ||||
staticconstint digits10; | (until C++11) | |
staticconstexprint digits10; | (since C++11) | |
The value ofstd::numeric_limits<T>::digits10 is the number of base-10 digits that can be represented by the typeT without change, that is, any number with this many significant decimal digits can be converted to a value of typeT and back to decimal form, without change due to rounding or overflow. For base-radix types, it is the value ofdigits() (digits-1 for floating-point types) multiplied by\(\small \log_{10}{radix}\)log10(radix) and rounded down.
T | value ofstd::numeric_limits<T>::digits10 |
| /* non-specialized */ | 0 |
| bool | 0 |
| char | std::numeric_limits<char>::digits*std::log10(2) |
| signedchar | std::numeric_limits<signedchar>::digits*std::log10(2) |
| unsignedchar | std::numeric_limits<unsignedchar>::digits*std::log10(2) |
| wchar_t | std::numeric_limits<wchar_t>::digits*std::log10(2) |
| char8_t(since C++20) | std::numeric_limits<char8_t>::digits*std::log10(2) |
| char16_t(since C++11) | std::numeric_limits<char16_t>::digits*std::log10(2) |
| char32_t(since C++11) | std::numeric_limits<char32_t>::digits*std::log10(2) |
| short | std::numeric_limits<short>::digits*std::log10(2) |
| unsignedshort | std::numeric_limits<unsignedshort>::digits*std::log10(2) |
| int | std::numeric_limits<int>::digits*std::log10(2) |
| unsignedint | std::numeric_limits<unsignedint>::digits*std::log10(2) |
| long | std::numeric_limits<long>::digits*std::log10(2) |
| unsignedlong | std::numeric_limits<unsignedlong>::digits*std::log10(2) |
| longlong(since C++11) | std::numeric_limits<longlong>::digits*std::log10(2) |
| unsignedlonglong(since C++11) | std::numeric_limits<unsignedlonglong>::digits*std::log10(2) |
| float | FLT_DIG (6 for IEEEfloat) |
| double | DBL_DIG (15 for IEEEdouble) |
| longdouble | LDBL_DIG (18 for 80-bit Intellongdouble;33 for IEEE quadruple) |
An 8-bit binary type can represent any two-digit decimal number exactly, but 3-digit decimal numbers 256..999 cannot be represented. The value ofdigits10 for an 8-bit type is 2 (8*std::log10(2) is 2.41)
The standard 32-bit IEEE 754 floating-point type has a 24 bit fractional part (23 bits written, one implied), which may suggest that it can represent 7 digit decimals (24*std::log10(2) is 7.22), but relative rounding errors are non-uniform and some floating-point values with 7 decimal digits do not survive conversion to 32-bit float and back: the smallest positive example is8.589973e9, which becomes8.589974e9 after the roundtrip. These rounding errors cannot exceed one bit in the representation, anddigits10 is calculated as(24-1)*std::log10(2), which is 6.92. Rounding down results in the value 6.
Likewise, the 16-digit string9007199254740993 does not survive text->double->text roundtrip, becoming9007199254740992: the 64-bit IEEE 754 type double guarantees this roundtrip only for 15 decimal digits.
[static](C++11) | number of decimal digits necessary to differentiate all values of this type (public static member constant)[edit] |
[static] | the radix or integer base used by the representation of the given type (public static member constant)[edit] |
[static] | number ofradix digits that can be represented without change(public static member constant)[edit] |
[static] | one more than the smallest negative power of the radix that is a valid normalized floating-point value (public static member constant)[edit] |
[static] | one more than the largest integer power of the radix that is a valid finite floating-point value (public static member constant)[edit] |
