NAME¶

std::numeric_limits::max_digits10 - std::numeric_limits::max_digits10

Synopsis¶

static constexpr int max_digits10 (since C++11)

The value of std::numeric_limits<T>::max_digits10 is the number of base-10 digits
that are necessary to uniquely represent all distinct values of the type T, such as
necessary for serialization/deserialization to text. This constant is meaningful for
all floating-point types.

Standard specializations¶

T Value of std::numeric_limits<T>::max_digits10
/* non-specialized */ 0
bool 0
char 0
signed char 0
unsigned char 0
wchar_t 0
char8_t (since C++20) 0
char16_t 0
char32_t 0
short 0
unsigned short 0
int 0
unsigned int 0
long 0
unsigned long 0
long long 0
unsigned long long 0
FLT_DECIMAL_DIG or
float std::ceil(std::numeric_limits<float>::digits * std::log10(2) +
1)
DBL_DECIMAL_DIG or
double std::ceil(std::numeric_limits<double>::digits * std::log10(2)
+ 1)
DECIMAL_DIG or LDBL_DECIMAL_DIG or
long double std::ceil(std::numeric_limits<long double>::digits *
std::log10(2) + 1)

Notes¶

Unlike most mathematical operations, the conversion of a floating-point value to
text and back is exact as long as at least max_digits10 were used (9 for float, 17
for double): it is guaranteed to produce the same floating-point value, even though
the intermediate text representation is not exact. It may take over a hundred
decimal digits to represent the precise value of a float in decimal notation.

Example¶

// Run this code

#include <cmath>
#include <iomanip>
#include <iostream>
#include <limits>
#include <sstream>

int main()
{
float value = 10.0000086;

constexpr auto digits10 = std::numeric_limits<decltype(value)>::digits10;
constexpr auto max_digits10 = std::numeric_limits<decltype(value)>::max_digits10;
constexpr auto submax_digits10 = max_digits10 - 1;

std::cout << "float:\n"
" digits10 is " << digits10 << " digits\n"
" max_digits10 is " << max_digits10 << " digits\n"
"submax_digits10 is " << submax_digits10 << " digits\n\n";

const auto original_precision = std::cout.precision();
for (auto i = 0; i < 5; ++i)
{
std::cout
<< " max_digits10: " << std::setprecision(max_digits10) << value << "\n"
"submax_digits10: " << std::setprecision(submax_digits10) << value
<< "\n\n";

value = std::nextafter(value, std::numeric_limits<decltype(value)>::max());
}
std::cout.precision(original_precision);
}

Output:¶

float:
digits10 is 6 digits
max_digits10 is 9 digits
submax_digits10 is 8 digits

max_digits10: 10.0000086
submax_digits10: 10.000009

max_digits10: 10.0000095
submax_digits10: 10.00001

max_digits10: 10.0000105
submax_digits10: 10.00001

max_digits10: 10.0000114
submax_digits10: 10.000011

max_digits10: 10.0000124
submax_digits10: 10.000012

See also¶

radix the radix or integer base used by the representation of the given type
[static] (public static member constant)
digits number of radix digits that can be represented without change
[static] (public static member constant)
digits10 number of decimal digits that can be represented without change
[static] (public static member constant)
min_exponent one more than the smallest negative power of the radix that is a valid
[static] normalized floating-point value
(public static member constant)
max_exponent one more than the largest integer power of the radix that is a valid
[static] finite floating-point value
(public static member constant)