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Floating-point literal

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Floating-point literal defines a compile-time constant whose value is specified in the source file.

Contents

[edit] Syntax

digit-sequence decimal-exponent suffix (optional) (1)
digit-sequence . decimal-exponent (optional) suffix (optional) (2)
digit-sequence (optional) . digit-sequence decimal-exponent (optional) suffix (optional) (3)
0x | 0X hex-digit-sequence hex-exponent suffix (optional) (4) (since C++17)
0x | 0X hex-digit-sequence . hex-exponent suffix (optional) (5) (since C++17)
0x | 0X hex-digit-sequence (optional) . hex-digit-sequence hex-exponent suffix (optional) (6) (since C++17)
1) digit-sequence representing a whole number without a decimal separator, in this case the exponent is not optional: 1e10, 1e-5L.
2) digit-sequence representing a whole number with a decimal separator, in this case the exponent is optional: 1., 1.e-2.
3) digit-sequence representing a fractional number. The exponent is optional: 3.14, .1f, 0.1e-1L.
4) Hexadecimal digit-sequence representing a whole number without a radix separator. The exponent is never optional for hexadecimal floating-point literals: 0x1ffp10, 0X0p-1.
5) Hexadecimal digit-sequence representing a whole number with a radix separator. The exponent is never optional for hexadecimal floating-point literals: 0x1.p0, 0xf.p-1.
6) Hexadecimal digit-sequence representing a fractional number with a radix separator. The exponent is never optional for hexadecimal floating-point literals: 0x0.123p-1, 0xa.bp10l.

decimal-exponent has the form

e | E exponent-sign (optional) digit-sequence

hex-exponent has the form

p | P exponent-sign (optional) digit-sequence (since C++17)

exponent-sign, if present, is either + or -

suffix, if present, is one of f, l, F, L, f16, f32, f64, f128, bf16, F16, F32, F64, F128, BF16(since C++23). The suffix determines the type of the floating-point literal:

  • (no suffix) defines double
  • f F defines float
  • l L defines long double
  • f16 F16 defines std::float16_t
  • f32 F32 defines std::float32_t
  • f64 F64 defines std::float64_t
  • f128 F128 defines std::float128_t
  • bf16 BF16 defines std::bfloat16_t
(since C++23)

Optional single quotes (') may be inserted between the digits as a separator; they are ignored when determining the value of the literal.

(since C++14)

[edit] Explanation

Decimal scientific notation is used, meaning that the value of the floating-point literal is the significand multiplied by the number 10 raised to the power of decimal-exponent. E.g. the mathematical meaning of 123e4 is ×ばつ104.

If the floating literal begins with the character sequence 0x or 0X, the floating literal is a hexadecimal floating literal. Otherwise, it is a decimal floating literal.

For a hexadecimal floating literal, the significand is interpreted as a hexadecimal rational number, and the digit-sequence of the exponent is interpreted as the (decimal) integer power of 2 by which the significand has to be scaled.

double d = 0x1.4p3;// hex fraction 1.4 (decimal 1.25) scaled by 23, that is 10.0

(since C++17)

[edit] Notes

The hexadecimal floating-point literals were not part of C++ until C++17, although they can be parsed and printed by the I/O functions since C++11: both C++ I/O streams when std::hexfloat is enabled and the C I/O streams: std::printf , std::scanf , etc. See std::strtof for the format description.

Feature-test macro Value Std Feature
__cpp_hex_float 201603L (C++17) Hexadecimal floating literals

[edit] Example

Run this code
#include <iomanip>
#include <iostream>
#include <limits>
#include <typeinfo>
 
#define OUT(x) '\n' << std::setw(16) << #x << x
 
int main()
{
 std::cout
 << "Literal" "\t" "Printed value" << std::left
 << OUT( 58. ) // double
 << OUT( 4e2 ) // double
 << OUT( 123.456e-67 ) // double
 << OUT( 123.456e-67f ) // float, truncated to zero
 << OUT( .1E4f ) // float
 << OUT( 0x10.1p0 ) // double
 << OUT( 0x1p5 ) // double
 << OUT( 0x1e5 ) // integer literal, not floating-point
 << OUT( 3.14'15'92 ) // double, single quotes ignored (C++14)
 << OUT( 1.18e-4932l ) // long double
 << std::setprecision (39)
 << OUT( 3.4028234e38f ) // float
 << OUT( 3.4028234e38 ) // double
 << OUT( 3.4028234e38l ) // long double
 << '\n';
 
 static_assert(3.4028234e38f == std::numeric_limits <float>::max());
 
 static_assert(3.4028234e38f == // ends with 4
 3.4028235e38f); // ends with 5
 
 static_assert(3.4028234e38 != // ends with 4
 3.4028235e38); // ends with 5
 
 // Both floating-point constants below are 3.4028234e38
 static_assert(3.4028234e38f != // a float (then promoted to double)
 3.4028234e38); // a double
}

Possible output: 

Literal Printed value
58. 58
4e2 400
123.456e-67 1.23456e-65
123.456e-67f 0
.1E4f 1000
0x10.1p0 16.0625
0x1p5 32
0x1e5 485
3.14'15'92 3.14159
1.18e-4932l 1.18e-4932
3.4028234e38f 340282346638528859811704183484516925440
3.4028234e38 340282339999999992395853996843190976512
3.4028234e38l 340282339999999999995912555211526242304

[edit] References

  • C++23 standard (ISO/IEC 14882:2024):
  • 5.13.4 Floating-point literals [lex.fcon]
  • C++20 standard (ISO/IEC 14882:2020):
  • 5.13.4 Floating-point literals [lex.fcon]
  • C++17 standard (ISO/IEC 14882:2017):
  • 5.13.4 Floating literals [lex.fcon]
  • C++14 standard (ISO/IEC 14882:2014):
  • 2.14.4 Floating literals [lex.fcon]
  • C++11 standard (ISO/IEC 14882:2011):
  • 2.14.4 Floating literals [lex.fcon]
  • C++98 standard (ISO/IEC 14882:1998):
  • 2.13.3 Floating literals [lex.fcon]

[edit] See also

user-defined literals (C++11) literals with user-defined suffix[edit]
C documentation for Floating constant

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