Floating-point literal

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

Syntax

1			digit-sequence	decimal-exponent suffix	(optional)
2			digit-sequence	.	decimal-exponent	(optional)	suffix	(optional)
3			digit-sequence	(optional)	.	digit-sequence	decimal-exponent	(optional)	suffix	(optional)
4	0x|0X		hex-digit-sequence	hex-exponent suffix	(optional)	(od C++17)
5	0x|0X		hex-digit-sequence	.	hex-exponent suffix	(optional)	(od C++17)
6	0x|0X		hex-digit-sequence	(optional)	.	hex-digit-sequence	hex-exponent suffix	(optional)	(od 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  (od 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 (od 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

 (od C++23) Optional single quotes ' may be inserted between the digits as a separator; they are ignored when determining the value of the literal. (od C++14)

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 123×104.

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

 (od C++17)

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	Comment
__cpp_hex_float	201603L	(C++17)	Hexadecimal floating literals

Example

#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 Result

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

References

• C++23 standard (ISO/IEC 14882:2023):
  • 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]