floating point literal

 

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

Syntax

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

The exponent has the form

e | E exponent-sign(optional) digit-sequence	(1)
p | P exponent-sign(optional) digit-sequence	(2)	(since C++17)

1) The exponent syntax for a decimal floating-point literal

2) The exponent syntax for hexadecimal floating-point literal

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

suffix, if present, is one of f, F, l, or L. The suffix determines the type of the floating-point literal:

• (no suffix) defines double
• f F defines float
• l L defines long double

Optional single quotes(') can be inserted between the digits as a separator, they are ignored when compiling.

(since C++14)

Explanation

Decimal scientific notation is used, meaning that the value of the floating-point literal is the significand mutiplied by the number 10 raised to the power of exponent. 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 integer power of 2 to which the significand has to be scaled. double d = 0x1.2p3; // hex fraction 1.2 (decimal 1.125) scaled by 2^3, that is 9.0

(since C++17)

Example

Run this code

#include <iostream>
int main()
{
  std::cout << 58.         << '\n'
            << 4e2         << '\n'
            << 123.456e-67 << '\n'
            << .1E4f       << '\n'
            << 0x10.1p0    << '\n';
}

Output:

58
400
1.23456e-65
1000
16.0625

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