IEEE 754 formats
│
English (en) │
single
, double
and extended
are FPC's data types implementing Pascal’s real
.
All of them are implemented according IEEE standard 754, where single
is “singleprecision”, double
is “doubleprecision”, and extended
has 80 bits.
single
value range  1.5E45 .. 3.4E38 
accuracy  69 significant decimal digits precision 
memory requirement  4 bytes or 32 bits 
property  The single datatype data field can hold floatingpoint values and signed and unsigned integer values.
Assigning other values will result in error messages from the compiler when the program is compiled, and the compile will be aborted. That is, the executable program is not created. 
Definition of a data field of data type Single:
var
s: single;
Examples of assigning valid values:
s := 123.45678;
// Note: '0' is an integer literal. 0.0 is an real literal.
// Here, FPC will make an implicit typecast from integer to single:
s := 0;
// a positive sign is optional
s := 123.45678;
Examples of assigning invalid values:
s := '123.45678';
s := '0';
s := '123.45678';
The difference between the two examples is that the upper example is the assignment of Integer and Floating literals, while the assignment of the lower example is literals of the String type.
Binary floatingpoint format
Any value stored as a single requires 32 bits, formatted as shown in the table below:
Bits  Usage 

31  Sign (0 = positive, 1 = negative) 
30 to 23  Exponent, biased by 127 
22 to 0  Fraction f of the number 1.f 
double
Any value stored as a double requires 64 bits, formatted as shown in the table below:
Bits  Usage 

63  Sign (0 = positive, 1 = negative) 
62 to 52  Exponent, biased by 1023 
51 to 0  Fraction f of the number 1.f 
Example of converting from raw data to double (Data is array [0..7] of byte
):
function ToDouble(const Data; IntelEndianness: Boolean = False):Double;inline;
var
ADouble: Double absolute Data;
AQWord: QWord absolute Result;
begin
Result := ADouble;
if not IntelEndianness then
AQWord := SwapEndian(AQWord);
end;
extended
extended
is a 80bit wide floatingpoint data type.
There are FPUs that internally use 80 bits for increased precision.
FPC allows to use this gain in precision.
extended
data type, it will be mapped to largest available floatingpoint number data available, i. e. usually double
.Using the maximum precision for constants
In this example:
var
f: double;
n: integer = 1758;
m: integer = 0;
begin
f := n * 1.2E6 + (2*m+1) * 50E3; // 2109650048
FPC will interpret the constant 1.2E6 as Single type, because it fits into the range of the Single type. This leads to some precision loss in the calculation: the result is 2109650048 instead of 2109650000.
You can use the FPC commandline flag CF64 to force floating point constants to have at least 64 bits precision. Or you can use {$MINFPCONSTPREC <n>} to force the compiler to evaluate all floating point constants always with the precision given by <n> = 32, 64 or DEFAULT (80 is not supported for implementation reasons). In FPC v3.3.1+, you can also use the directive {$excessprecision on} which exists also in Delphi.
simple data types 


complex data types 