IEEE 754 formats

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Revision as of 22:52, 2 April 2018 by Kai Burghardt (talk | contribs) (Kai Burghardt moved page Single to IEEE 754 formats: article intended to cover all `single`, `double` and `extended`)
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English (en)

single and double are Pascal's data types implementing the platform-dependent real. Both are implemented according IEEE standard 754, where single is “single-precision” and double is “double-precision”.

single

value range 1.5E-45 .. 3.4E38
accuracy 6-9 significant decimal digits precision
memory requirement 4 bytes or 32 bits
property The single- data-type data field can hold floating-point 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;
    s := 0;
    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 FloatingCommand literals, while the assignment of the lower example is literals of the String type.

Binary floating-point 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