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3.7 Double-precision Floating-point

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### 3.7 Double-precision Floating-point

3.7 Double-precision Floating-point

The standard defines the encoding for the double-precision floating- point data type "double" (64 bits or 8 bytes). The encoding used is the IEEE standard for normalized double-precision floating-point numbers [3]. The standard encodes the following three fields, which describe the double-precision floating-point number:

```      S: The sign of the number.  Values 0 and 1 represent positive and
negative, respectively.  One bit.

E: The exponent of the number, base 2.  11 bits are devoted to
this field.  The exponent is biased by 1023.

F: The fractional part of the number's mantissa, base 2.  52 bits
are devoted to this field.
```

Therefore, the floating-point number is described by:

```         (-1)**S * 2**(E-Bias) * 1.F
```

It is declared as follows:

```         double identifier;

+------+------+------+------+------+------+------+------+
|byte 0|byte 1|byte 2|byte 3|byte 4|byte 5|byte 6|byte 7|
S|    E   |                    F                        |
+------+------+------+------+------+------+------+------+
1|<--11-->|<-----------------52 bits------------------->|
<-----------------------64 bits------------------------->
DOUBLE-PRECISION FLOATING-POINT
```

Just as the most and least significant bytes of a number are 0 and 3, the most and least significant bits of a double-precision floating- point number are 0 and 63. The beginning bit (and most significant bit) offsets of S, E , and F are 0, 1, and 12, respectively. Note that these numbers refer to the mathematical positions of the bits, and NOT to their actual physical locations (which vary from medium to medium).

The IEEE specifications should be consulted concerning the encoding for signed zero, signed infinity (overflow), and denormalized numbers (underflow) [3]. According to IEEE specifications, the "NaN" (not a number) is system dependent and should not be interpreted within XDR as anything other than "NaN".

Next: 3.8 Quadruple-precision Floating-point

Connected: An Internet Encyclopedia
3.7 Double-precision Floating-point