# Double precision

In computing, double precision is a computer numbering format that occupies two storage locations in computer memory at address and address+1. A double precision number, sometimes simply a double, may be defined to be an integer, fixed point, or floating point.

Modern computers with 32-bit stores (single precision) provide 64-bit double precision. Double precision floating point is an IEEE 754 standard for encoding floating point numbers that uses 8 bytes.

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## Double precision memory format

```Sign bit: 1
Exponent width: 11
Significand precision: 53
```

The format is written with an implicit integer bit with value 1 unless the written exponent is all zeros. Thus only 52 bits of the fraction appear in the memory format.

```syyy yyyy yyyy xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx xxxx
```

### Exponent encodings

```Emin  (0x001) = -1022
Emax (0x7fe) = 1023
Exponent bias (0x3ff) = 1023
```

The true exponent = written exponent - exponent bias

```0x000 and 0x7ff  are reserved exponents
0x000 is used to represent zero and denormals
0x7ff is used to represent infinity and NaNs
```

All bit patterns are valid encodings.

## Double precision examples

``` 3ff0 0000 0000 0000   = 1
```
``` c000 0000 0000 0000   = -2
```
``` 7fef ffff ffff ffff   ~ 1.7976931348623 x 10308 (Max Double)
```
``` 3fd5 5555 5555 5555   ~ 1/3
```

(1/3 rounds down instead of up like single precision, because of the odd number of bits in the significand.)

``` 0000 0000 0000 0000   = 0
8000 0000 0000 0000   = -0
```
``` 7ff0 0000 0000 0000   = Infinity
fff0 0000 0000 0000   = -Infinity
```

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