Double precision

From Academic Kids

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.

Contents

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

See also

pl:Double

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