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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

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 (52 xs)
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Exponent encodings

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

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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

In baseball, a double is a two-base hit. See double (baseball).





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