3.6.5 Sample double precision floating-point values for IEEE 754 arithmetic

Sample double bit patterns, together with their mathematical values.

Table 3-10 Sample double-precision floating-point values

Double value S Exp Frac Mathematical value
0x3FF0000000000000 0 0x3FF 000...000 1.0
0xBFF0000000000000 1 0x3FF 000...000 -1.0
0x3FF0000000000001a 0 0x3FF 000...001 1.000 000 000 000 000 222
0x3FE8000000000000 0 0x3FE 100...000 0.75
0x0010000000000000b 0 0x001 000...000 2.23*10-308
0x0000000000000001c 0 0x000 000...001 4.94*10-324
0x7FEFFFFFFFFFFFFFd 0 0x7FE 111...111 1.80*10308
0x7FF0000000000000 0 0x7FF 000...000 Plus infinity
0xFFF0000000000000 1 0x7FF 000...000 Minus infinity
0x0000000000000000e 0 0x000 000...000 0.0
0x7FF0000000000001 0 0x7FF 000...001 Signaling NaN
0x7FF8000000000000f 0 0x7FF 100...000 Quiet NaN
a

The smallest representable number that can be seen to be greater than 1.0. The amount that it differs from 1.0 is known as the machine epsilon. This is 0.000 000 119 in float, and 0.000 000 000 000 000 222 in double. The machine epsilon gives a rough idea of the number of significant figures the format can keep track of. float can do six or seven places. double can do fifteen or sixteen.

b

The smallest value that can be represented as a normalized number in each format. Numbers smaller than this can be stored as denormals, but are not held with as much precision.

c

The smallest positive number that can be distinguished from zero. This is the absolute lower limit of the format.

d

The largest finite number that can be stored. Attempting to increase this number by addition or multiplication causes overflow and generates infinity (in general).

e

Zero. Strictly speaking, they show plus zero. Zero with a sign bit of 1, minus zero, is treated differently by some operations, although the comparison operations (for example == and !=) report that the two types of zero are equal.

f 

There are two types of NaNs, signaling NaNs and quiet NaNs. Quiet NaNs have a 1 in the first bit of Frac, and signaling NaNs have a zero there. The difference is that signaling NaNs cause an exception when used, whereas quiet NaNs do not.

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