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Runtime Environment - Floating-Point Support
5.7.1.1 Single-Precision Floating-Point Format
31
32
MSB
Figure 5-3 illustrates the single-precision floating-point format.
Single-
precision values are represented in 32 bits: a sign bit (bit 31 ), an 8-bit biased
exponent (bits 23-30), and a 23-bit mantissa (bits 0-22).
23 22
o
LSB
Figure 5-3. Single-Precision Format
Given a sign bit
s,
an exponent e, and a mantissa f, the value
V
of the float-
ing-point number X= (s,e,f) is:
•
If s=O, e=255, and f=O, the V
=
+
00
•
If s=1, e=255, and f=O, the V
=
-00
•
If 0<e<255 and f:l:O, then V
=
(-1)S
x
2
e -
127
(.f);
V is not valid if
X= (s,e,f) is not a normalized floating-point number
•
If s=O, e=O, and f=O, the V
=
0
•
For all other cases,
V
=
not valid
Precision of single-precision values is greater than six decimal digits; the range
includes:
•
Positive values: 5.87747 x 10-
39 to 1.70141
x
10 38
•
Negative values:
-1.70141 x 10 38 to -5.87747 x 10- 39
•
0
•
±oo
5.7.1.2 Double-Precision Floating-Point Format
63
62
Figure 5-4 illustrates the double-precision floating-point format.
Double-
precision values are represented in 64 bits: a sign bit (bit 63) an 11-bit biased
exponent (bits 52-62), and a 52-bit mantissa (bits 0-51).
52 51
o
.!~'...
~:'.
,"
MSB
5-18
LSB
Figure 5-4. Double-Precision Format
Given a sign bit
s,
an exponent e, and a mantissa f, the value V of the float-
ing-point number X= (s,e,f) is:
•
If s=O, e=2047, and f=O, the V
=
+00
•
If s=1, e=2047, and f=O, the V
=
-00
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