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參數(shù)資料
| 型號： | fp_add_sub |
| 廠商： | Altera Corporation |
| 英文描述： | Floating-Point Adder/Subtractor(浮點型加法器/減法器) |
| 中文描述： | 浮點加法器/減法（浮點型加法器/減法器） |
| 文件頁數(shù)： | 4/8頁 |
| 文件大小： | 132K |
| 代理商： | FP_ADD_SUB |
4
Altera Corporation
FS 2: fp_add_sub Floating-Point Adder/Subtractor
Floating-Point
Addition &
Subtraction
To add or subtract two floating-point numbers, the mantissas must be
aligned. Then, the exponents must be compared to determine which
number is larger. If the difference between the exponents is slight, the
number with the smaller exponent may be larger if mantissas MA and MB
are not normalized, which reduces the function’s precision. To avoid this
problem, designers should ensure that all inputs are normalized by
making sure that the MSB of each mantissa is 1.
The relative values of the exponents are checked by subtracting one
exponent from the other. The mantissa with the larger exponent is
retained, and the mantissa with the smaller exponent is right-shifted until
the radix point is properly aligned (i.e., until the exponents are equal). If
the exponents differ by more than the number of bits in the mantissa, the
smaller number becomes insignificant. The shifting is performed by the
LPM function
lpm_clshift
.
After the mantissas pass through the shifters, an unsigned integer
adder/subtractor performs an operation that is determined by the sign of
the inputs (
sa
and
sb
) and the
add_sub
then passed through a programmable inverter, which is controlled by the
sign decision logic. This process ensures that the mantissa has the proper
sign. After the addition or subtraction has taken place, the post-
normalizer normalizes the result, if necessary, by adjusting the mantissa
and exponent of the result so that the MSB of the mantissa is 1.
port. The result of the adder is
Examples of floating-point addition and subtraction for 8-bit mantissa,
7-bit exponent floating-point numbers are provided below.
Example 1: Positive Number Plus Positive Number
0.3046875
+0.01001110
+0.01001110
+0.01111010
+0.11110100
+0.953125
×
2
45
×
×
×
×
2
44
+ +0.34375
+ +0.01011000
+ +0.00101100
×
2
44
=
=
=
=
=
2
45
2
45
2
45
2
44
×
×
2
44
2
45
×
= +1.677
×
10
13
Example 2: Negative Number Plus Positive Number
–0.82421875
–0.11010011
–0.11010011
–0.10110011
–0.69921875
×
×
×
×
×
2
76
2
76
2
76
2
76
2
76
+ +0.25390625
+ +0.01000001
+ +0.00100000
×
×
×
2
75
2
75
2
76
=
=
=
=
= –5.2831
×
10
22
In example 2, the mantissa shift causes a loss of precision.
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