XC886/888CLM
CORDIC Coprocessor
User’s Manual
11-13
V1.3, 2010-02
CORDIC Coprocessor, V 1.2.1
The Z data is a normalized representation of the actual angle. The internal scaling is
such that [-
π
,((2
19
-1)/2
19
)
π
] is equivalent to [-2
19
,(2
19
-1)]. The last 4 LSB bits are
truncated, as 16-bit data is transferred to the data bus when addressed. From user’s
point, the angles [-
π
,((2
15
-1)/2
15
)
π
] are therefore represented by the range [-2
15
,(2
15
-1)].
11.3.2
Linear Function Emulated Look-Up Table
The emulated LUT for linear function is actually a shift register. The emulated LUT has
1 integer bit (MSB) followed by 15-bit fractional part of the form 1Q16.
In linear function, where Z is a real number, the internal Z data is of the form signed
4Q20. The externally read data has the last 4 bits of the fractional part truncated,
resulting in a sign bit followed by 4-bit integer part, and finally 11-bit fractional part.
Table 11-5
Precomputed Scaled Values for atanh(2
-i
)
Iteration No.
Scaled atanh(2
-i
) in hex
Iteration No. Scaled atanh(2
-i
) in hex
i = 0
-
i = 8
28C
i = 1
16618
i = 9
146
i = 2
A681
i = 10
A3
i = 3
51EA
i = 11
51
i = 4
28CC
i = 12
29
i = 5
1461
i = 13
14
i = 6
A30
i = 14
A
i = 7
518
i = 15
5
*