Infineon XC886CLM, User Manual

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XC886/888CLM
CORDIC Coprocessor
User’s Manual 11-5 V1.3, 2010-02
CORDIC Coprocessor, V 1.2.1
11.2.4 CORDIC Coprocessor Operating Modes
Table 11-2 gives an overview of the CORDIC Coprocessor operating modes. In this
table, X , Y and Z represent the initial data, while X
final
, Y
final
and Z
final
represent the final
result data when all processing is complete and BSY is no longer active.
The CORDIC equations are:
x
i+1
= x
i
- m · d
i
· y
i
· 2
-i
(11.4)
y
i+1
= y
i
+ d
i
· x
i
· 2
-i
(11.5)
z
i+1
=
z
i
-
d
i
·
e
i
(11.6)
Table 11-2 CORDIC Coprocessor Operating Modes and Corresponding Result
Data
Function Rotation Mode Vectoring Mode
d
i
= sign (
z
i
),
z
i
→
0
d
i
= -sign (
y
i
),
y
i
→
0
Circular
m
= 1
e
i
= atan(2
-i
)
X
final
= K[
X
cos(
Z
) -
Y
sin(
Z
)] / MPS
Y
final
= K[
Y
cos(
Z
) +
X
sin(
Z
)] / MPS
Z
final
= 0
where K
≈
1.64676
X
final
= K sqrt(
X
2
+
Y
2
) / MPS
Y
final
= 0
Z
final
= Z + atan( Y / X )
where K
≈
1.64676
For solving cos( Z ) and sin( Z ), set X
= 1 / K,
Y
= 0.
Useful domain: Full range of X , Y
and
Z
supported due to pre-
processing logic.
For solving magnitude of vector
(sqrt(x
2
+y
2
)), set
X
= x / K,
Y
= y / K.
Useful domain: Full range of X and
Y
supported due to pre- and post-
processing logic.
For solving atan( Y / X ), set Z = 0.
Useful domain: Full range of
X
and
Y
, except
X
= 0.
Relationships:
tan(v) = sin(v) / cos(v) Relationships:
acos(w) = atan[sqrt(1-w
2
) / w]
asin(w) = atan[w / sqrt(1-w
2
)]
Linear
m = 0
e
i
= 2
-i
X
final
=
X
/ MPS
Y
final
= [ Y + X Z ] / MPS
Z
final
= 0
X
final
=
X
/ MPS
Y
final
= 0
Z
final
=
Z
+
Y
/
X
For solving X · Z , set Y = 0.
Useful domain: |
Z
|
≤
2.
For solving ratio Y / X , set Z = 0.
Useful domain: |
Y
/
X
|
≤
2,
X
> 0.
*