Infineon XC886CLM, User Manual

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XC886/888CLM
CORDIC Coprocessor
User’s Manual 11-6 V1.3, 2010-02
CORDIC Coprocessor, V 1.2.1
Usage Notes
• For solving the respective functions, user must initialize the CORDIC data (X, Y and
Z) with meaningful initial values within domain of convergence to ensure result
convergence. The ‘useful domain’ listed in
Table 11-2 covers the supported domain
of convergence for the CORDIC algorithm and excludes the not-meaningful range(s)
for the function. For details regarding the supported domain of convergence, refer to
Chapter 11.2.4.1 . For result data accuracy, refer to Chapter 11.2.6 .
• Function limitations must be considered, e.g., setting initial X = 0 for atan(Y / X) is not
meaningful. Violations of such function limitations may yield incoherent CORDIC
result data.
• All data inputs are processed and handled as twos complement. Only exception is
user-option for X result data (only) to be read as unsigned value.
• The only case where the result data is always positive and larger than the initial data
is X result data (only) in circular vectoring mode; therefore, the user may want to use
the MSB bit as data bit instead of sign bit. By setting X_USIGN = 1, X result data will
be processed as unsigned data.
• For circular and hyperbolic functions, and due to the corresponding fixed LUT, the
Z data is always handled as signed integer S19 (accessible as S15). The LUTs
contain scaled integer values (S19) of atan(2
-i
) for i = 0, 1, 2, ..., 15 and atanh(2
-i
) for
Hyperbolic
m = -1
e
i
= atanh(2
-i
)
X
final
= k[
X
cosh(
Z
) -
Y
sinh(
Z
)] /
MPS
Y
final
= k[
Y
cosh(
Z
) +
X
sinh(
Z
)] /
MPS
Z
final
= 0
where k
≈
0.828
X
final
= k sqrt(
X
2
-
Y
2
) / MPS
Y
final
= 0
Z
final
=
Z
+ atanh(
Y
/
X
)
where k
≈
0.828
For solving cosh(
Z
) and sinh(
Z
) and
e
Z
, set X = 1 / k, Y = 0.
Useful domain: |
Z
|
≤
1.11rad,
Y
= 0.
For solving sqrt(x
2
-y
2
), set
X
= x / k,
Y = y / k.
Useful domain: |y| < |x|,
X
> 0.
For solving atanh( Y / X ), set Z = 0.
Useful domain: |atanh(
Y
/
X
)|
≤
1.11rad, X > 0.
Relationships:
tanh(v) = sinh(v) / cosh(v)
e
v
= sinh(v) + cosh(v)
w
t
= e
t ln(w)
Relationships:
ln(w) = 2 atanh[(w-1) / (w+1)]
sqrt(w) = sqrt((w+0.25)
2
-(w-0.25)
2
)
acosh(w) = ln[w+sqrt(1-w
2
)]
asinh(w) = ln[w+sqrt(1+w
2
)]
Table 11-2 CORDIC Coprocessor Operating Modes and Corresponding Result
Data
(cont’d)
Function Rotation Mode Vectoring Mode
*