CORDIC co-processor (CORDIC) RM0440
474/2126 RM0440 Rev 4
Square root
This function calculates the square root of the input argument x.
The primary argument is the input value x. Only values of x in the range 0.027 to 2.34 are
supported. The value x must be scaled by a factor 2
-n
, such that x ∙ 2
-n
< (1 - 2
(-n-2)
).
The scaled value x ∙ 2
-n
is programmed in ARG1 and the factor n must be programmed in
the SCALE parameter.
Table 114 lists the valid scaling factors, n, and the corresponding ranges of x and ARG1.
The secondary argument is not used.
The primary result is the square root of x. RES1 must be multiplied by 2
n
to obtain the
correct value.
The secondary result is not used.
17.3.3 Fixed point representation
The CORDIC operates in fixed point signed integer format. Input and output values can be
either q1.31 or q1.15.
In q1.31 format, numbers are represented by one sign bit and 31 fractional bits (binary
decimal places). The numeric range is therefore -1 (0x80000000) to 1 - 2
-31
(0x7FFFFFFF).
In q1.15 format, the numeric range is 1 (0x8000) to 1 - 2
-15
(0x7FFF). This format has the
advantage that two input arguments can be packed into a single 32-bit write, and two results
can be fetched in one 32-bit read.
17.3.4 Scaling factor
Several of the functions listed in Section 17.3.2 specify a scaling factor, SCALE. This allows
the function input range to be extended to cover the full range of values supported by the
CORDIC, without saturating the input, output or internal registers. If the scaling factor is
Table 113. Square root parameters
Parameter Description Range
ARG1 x ∙ 2
-n
[0.027 0.875]
ARG2 Not applicable -
RES1 [0.04 1]
RES2 Not applicable -
SCALE n [0 2]
Table 114. Square root scaling factors and corresponding ranges
n x range ARG1 range
0 0.027 ≤ x< 0.75 0.027 ≤ ARG1 < 0.75
1 0.75 ≤ x< 1.75 0.375 ≤ ARG1 < 0.875
21.75 ≤ x≤ 2.341 0.4375 ≤ ARG1 ≤ 0.585
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