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CORDIC-based approximation of Cartesian-to-polar conversion
[theta,r] = cordiccart2pol(x,y)
[theta,r] = cordiccart2pol(x,y, niters)
[theta,r] = cordiccart2pol(x,y, niters,'ScaleOutput',b)
[theta,r] = cordiccart2pol(x,y,
'ScaleOutput',b)
[theta,r] = cordiccart2pol(x,y) using a CORDIC algorithm approximation, returns the polar coordinates, angle theta and radius r, of the Cartesian coordinates, x and y.
[theta,r] = cordiccart2pol(x,y, niters) performs niters iterations of the algorithm.
[theta,r] = cordiccart2pol(x,y, niters,'ScaleOutput',b) specifies both the number of iterations and, depending on the Boolean value of b, whether to scale the r output by the inverse CORDIC gain value.
[theta,r] = cordiccart2pol(x,y, 'ScaleOutput',b) scales the r output by the inverse CORDIC gain value, depending on the Boolean value of b.
x,y |
x,y are Cartesian coordinates. x and y must be the same size. If they are not the same size, at least one value must be a scalar value. Both x and y must have the same data type. |
niters |
niters is the number of iterations the CORDIC algorithm performs. This argument is optional. When specified, niters must be a positive, integer-valued scalar. If you do not specify niters, or if you specify a value that is too large, the algorithm uses a maximum value. For fixed-point operation, the maximum number of iterations is the word length of r or one less than the word length of theta, whichever is smaller. For floating-point operation, the maximum value is 52 for double or 23 for single. Increasing the number of iterations can produce more accurate results but also increases the expense of the computation and adds latency. |
Optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes ('').
theta |
theta contains the polar coordinates angle values, which are in the range [–pi, pi] radians. If x and y are floating-point, then theta has the same data type as x and y. Otherwise, theta is a fixed-point data type with the same word length as x and y and with a best-precision fraction length for the [-pi, pi] range. |
r |
r contains the polar coordinates radius magnitude values. r is real-valued and can be a scalar value or have the same dimensions as theta If the inputs x,y are fixed-point values, r is also fixed point (and is always signed, with binary point scaling). Both x,y input values must have the same data type. If the inputs are signed, then the word length of r is the input word length + 2. If the inputs are unsigned, then the word length of r is the input word length + 3. The fraction length of r is always the same as the fraction length of the x,y inputs. |
Convert fixed-point Cartesian coordinates to polar coordinates.
[thPos,r]=cordiccart2pol(sfi([0.75:-0.25:-1.0],16,15),sfi(0.5,16,15)) thPos = 0.5881 0.7854 1.1072 1.5708 2.0344 2.3562 2.5535 2.6780 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13 r = 0.9014 0.7071 0.5591 0.5000 0.5591 0.7071 0.9014 1.1180 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 18 FractionLength: 15 [thNeg,r]=... cordiccart2pol(sfi([0.75:-0.25:-1.0],16,15),sfi(-0.5,16,15)) thNeg = -0.5881 -0.7854 -1.1072 -1.5708 -2.0344 -2.3562 -2.5535 -2.6780 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 13 r = 0.9014 0.7071 0.5591 0.5000 0.5591 0.7071 0.9014 1.1180 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 18 FractionLength: 15
[1] Volder, JE. "The CORDIC Trigonometric Computing Technique." IRE Transactions on Electronic Computers. Vol. EC-8, September 1959, pp. 330–334.
[2] Andraka, R. "A survey of CORDIC algorithm for FPGA based computers." Proceedings of the 1998 ACM/SIGDA sixth international symposium on Field programmable gate arrays. Feb. 22–24, 1998, pp. 191–200.
[3] Walther, J.S. "A Unified Algorithm for Elementary Functions." Hewlett-Packard Company, Palo Alto. Spring Joint Computer Conference, 1971, pp. 379–386. (from the collection of the Computer History Museum). www.computer.org/csdl/proceedings/afips/1971/5077/00/50770379.pdf
[4] Schelin, Charles W. "Calculator Function Approximation." The American Mathematical Monthly. Vol. 90, No. 5, May 1983, pp. 317–325.