Swift CORDIC Algorithm gives constant answer - swift

Question

I tried to translate the MATLAB language on Cordic wikipedia webpage
However when I type those:
print(cordic(beta: Double.pi/9, n: 20))
print(cordic(beta: Double.pi/8, n: 20))
I get
[-0.17163433840184755, 0.98516072489744066]
[-0.17163433840184755, 0.98516072489744066]
It's always giving me a constant answer. Why? I'm sure that the "angle" and "Kvalues" arrays are properly calculated.
Here's the code:
import Foundation
var angles: [Double] = []
for i: Double in stride(from: 0, to: 27, by: 1) {
angles.append(atan(pow(2, -i)))
}
var Kvalues: [Double] = []
for i: Double in stride(from: 0, to: 23, by: 1) {
Kvalues.append(1/sqrt(abs(Double(1) + pow(2,-2 * i))))
if i > 0 {
Kvalues[Kvalues.count - 1] *= Kvalues[Kvalues.count - 2]
}
}
func min(_ a: Int, _ b: Int) -> Int {
return a > b ? b : a
}
func cordic(beta: Double, n: Int) -> [Double] {
var beta1 = beta
let Kn = Kvalues[min(n, Kvalues.count - 1)]
var v: [Double] = [1,0]
var poweroftwo: Double = 1
var angle = angles[0]
for j in 0 ..< n {
let sigma: Double = beta < 0 ? -1 : 1
let factor: Double = sigma * poweroftwo
v = [v[0] - v[1] * factor, v[1] + v[0] * factor]
beta1 -= sigma * angle
poweroftwo /= 2
angle = j + 2 > angles.count ? angle / 2 : angles[j + 2]
}
return [v[0] * Kn, v[1] * Kn]
}
print(cordic(beta: Double.pi/9, n: 20))
print(cordic(beta: Double.pi/8, n: 20))

Answer 1

You get the same result for different input because in
let sigma: Double = beta < 0 ? -1 : 1
beta should be beta1, which is the local variable that is
updated in the loop.
But even after fixing that the results are not correct, and that is
caused by two "off-by-one" index errors. The arrays in the algorithm
description are 1-based and Swift arrays are 0-based. So
let Kn = Kvalues[min(n, Kvalues.count - 1)]
// should be
let Kn = Kvalues[min(n-1, Kvalues.count - 1)]
and
angle = j + 2 > angles.count ? angle / 2 : angles[j + 2]
// should be
angle = j + 1 >= angles.count ? angle / 2 : angles[j + 1]
The angles and Kvalues arrays should be defined for i from 0 up to and including 27 resp. 23.
Finally, there is no need to define your own min function as there is one in the Swift standard library.
Putting it all together your code would be:
var angles: [Double] = []
for i: Double in stride(from: 0, through: 27, by: 1) {
angles.append(atan(pow(2, -i)))
}
var Kvalues: [Double] = []
for i: Double in stride(from: 0, through: 23, by: 1) {
Kvalues.append(1/sqrt(abs(Double(1) + pow(2,-2 * i))))
if i > 0 {
Kvalues[Kvalues.count - 1] *= Kvalues[Kvalues.count - 2]
}
}
func cordic(beta: Double, n: Int) -> [Double] {
var beta1 = beta
let Kn = Kvalues[min(n-1, Kvalues.count - 1)]
var v: [Double] = [1,0]
var poweroftwo: Double = 1
var angle = angles[0]
for j in 0 ..< n {
let sigma: Double = beta1 < 0 ? -1 : 1
let factor: Double = sigma * poweroftwo
v = [v[0] - v[1] * factor, v[1] + v[0] * factor]
beta1 -= sigma * angle
poweroftwo /= 2
angle = j + 1 >= angles.count ? angle / 2 : angles[j + 1]
}
return [v[0] * Kn, v[1] * Kn]
}
And that produces good approximations:
print(cordic(beta: Double.pi/9, n: 20)) // [0.93969210812600046, 0.34202155184390554]
print(cordic(beta: Double.pi/8, n: 20)) // [0.92388022188807306, 0.38268176805806309]
The exact values are
print(cos(Double.pi/9), sin(Double.pi/9)) // 0.939692620785908 0.342020143325669
print(cos(Double.pi/8), sin(Double.pi/8)) // 0.923879532511287 0.38268343236509