CORDIC: Difference between revisions
m
→{{header|RPL}}
(Create task with RPL implementation) |
m (→{{header|RPL}}) |
||
Line 30:
*Implement the CORDIC algorithm, using only the 4 arithmetic operations and right shifts in the main loop if possible.
*Use your implementation to calculate the cosine of the following angles, expressed in radians: -9, 0, 1.5 and 6
=={{header|Julia}}==
<syntaxhighlight lang="julia">""" Modified from MATLAB example code at en.wikipedia.org/wiki/CORDIC """
using Printf
"""
Compute v = [cos(alpha), sin(alpha)] (alpha in radians).
Increasing the iteration value will increase the precision.
"""
function cordic(alpha, iteration = 24)
# Fix for the Wikipedia's MATLAB code bug in cosine when |θ| > 2π
newsgn = isodd(Int(floor(alpha / 2π))) ? 1 : -1
alpha < -π/2 && return newsgn * cordic(alpha + π, iteration)
alpha > π/2 && return newsgn * cordic(alpha - π, iteration)
# Initialization of tables of constants used by CORDIC
# need a table of arctangents of negative powers of two, in radians:
# angles = atan(2.^-(0:27));
angles = [
0.78539816339745, 0.46364760900081, 0.24497866312686, 0.12435499454676,
0.06241880999596, 0.03123983343027, 0.01562372862048, 0.00781234106010,
0.00390623013197, 0.00195312251648, 0.00097656218956, 0.00048828121119,
0.00024414062015, 0.00012207031189, 0.00006103515617, 0.00003051757812,
0.00001525878906, 0.00000762939453, 0.00000381469727, 0.00000190734863,
0.00000095367432, 0.00000047683716, 0.00000023841858, 0.00000011920929,
0.00000005960464, 0.00000002980232, 0.00000001490116, 0.00000000745058, ]
# and a table of products of reciprocal lengths of vectors [1, 2^-2j]:
# Kvalues = cumprod(1./sqrt(1 + 1j*2.^(-(0:23))))
Kvalues = vec([
0.70710678118655, 0.63245553203368, 0.61357199107790, 0.60883391251775,
0.60764825625617, 0.60735177014130, 0.60727764409353, 0.60725911229889,
0.60725447933256, 0.60725332108988, 0.60725303152913, 0.60725295913894,
0.60725294104140, 0.60725293651701, 0.60725293538591, 0.60725293510314,
0.60725293503245, 0.60725293501477, 0.60725293501035, 0.60725293500925,
0.60725293500897, 0.60725293500890, 0.60725293500889, 0.60725293500888, ])
Kn = Kvalues[min(iteration, length(Kvalues))]
# Initialize loop variables:
v = [1, 0] # start with 2-vector cosine and sine of zero
poweroftwo = 1
angle = angles[1]
# Iterations
for j = 0:iteration-1
if alpha < 0
sigma = -1
else
sigma = 1
end
factor = sigma * poweroftwo
# Note the matrix multiplication can be done using scaling by powers of two and addition subtraction
R = [1 -factor
factor 1]
v = R * v # 2-by-2 matrix multiply
alpha -= sigma * angle # update the remaining angle
poweroftwo /= 2
# update the angle from table, or eventually by just dividing by two
if j + 2 > length(angles)
angle /= 2
else
angle = angles[j + 2]
end
end
# Adjust length of output vector to be [cos(alpha), sin(alpha)]:
v .*= Kn
return v
end
function test_cordic()
println(" x sin(x) diff. sine cos(x) diff. cosine ")
for θ in -90:15:90
cosθ, sinθ = cordic(deg2rad(θ))
@printf("%+05.1f° %+.8f (%+.8f) %+.8f (%+.8f)\n",
θ, sinθ, sinθ - sind(θ), cosθ, cosθ - cosd(θ))
end
println("\nx(radians) sin(x) diff. sine cos(x) diff. cosine ")
for θr in [-9, 0, 1.5, 6]
cosθ, sinθ = cordic(θr)
@printf("%+3.1f %+.8f (%+.8f) %+.8f (%+.8f)\n",
θr, sinθ, sinθ - sin(θr), cosθ, cosθ - cos(θr))
end
end
test_cordic()
</syntaxhigh;ight>{{out}}
<pre>
x sin(x) diff. sine cos(x) diff. cosine
-90.0° -1.00000000 (+0.00000000) -0.00000007 (-0.00000007)
-75.0° -0.96592585 (-0.00000003) +0.25881895 (-0.00000009)
-60.0° -0.86602545 (-0.00000005) +0.49999992 (-0.00000008)
-45.0° -0.70710684 (-0.00000006) +0.70710672 (-0.00000006)
-30.0° -0.49999992 (+0.00000008) +0.86602545 (+0.00000005)
-15.0° -0.25881895 (+0.00000009) +0.96592585 (+0.00000003)
+00.0° -0.00000007 (-0.00000007) +1.00000000 (-0.00000000)
+15.0° +0.25881895 (-0.00000009) +0.96592585 (+0.00000003)
+30.0° +0.49999992 (-0.00000008) +0.86602545 (+0.00000005)
+45.0° +0.70710684 (+0.00000006) +0.70710672 (-0.00000006)
+60.0° +0.86602545 (+0.00000005) +0.49999992 (-0.00000008)
+75.0° +0.96592585 (+0.00000003) +0.25881895 (-0.00000009)
+90.0° +1.00000000 (-0.00000000) -0.00000007 (-0.00000007)
x(radians) sin(x) diff. sine cos(x) diff. cosine
-9.0 -0.41211842 (+0.00000006) -0.91113029 (-0.00000003)
+0.0 -0.00000007 (-0.00000007) +1.00000000 (-0.00000000)
+1.5 +0.99749499 (+0.00000000) +0.07073719 (-0.00000002)
+6.0 -0.27941552 (-0.00000002) +0.96017028 (-0.00000001)
</pre>
=={{header|RPL}}==
| |||