CORDIC: Difference between revisions
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*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
<br>
=={{header|C}}==
{{trans|Wren}}
<syntaxhighlight lang="c">#include <stdio.h>
#include <math.h>
/* The following are pre-computed to avoid using atan and sqrt functions. */
const double 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
};
const double kvalues[] = {
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
};
double radians(double degrees) { return degrees * M_PI / 180.0; }
void Cordic(double alpha, int n, double *c_cos, double *c_sin) {
int i, ix, sigma;
double kn, x, y, atn, t, theta = 0.0, pow2 = 1.0;
int newsgn = (int)floor(alpha / (2.0 * M_PI)) % 2 == 1 ? 1 : -1;
if (alpha < -M_PI/2.0 || alpha > M_PI/2.0) {
if (alpha < 0) {
Cordic(alpha + M_PI, n, &x, &y);
} else {
Cordic(alpha - M_PI, n, &x, &y);
}
*c_cos = x * newsgn;
*c_sin = y * newsgn;
return;
}
ix = n - 1;
if (ix > 23) ix = 23;
kn = kvalues[ix];
x = 1;
y = 0;
for (i = 0; i < n; ++i) {
atn = angles[i];
sigma = (theta < alpha) ? 1 : -1;
theta += sigma * atn;
t = x;
x -= sigma * y * pow2;
y += sigma * t * pow2;
pow2 /= 2.0;
}
*c_cos = x * kn;
*c_sin = y * kn;
}
int main() {
int i, th;
double thr, c_cos, c_sin;
double angles[] = {-9.0, 0.0, 1.5, 6.0 };
char *f;
printf(" x sin(x) diff. sine cos(x) diff. cosine\n");
f = "%+03d.0° %+.8f (%+.8f) %+.8f (%+.8f)\n";
for (th = -90; th <= +90; th += 15) {
thr = radians(th);
Cordic(thr, 24, &c_cos, &c_sin);
printf(f, th, c_sin, c_sin - sin(thr), c_cos, c_cos - cos(thr));
}
printf("\nx(rads) sin(x) diff. sine cos(x) diff. cosine\n");
f = "%+4.1f %+.8f (%+.8f) %+.8f (%+.8f)\n";
for (i = 0; i < 4; ++i) {
thr = angles[i];
Cordic(thr, 24, &c_cos, &c_sin);
printf(f, thr, c_sin, c_sin - sin(thr), c_cos, c_cos - cos(thr));
}
return 0;
}</syntaxhighlight>
{{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(rads) 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|FreeBASIC}}==
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