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Thiele's interpolation formula: Difference between revisions
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pi estimate using tan interpolation: 3.141592653589794
</pre>
=={{header|zkl}}==
{{trans|C}}
Please see the C example for the comments I've removed (this is an as pure-as-I-make-it translation).
<lang zkl>const N=32, N2=(N * (N - 1) / 2), STEP=0.05;
fcn rho(xs,ys,rs, i,n){
if (n < 0) return(0.0);
if (not n) return(ys[i]);
idx := (N - 1 - n) * (N - n) / 2 + i;
if (Void==rs[idx])
rs[idx] = (xs[i] - xs[i + n])
/ (rho(xs, ys, rs, i, n - 1) - rho(xs, ys, rs, i + 1, n - 1))
+ rho(xs, ys, rs, i + 1, n - 2);
return(rs[idx]);
}
fcn thiele(xs,ys,rs, xin, n){
if (n > N - 1) return(1.0);
rho(xs, ys, rs, 0, n) - rho(xs, ys, rs, 0, n - 2)
+ (xin - xs[n]) / thiele(xs, ys, rs, xin, n + 1);
}
///////////
reg t_sin=L(), t_cos=L(), t_tan=L(),
r_sin=L(), r_cos=L(), r_tan=L(), xval=L();
i_sin := thiele.fpM("11101",t_sin, xval, r_sin, 0);
i_cos := thiele.fpM("11101",t_cos, xval, r_cos, 0);
i_tan := thiele.fpM("11101",t_tan, xval, r_tan, 0);
foreach i in (N){
xval.append(x:=STEP*i);
t_sin.append(x.sin());
t_cos.append(x.cos());
t_tan.append(t_sin[i] / t_cos[i]);
}
foreach i in (N2){ r_sin+Void; r_cos+Void; r_tan+Void; }
print("%16.14f\n".fmt( 6.0 * i_sin(0.5)));
print("%16.14f\n".fmt( 3.0 * i_cos(0.5)));
print("%16.14f\n".fmt( 4.0 * i_tan(1.0)));</lang>
{{out}}
<pre>
3.14159265358979
3.14159265358979
3.14159265358979
</pre>
{{omit from|GUISS}}
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