Anonymous user
Thiele's interpolation formula: Difference between revisions
→{{header|OCaml}}
Line 802:
3.14159265358979
3.14159265358980
</pre>
=={{header|Nim}}==
{{trans|Java}}
<lang Nim>import strformat
import math
const N = 32
const N2 = N * (N - 1) div 2
const STEP = 0.05
var xval = newSeq[float](N)
var tsin = newSeq[float](N)
var tcos = newSeq[float](N)
var ttan = newSeq[float](N)
var rsin = newSeq[float](N2)
var rcos = newSeq[float](N2)
var rtan = newSeq[float](N2)
proc rho(x, y: openArray[float], r: var openArray[float], i, n: int): float =
if n < 0:
return 0
if n == 0:
return y[i]
let idx = (N - 1 - n) * (N - n) div 2 + i
if r[idx] != r[idx]:
r[idx] = (x[i] - x[i + n]) /
(rho(x, y, r, i, n - 1) - rho(x, y, r, i + 1, n - 1)) +
rho(x, y, r, i + 1, n - 2)
return r[idx]
proc thiele(x, y: openArray[float], r: var openArray[float], xin: float, n: int): float =
if n > N - 1:
return 1
return rho(x, y, r, 0, n) - rho(x, y, r, 0, n - 2) +
(xin - x[n]) / thiele(x, y, r, xin, n + 1)
for i in 0..<N:
xval[i] = float(i) * STEP
tsin[i] = sin(xval[i])
tcos[i] = cos(xval[i])
ttan[i] = tsin[i] / tcos[i]
for i in 0..<N2:
rsin[i] = NaN
rcos[i] = NaN
rtan[i] = NaN
echo fmt"{6 * thiele(tsin, xval, rsin, 0.5, 0):16.14}"
echo fmt"{3 * thiele(tcos, xval, rcos, 0.5, 0):16.14}"
echo fmt"{4 * thiele(ttan, xval, rtan, 1.0, 0):16.14}"</lang>
{{out}}
<pre>
3.1415926535898
3.1415926535898
3.1415926535898
</pre>
| |||