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Thiele's interpolation formula: Difference between revisions
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tan interpolation: 3.14826236377727
</pre>
=={{header|PicoLisp}}==
{{trans|C}}
<lang PicoLisp>(scl 18)
(load "@lib/math.l")
(setq
*X-Table (range 0.0 1.55 0.05)
*SinTable (mapcar sin *X-Table)
*CosTable (mapcar cos *X-Table)
*TanTable (mapcar tan *X-Table)
*TrigRows (length *X-Table) )
(let N2 (>> 1 (* *TrigRows (dec *TrigRows)))
(setq
*InvSinTable (need N2)
*InvCosTable (need N2)
*InvTanTable (need N2) ) )
(de rho (Tbl Inv I N)
(cond
((lt0 N) 0)
((=0 N) (get *X-Table I))
(T
(let Idx (+ I (>> 1 (* (- *TrigRows 1 N) (- *TrigRows N))))
(or
(get Inv Idx)
(set (nth Inv Idx) # only happens if value not computed yet
(+
(rho Tbl Inv (inc I) (- N 2))
(*/
(- (get Tbl I) (get Tbl (+ I N)))
1.0
(-
(rho Tbl Inv I (dec N))
(rho Tbl Inv (inc I) (dec N)) ) ) ) ) ) ) ) ) )
(de thiele (Tbl Inv X N)
(if (> N *TrigRows)
1.0
(+
(-
(rho Tbl Inv 1 (dec N))
(rho Tbl Inv 1 (- N 3)) )
(*/
(- X (get Tbl N))
1.0
(thiele Tbl Inv X (inc N)) ) ) ) )
(de iSin (X)
(thiele *SinTable *InvSinTable X 1) )
(de iCos (X)
(thiele *CosTable *InvCosTable X 1) )
(de iTan (X)
(thiele *TanTable *InvTanTable 1.0 1) )</lang>
Test:
<lang PicoLisp>(prinl (round (* 6 (iSin 0.5)) 15))
(prinl (round (* 3 (iCos 0.5)) 15))
(prinl (round (* 4 (iTan 1.0)) 15))</lang>
Output:
<pre>3.141592653589793
3.141592653589793
3.141592653589793</pre>
=={{header|PowerShell}}==
<lang PowerShell>Function Reciprocal-Difference( [Double[][]] $function )
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