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User:Spekkio: Difference between revisions
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Line 33:
maclaurin series for different functions sin/cos/sqrt/pow etc... (see my recent post in [[Talk:Nth root]])
<lang lisp>(defun pie() 31415926535897932385/10000000000000000000)▼
▲(defun pie() 31415926535897932385/10000000000000000000)
(defun factorial (n)
Line 43 ⟶ 42:
(defun powint (a b)
(if (= b 0)
(
(* a (powint a (- b 1)))
(* (/ 1 a) (powint a (+ b 1)))
)
)
)
(defun binom (alpha n)
Line 56 ⟶ 60:
(+ (* (binom b n) (powint (- a 1) n)) (power a b (- n 1)))))
(defun powertest(a b n prev)
(let (( power10 (power a b (+ 10 n)) ))
(if
(= (*
(powertest a b (+ 10 n) power10)
)
)
)
(defun pow (a b
(if (< a 0)
(if (< b 1)
0
(powertest a b 1 1)
)
(if (< a 2)
(powertest a b 1 1)
0
)
)
)
(defun logS(x n) (if (= n 0) (* 2 x) (+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1))) (logS x (- n 1)) ) ))
Line 74 ⟶ 91:
(defun squaren(x n) (expon (* 1/2 (loge x n)) n))
(defun squarentest(a n prev)
(let (( square10 (squaren a (+ 10 n)) ))
(if
(= (*
(squarentest a (+ 10 n) square10)
)
)
)
(defun sqrtn (a) (squarentest a 1 0))
(defun powern(x a n) (expon (* a (loge x n)) n))
(defun powerntest(a b n prev)
(let ((n10 (+ 10 n)))
(let (( power10 (powern a b n10) ))
(if
(= (*
(powerntest a b
)
)
))
(defun pown (a b) (powerntest a b 1 0))
(defun sine(x n)
Line 121 ⟶ 143:
(defun asinetest(x n prev)
(let (( asine10 (asine x (+ 10 n)) ))
(if
(= (*
(asinetest x (+ 10 n) asine10)
)
)
)
Line 132 ⟶ 156:
(if (< x 1)
(if (> x -1)
(asinetest x 1 0)
(/ (pie) -2)
)
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