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Revision as of 14:03, 19 December 2011

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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() 31415926535897932384626433832795028841971693993751058209749/10000000000000000000000000000000000000000000000000000000000)
<lang lisp>(defun pie() 31415926535897932385/10000000000000000000)
 
(defun factorial (n)
Line 51:
 
(defun binom (alpha n)
(if (= n 0)
1
(if (= n 1)
alpha
(* (binom alpha (- n 1)) (/ (+ (- alpha n) 1) n))))
)
 
(defun power (a b n)
(if (= n 0)
1
(+
(+ (* (binom b n) (powint (- a 1) n)) (power a b (- n 1)))))
(* (binom b n) (powint (- a 1) n))
(power a b (- n 1)))))
 
(defun powertestpowerw(a b n prev)
(let ((cosn power10(* (power abinom b n) (+powint 10(- n)a 1) n))
))
(if
(handler-case
(= (* power10 1.0) (* prev 1.0))
(progn
power10
(float cosn)
(powertest a b (+ 10 n) power10)
(if (= (+ prev cosn) prev ) prev
(powerw a b (1+ n) (+ prev cosn)))
)
(arithmetic-error (x) prev ))
)
)
Line 74 ⟶ 82:
(if (< b 1)
0
(powertestpowerw a b 10 10)
)
(if (< a 2)
(powertestpowerw a b 10 10)
0
)
Line 83 ⟶ 91:
)
 
(defun logw(x n prev)
(defun logS(x n) (if (= n 0) (* 2 x) (+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1))) (logS x (- n 1)) ) ))
(let ((cosn (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1)))
 
))
(defun loge(x n) (logS (/ (- x 1) (+ 1 x)) n))
(handler-case
 
(progn
(defun expon(x n) (if (= n 0) 1 (+ (/ (powint x n) (factorial n)) (expon x (- n 1)))))
(float cosn)
 
(defunlogw squaren(x (1+ n) (expon+ (*prev 1/2 (loge x n)) ncosn))
)
 
(defunarithmetic-error squarentest(a nx) prev ))
(let (( square10 (squaren a (+ 10 n)) ))
(if
(= (* square10 1.0) (* prev 1.0))
square10
(squarentest a (+ 10 n) square10)
)
)
)
 
(defun sqrtn logS(ax n) (squarentestif a(= 1n 0) (* 2 x)
(+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1)))
(logS x (- n 1)) ) ))
 
(defun powernloge(x a n) (exponlogw (* a/ (loge- x n1) (+ 1 x)) n0 0) )
 
(defun powerntestlogetest(a b n prev)
(let ((n10 (+ 10 n)))
(let (( power10log10 (powernloge a b n10) ))
(if
(= (*float power10 1.0log10) (*float prev 1.0))
power10log10
(powerntestlogetest a b n10 power10log10)
)
)
))
 
(defun pownln (a b) (powerntest a b 1 0)x)
(if (> x 0)
(loge x)
nil
))
 
(defun sineexpw(x n prev)
(let ((cosn (if/ (=powint x n) 0(factorial n))
))
x
(handler-case
(+ (* (/ (powint -1 n) (factorial (+ (* 2 n) 1)) ) (powint x (+ (* 2 n) 1))) (sine x (- n 1)))))
(progn
 
(float cosn)
(defun sinetest(x n)
(expw x (1+ n) (+ prev cosn))
(if
)
(= (* (sine x (+ 10 n)) 1.0) (* (sine x n) 1.0))
(arithmetic-error (x) prev ))
(sine x (+ 10 n))
)
(sinetest x (+ 10 n))
)
)
 
(defun mysin expon(x) (sinetestexpw x 10 0))
 
(defun cosisquareroot(x n) (ifexpon (= n 0)* 1 (+ (* (/ (powint -1 n) (factorial (* 2 n)) ) (powintloge x (* 2 n))) (cosi x (- n 1)))))
 
(defun tangpowern(x na) (/expon (sine* x n)a (cosiloge x n))))
 
(defun asinee (x) n(expon x))
(if (= n 0)
x
(+ (/ (* (factorial (* 2 n)) (powint x (+ (* 2 n) 1))) (* (powint 4 n) (powint (factorial n) 2) (+ (* 2 n) 1))) (asine x (- n 1)))))
 
(defun pown (a b) (powern a b))
 
(defun asinetestsinew(x n prev)
(let ((cosn asine10(* (asine/ x(powint -1 n) (factorial (+ 10(* 2 n) 1)) ) (powint x (+ (* 2 n) 1)))
))
(if
(handler-case
(= (* asine10 1.0) (* prev 1.0))
(progn
asine10
(float cosn)
(asinetest x (+ 10 n) asine10)
(sinew x (1+ n) (+ prev cosn))
)
(arithmetic-error (x) (+ prev cosn) ))
)
)
 
(defun sine(x) (sinew x 0 0))
 
(defun cosinew(x n prev)
(let ((cosn (* (/ (powint -1 n) (factorial (* 2 n))) (powint x (* 2 n)))))
(handler-case
(progn
(float cosn)
(cosinew x (1+ n) (+ prev cosn))
)
(arithmetic-error (x) (+ prev cosn) ))
)
)
 
(defun cosine(x) (cosinew x 0 0))
 
(defun tang(x) (/ (sine x) (cosine x)))
 
(defun asinew(x n prev)
(let ((cosn (/ (* (factorial (* 2 n)) (powint x (+ (* 2 n) 1))) (* (powint 4 n) (powint (factorial n) 2) (+ (* 2 n) 1)))
))
(handler-case
(progn
(float cosn)
(asinew x (1+ n) (+ prev cosn))
)
(arithmetic-error (x) prev ))
)
)
 
(defun myasinasine (x)
(if (< x 1)
(if (> x -1)
(asinetestasinew x 10 0)
(/ (pie) -2)
)
Line 178 ⟶ 214:
test:
test:
[14]> (*float (myasinasine 9/100) 1.0)
0.09012195
[14]> (asin 9/100)
Line 191 ⟶ 227:
 
Test 2:
[4]> (*float (myasinasine (mysinsine 1)) 1.0)
1.0
[4]> (asin (sin 1))
Line 197 ⟶ 233:
 
Test 3:
[15]> (*float (mysinsine (* 45 (/ (* 2 (pie)) 360) )) 1.0)
0.70710677
[15]> (*float (sqrtnsquareroot 1/2) 1.0)
0.70710677
[15]> (= (*float (sqrtnsquareroot 1/2) 1.0) (* (mysinsine (* 45 (/ (* 2 (pie)) 360) )) 1.0))
T
Anonymous user
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