User:Spekkio

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(defun pie() 31415926535897932384626433832795028841971693993751058209749/10000000000000000000000000000000000000000000000000000000000)
 
(defun factorial-rec (n)
(if (= n 0)
1
(* n (factorial-rec (- n 1)))))
 
(defun factorial (n &key (result 1))
(if (< n 2)
result
(factorial (- n 1) :result (* result n))))
 
(defun powint (a b &key (result 1))
(if (= b 0)
result
(if (> b 0)
(powint a (- b 1) :result (* result a))
(powint a (+ b 1) :result (* result (/ 1 a)))
)
)
)
 
(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)))))
 
(defun powerw(a b n prev)
(let ((cosn (* (binom b n) (powint (- a 1) n))
))
(handler-case
(progn
(float cosn)
(if (= (+ prev cosn) prev ) prev
(powerw a b (1+ n) (+ prev cosn)))
)
(arithmetic-error (x) prev ))
)
)
 
(defun pow (a b)
(if (< a 0)
(if (< b 1)
0
(powerw a b 0 0)
)
(if (< a 2)
(powerw a b 0 0)
0
)
)
)
 
(defun logw(x n prev)
(let ((cosn (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1)))
))
(handler-case
(progn
(float cosn)
(logw x (1+ n) (+ prev cosn))
)
(arithmetic-error (x) prev ))
)
)
 
(defun logS(x n) (if (= n 0) (* 2 x)
(+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1)))
(logS x (- n 1)) ) ))
 
(defun loge(x) (logw (/ (- x 1) (+ 1 x)) 0 0) )
 
(defun logetest(a n prev)
(let ((n10 (+ 10 n)))
(let (( log10 (loge a n10) ))
(if
(= (float log10) (float prev))
log10
(logetest a n10 log10)
)
)
))
 
(defun ln (x)
(if (> x 0)
(loge x)
nil
))
 
(defun expw(x n prev)
(let ((cosn (/ (powint x n) (factorial n))
))
(handler-case
(progn
(float cosn)
(expw x (1+ n) (+ prev cosn))
)
(arithmetic-error (x) prev ))
)
)
 
(defun expon(x) (expw x 0 0))
 
(defun squareroot(x) (expon (* 1/2 (loge x))))
 
(defun powern(x a) (expon (* a (loge x))))
 
(defun e (x) (expon x))
 
(defun pown (a b) (powern a b))
 
(defun sinew(x &key (n 0) (prev 0))
(let ((cosn (* (/ (powint -1 n) (factorial (+ (* 2 n) 1)) ) (powint x (+ (* 2 n) 1)))
))
(handler-case
(progn
(float cosn)
(sinew x :n (1+ n) :prev (+ prev cosn))
)
(arithmetic-error (x) (+ prev cosn) ))
)
)
 
(defun sine(x) (if (= x 0) 0 (sinew x)))
 
(defun cosinew(x &key (n 0) (prev 0))
(let ((cosn (* (/ (powint -1 n) (factorial (* 2 n))) (powint x (* 2 n)))))
(handler-case
(progn
(float cosn)
(cosinew x :n (1+ n) :prev (+ prev cosn))
)
(arithmetic-error (x) (+ prev cosn) ))
)
)
 
(defun cosine(x) (cosinew x))
 
(defun tang(x) (/ (sine x) (cosine x)))
 
(defun asinew(x &key (n 0) (prev 0))
(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 :n (1+ n) :prev (+ prev cosn))
)
(arithmetic-error (x) prev ))
)
)
 
(defun asinew2(x)
(let ((n 0))
(let ((next 0))
 
(loop while (handler-case (float next) (arithmetic-error (err) NIL)) do
(progn
(setq next (+ (/ (* (factorial (* 2 n)) (powint x (+ (* 2 n) 1))) (* (powint 4 n) (powint (factorial n) 2) (+ (* 2 n) 1))) next))
(setq n (+ n 1))
)
)
)))
 
 
(defun asine (x)
(if (< x 1)
(if (> x -1)
(asinew x)
(/ (pie) -2)
)
(/ (pie) 2)
)
)
 
(defun fibcalc (n)
(let ((sqrtFive (squareroot 5)))
(/ (- (powint (* 1/2 (+ 1 sqrtFive)) n) (powint (* 1/2 (- 1 sqrtFive)) n)) sqrtFive)))
 
(defun fibrec (n)
(if (= n 0)
0
(if (= n 1)
1
(+ (fibrec (- n 1)) (fibrec (- n 2))))))
 
 
(defun test() (let ((n 0)) (loop while (< n 10) collect n do (if (= (float (sine n)) (sin n)) () (progn (write n) (write (terpri)) (write (sin n)) (write (terpri)) (write (float (sine n))) (write (terpri)) )) (setq n (+ n 1/10)))))

test:

[14]> (float (asine 9/100))
0.09012195
[14]> (asin 9/100)
0.090121955


Compare with Mathematica:

In[14]:= N[ArcSin[9/100], 8]
Out[14]= 0.090121945

(myasin) seems to be more accurate, though trying to compute (myasin 9999999/10000000) is very slow.

Test 2:

[4]> (float (asine (sine 1)))
1.0
[4]> (asin (sin 1))
1.0

Test 3:

[15]> (float (sine (* 45 (/ (* 2 (pie)) 360) )))
0.70710677
[15]> (float (squareroot 1/2))
0.70710677
[15]> (= (float (squareroot 1/2)) (float (sine (* 45 (/ (* 2 (pie)) 360) ))))
T
[15]> (= (sine (* 45 (/ (* 2 (pie)) 360) )) (sine (/ (pie) 4)))
T
[15]> (= (cosine (/ (pie) 4)) (sine (/ (pie) 4)))
NIL
[15]> (= (float (cosine (/ (pie) 4))) (float (sine (/ (pie) 4))))
T