User:Spekkio

My Favorite Languages
Language	Proficiency
C	Active
C++	Beginner
Java	Active
JavaScript	Active
SQL	Active
Mathematica	Active
MATLAB	Active
UNIX Shell	Beginner
Lisp	Beginner
Erlang	Beginner
POV-Ray	Beginner
Pascal	Rusty
x86 Assembly	Rusty

Hello! I'm a Electronic Engineer, working with electronics developement.

I love computer programming, and my hobby is to program small simple computer programs.

I usually get stuck on an idea that I think would be fun to try and solve.

I love learning new programming languages.

Found this page recently, and it is perfect for me. :D

Currently I'm working on Huffman coding in C, and implementing a multi precision library to calculate

maclaurin series for different functions sin/cos/sqrt/pow etc... (see my recent post in Talk:Nth root)

<lang lisp> (defun factorial (n)

 (if (= n 0)
     1
   (* n (factorial (- n 1)))))

(defun powint (a b)

 (if (= b 0)
     1
   (* a (powint a (- b 1)))))

(defun binom (alpha n)

 (if (= n 1)
     alpha
   (* (binom alpha (- n 1)) (/ (+ (- alpha n) 1) n))))

(defun pow (a b n)

 (if (= n 0)
     1
   (+ (* (binom b n) (powint (- a 1) n)) (pow a b (- n 1)))))

(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 n) (logS (/ (- x 1) (+ 1 x)) n))

(defun expon(x n) (if (= n 0) 1 (+ (/ (powint x n) (factorial n)) (expon x (- n 1)))))

(defun sqrtn(x n) (expon (* 1/2 (loge x n)) n))

(defun pown(x a n) (expon (* a (loge x n)) n))

(defun sine(x n)

 (if (= n 0)
     x
   (+ (* (/ (powint -1 n) (factorial (+ (* 2 n) 1)) ) (powint x (+ (* 2 n) 1))) (sine x (- n 1)))))

(defun sinetest(x n)

 (if
     (= (* (sine x (1+ n)) 1.0) (* (sine x n) 1.0))
     (sine x n)
   (sinetest x (1+ n))
     )

)

(defun mysin (x) (sinetest x 1))

(defun cosi(x n) (if (= n 0) 1 (+ (* (/ (powint -1 n) (factorial (* 2 n)) ) (powint x (* 2 n))) (cosi x (- n 1)))))

(defun tang(x n) (/ (sine x n) (cosi x n)))

(defun asine (x n) (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 asinetest(x n)

 (if
     (= (* (asine x (1+ n)) 1.0) (* (asine x n) 1.0))
     (asine x n)
   (asinetest x (1+ n))
     )

)

(defun myasin (x) (asinetest x 1)) (defun fibcalc (n p)

 (let ((sqrtFive (sqrtn 5 p)))
 (/ (- (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))))))

</lang>

test:

[3]> (asin 1/10)
0.100167416
[3]> (* (myasin 1/10) 1.0)
0.10016742

Compare with Mathematica:

In: N[ArcSin[1/10], 10]
Out: 0.1001674212

(myasin) seems to be more accurate, though trying to compute (myasin 1) is very slow.

Test 2:

[4]> (* (myasin (mysin 1)) 1.0)
0.9999999
[4]> (asin (sin 1))
1.0