User:Spekkio: Difference between revisions
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maclaurin series for different functions sin/cos/sqrt/pow etc... (see my recent post in [[Talk:Nth root]]) |
maclaurin series for different functions sin/cos/sqrt/pow etc... (see my recent post in [[Talk:Nth root]]) |
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<lang lisp>(defun pie() 31415926535897932384626433832795028841971693993751058209749/10000000000000000000000000000000000000000000000000000000000) |
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<lang lisp>(defun pie() 31415926535897932385/10000000000000000000) |
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(defun factorial (n) |
(defun factorial (n) |
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(defun binom (alpha n) |
(defun binom (alpha n) |
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(if (= n 0) |
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1 |
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(if (= n 1) |
(if (= n 1) |
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alpha |
alpha |
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(* (binom alpha (- n 1)) (/ (+ (- alpha n) 1) n)))) |
(* (binom alpha (- n 1)) (/ (+ (- alpha n) 1) n)))) |
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) |
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(defun power (a b n) |
(defun power (a b n) |
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(if (= n 0) |
(if (= n 0) |
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1 |
1 |
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(+ |
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(+ (* (binom b n) (powint (- a 1) n)) (power a b (- n 1))))) |
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(* (binom b n) (powint (- a 1) n)) |
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(power a b (- n 1))))) |
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(defun |
(defun powerw(a b n prev) |
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(let (( |
(let ((cosn (* (binom b n) (powint (- a 1) n)) |
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)) |
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(if |
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(handler-case |
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(= (* power10 1.0) (* prev 1.0)) |
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(progn |
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power10 |
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(float cosn) |
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(powertest a b (+ 10 n) power10) |
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) |
(if (= (+ prev cosn) prev ) prev |
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(powerw a b (1+ n) (+ prev cosn))) |
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) |
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(arithmetic-error (x) prev )) |
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) |
) |
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) |
) |
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(if (< b 1) |
(if (< b 1) |
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0 |
0 |
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( |
(powerw a b 0 0) |
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) |
) |
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(if (< a 2) |
(if (< a 2) |
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( |
(powerw a b 0 0) |
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0 |
0 |
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) |
) |
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) |
) |
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(defun logw(x n prev) |
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(defun logS(x n) (if (= n 0) (* 2 x) (+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1))) (logS x (- n 1)) ) )) |
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(let ((cosn (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1))) |
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)) |
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(defun loge(x n) (logS (/ (- x 1) (+ 1 x)) n)) |
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(handler-case |
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(progn |
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(defun expon(x n) (if (= n 0) 1 (+ (/ (powint x n) (factorial n)) (expon x (- n 1))))) |
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(float cosn) |
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( |
(logw x (1+ n) (+ prev cosn)) |
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) |
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( |
(arithmetic-error (x) prev )) |
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(let (( square10 (squaren a (+ 10 n)) )) |
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(if |
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(= (* square10 1.0) (* prev 1.0)) |
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square10 |
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(squarentest a (+ 10 n) square10) |
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) |
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) |
) |
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) |
) |
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(defun |
(defun logS(x n) (if (= n 0) (* 2 x) |
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(+ (* 2 (/ (powint x (+ (* 2 n) 1)) (+ (* 2 n) 1))) |
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(logS x (- n 1)) ) )) |
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(defun |
(defun loge(x) (logw (/ (- x 1) (+ 1 x)) 0 0) ) |
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(defun |
(defun logetest(a n prev) |
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(let ((n10 (+ 10 n))) |
(let ((n10 (+ 10 n))) |
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(let (( |
(let (( log10 (loge a n10) )) |
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(if |
(if |
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(= ( |
(= (float log10) (float prev)) |
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log10 |
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( |
(logetest a n10 log10) |
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) |
) |
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) |
) |
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)) |
)) |
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(defun |
(defun ln (x) |
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(if (> x 0) |
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(loge x) |
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nil |
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)) |
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(defun |
(defun expw(x n prev) |
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( |
(let ((cosn (/ (powint x n) (factorial n)) |
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)) |
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x |
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(handler-case |
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(+ (* (/ (powint -1 n) (factorial (+ (* 2 n) 1)) ) (powint x (+ (* 2 n) 1))) (sine x (- n 1))))) |
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(progn |
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(float cosn) |
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(defun sinetest(x n) |
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(expw x (1+ n) (+ prev cosn)) |
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(if |
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) |
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(= (* (sine x (+ 10 n)) 1.0) (* (sine x n) 1.0)) |
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(arithmetic-error (x) prev )) |
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(sine x (+ 10 n)) |
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) |
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(sinetest x (+ 10 n)) |
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) |
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) |
) |
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(defun |
(defun expon(x) (expw x 0 0)) |
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(defun |
(defun squareroot(x) (expon (* 1/2 (loge x)))) |
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(defun |
(defun powern(x a) (expon (* a (loge x)))) |
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(defun |
(defun e (x) (expon x)) |
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(if (= n 0) |
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x |
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(+ (/ (* (factorial (* 2 n)) (powint x (+ (* 2 n) 1))) (* (powint 4 n) (powint (factorial n) 2) (+ (* 2 n) 1))) (asine x (- n 1))))) |
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(defun pown (a b) (powern a b)) |
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(defun |
(defun sinew(x n prev) |
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(let (( |
(let ((cosn (* (/ (powint -1 n) (factorial (+ (* 2 n) 1)) ) (powint x (+ (* 2 n) 1))) |
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)) |
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(if |
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(handler-case |
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(= (* asine10 1.0) (* prev 1.0)) |
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(progn |
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asine10 |
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(float cosn) |
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(asinetest x (+ 10 n) asine10) |
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) |
(sinew x (1+ n) (+ prev cosn)) |
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) |
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(arithmetic-error (x) (+ prev cosn) )) |
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) |
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) |
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(defun sine(x) (sinew x 0 0)) |
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(defun cosinew(x n prev) |
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(let ((cosn (* (/ (powint -1 n) (factorial (* 2 n))) (powint x (* 2 n))))) |
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(handler-case |
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(progn |
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(float cosn) |
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(cosinew x (1+ n) (+ prev cosn)) |
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) |
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(arithmetic-error (x) (+ prev cosn) )) |
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) |
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) |
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(defun cosine(x) (cosinew x 0 0)) |
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(defun tang(x) (/ (sine x) (cosine x))) |
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(defun asinew(x n prev) |
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(let ((cosn (/ (* (factorial (* 2 n)) (powint x (+ (* 2 n) 1))) (* (powint 4 n) (powint (factorial n) 2) (+ (* 2 n) 1))) |
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)) |
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(handler-case |
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(progn |
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(float cosn) |
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(asinew x (1+ n) (+ prev cosn)) |
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) |
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(arithmetic-error (x) prev )) |
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) |
) |
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) |
) |
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(defun |
(defun asine (x) |
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(if (< x 1) |
(if (< x 1) |
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(if (> x -1) |
(if (> x -1) |
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( |
(asinew x 0 0) |
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(/ (pie) -2) |
(/ (pie) -2) |
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) |
) |
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test: |
test: |
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test: |
test: |
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[14]> ( |
[14]> (float (asine 9/100)) |
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0.09012195 |
0.09012195 |
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[14]> (asin 9/100) |
[14]> (asin 9/100) |
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Test 2: |
Test 2: |
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[4]> ( |
[4]> (float (asine (sine 1))) |
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1.0 |
1.0 |
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[4]> (asin (sin 1)) |
[4]> (asin (sin 1)) |
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Line 197: | Line 233: | ||
Test 3: |
Test 3: |
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[15]> ( |
[15]> (float (sine (* 45 (/ (* 2 (pie)) 360) ))) |
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0.70710677 |
0.70710677 |
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[15]> ( |
[15]> (float (squareroot 1/2)) |
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0.70710677 |
0.70710677 |
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[15]> (= ( |
[15]> (= (float (squareroot 1/2) 1.0) (* (sine (* 45 (/ (* 2 (pie)) 360) )))) |
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T |
T |
Revision as of 14:03, 19 December 2011
My Favorite Languages | |
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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 pie() 31415926535897932384626433832795028841971693993751058209749/10000000000000000000000000000000000000000000000000000000000)
(defun factorial (n)
(if (= n 0) 1 (* n (factorial (- n 1)))))
(defun powint (a b)
(if (= b 0) 1 (if (> b 0) (* a (powint a (- b 1))) (* (/ 1 a) (powint a (+ b 1))) )
) )
(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 n prev) (let ((cosn (* (/ (powint -1 n) (factorial (+ (* 2 n) 1)) ) (powint x (+ (* 2 n) 1))) )) (handler-case (progn (float cosn) (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 asine (x)
(if (< x 1) (if (> x -1)
(asinew x 0 0) (/ (pie) -2) )
(/ (pie) 2) )
)
(defun fibcalc (n)
(let ((sqrtFive (sqrtn 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))))))
</lang>
test: 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) 1.0) (* (sine (* 45 (/ (* 2 (pie)) 360) )))) T