Mathematics with Fuzuli

Our new general purpose interpreter and language Fuzuli was first introduced in Practical Code Solutions and has the official web page in FuzuliProject.org.

Fuzuli has several packages which are mostly wrappers of C++ libraries. One of them is the math package. It is math.nfl and stated in /usr/lib/fuzuli/nfl in Linux installations by default.

The math.nfl package simple wraps some basic mathematical functions such as square root, exponential, logarithms, floor, ceil and round as well as trigonometric functions such as sin, cos, tan, atan, acos, etc. These functions are directly inherited from the standard C++ library.  A list of functions in the math.nfl package is shown below:

Function	Description	Example	Result
PI	Returns a short presentation of PI	(let a (sin (/ PI 2)))	1.0
sin	Returns sin of a given reference	(let a (sin 0))	0.0
cos	Returns cos of a given reference	(let a (cos 0))	1.0
tan	Returns tan of a given reference	(print (tan 1))	1.55741
abs	Returns absolute value	(print (abs -5))	5
sqrt	Returns square root	(print (sqrt 25))	5
exp	Returns E^x	(print (exp 1))	2.71828
log	Returns natural logarithm	(print (log (exp 1)))	1.0
log10	Returns logarithm in base 10	(print (log10 10))	1.0
log2	Returns logarithm in base 2	(print (log2 2))	1.0
cosh	Returns hyperbolic cos	(cosh x)
sinh	Returns hyperbolic sin	(sinh x)
tanh	Returns hyperbolic tan	(tanh x)
asin	Returns inverse sine	(asin 1)
acos	Returns inverse cosine	(acos 0)
atan	Returns inverse tangent	(atan 1.55741)	1
atan2	Two arguments arctan function	(atan2 1 1)	0.7853981634
pow	Returns a^x	(print (pow 5 2))	25
ceil	Returns ceil of a given reference	(print (ceil 2.3))	3.0
floor	Returns floor of a given reference	(print (floor 2.3))	2.0
round	Returns round of a given reference. (nearest integer)	(print (round 2.3))	2.0
isinf	Returns 1 if the given reference is either negative or positive infinitive else returns 0	(print (isinf (/ 19 0)))	1

The table shown above is hopefully enough to introduce our functions in the math package. Any Fuzuli program should include the math package using the (require) expression if any math function shown above is planned to use. Look at the code below:

(require "/usr/lib/fuzuli/nfl/math.nfl")
(print (isinf (/ 19 0)))

Although math functions are collected in an external package, Fuzuli supports built-in arithmetic functions. The code shown below is calculating ordinary least squares regression coefficients. As you see, no math functions required and only the arithmetic functions are used.

(let x (list 1 2 3 4 5 6 7 8 9 10))
(let y (list 10 20 30 40 50 60 70 80 90 100))

(function sum (params a)
 (block
  (def s FLOAT)
  (def i INTEGER)
  (let s 0.0)
  (for (let i 0) (< i (length a)) (inc i)
   (let s (+ s (nth a i)))
  )
  (return s)
 )
)

(function mean (params a)
 (block 
  (def total FLOAT)
  (def result FLOAT)

  (let total (sum a))
  (let result (/ total (length a)))
   
  (return result)
 )
)


(function covariance (params c d)
 (block
  (def meana FLOAT)
  (def meanb FLOAT)
  (def xy FLOAT)
  (def i INTEGER)
  (let meana (mean c)) 
  (let meanb (mean d))
  (let xy 0.0)
  (for (let i 0) (< i (length a)) (inc i)
   (block
    (let xy (+ xy (* (- (nth c i) meana) (- (nth d i) meanb ))))
   )
  ) 
  (return xy)
 )

)


(let beta1 (/ (covariance x y) (covariance x x)))
(let beta0 (- (mean y) (* beta1 (mean x))))
(print "beta0 " beta0  "\n") 
(print "beta1 " beta1  "\n")

The result is 0.0 for beta0 and 10.0 for beta1.

See you in next entry. Have fun!