math.scm

#|
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|#
;; various extra math functions

;; hyperbolics

(define sinh (lambda (x) (/ (- (exp x) (exp (- x))) 2.0)))

(define cosh (lambda (x) (/ (+ (exp x) (exp (- x))) 2.0)))

(define tanh (lambda (x) (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x))))))

(define coth (lambda (x) (/ (+ (exp x) (exp (- x))) (- (exp x) (exp (- x))))))

(define sech (lambda (x) (/ 2.0 (+ (exp x) (exp (- x))))))

(define csch (lambda (x) (/ 2.0 (- (exp x) (exp (- x))))))

(define asinh (lambda (x) (log (+ x (sqrt (+ (* x x) 1.))))))

(define acosh (lambda (x) (log (+ x (sqrt (- (* x x) 1.))))))

(define atanh (lambda (x) (* 0.5 (log (/ (+ 1. x) (- 1. x))))))

(define acoth (lambda (x) (* 0.5 (log (/ (+ x 1.) (- x 1.))))))

(define asech (lambda (x) (log (+ (/ 1. x) (sqrt (- (/ 1. (* x x)) 1.))))))

(define acsch (lambda (x) (log (+ (/ 1. x) (sqrt (+ (/ 1. (* x x)) 1.))))))

;; trigonometrics

(define cot (lambda (x) (* +1.0i (/ (+ (exp (* +1.0i x)) (exp (* +1.0i x -1.0)))
                                      (- (exp (* +1.0i x)) (exp (* +1.0i x -1.0)))))))
(define sec (lambda (x) (/ 2. (+ (exp (* +1.0i x)) (exp (* +1.0i x -1.0))))))

(define csc (lambda (x) (/ 2. (- (exp (* +1.0i x)) (exp (* +1.0i x -1.0))))))

(define acsc (lambda (x) (asin (/ 1. x))))

(define asec (lambda (x) (acos (/ 1. x))))

(define acot (lambda (x) (atan (/ 1. x))))

;; misc stuff

;;; logarithms logb: log base b
(define (logb x b)  (/ (log x) (log b)))

(define (log10 x)   (/ (log x) (log 10)))

(define (lg x)      (/ (log x) (log 2)))

(define (10log10 x) (* 10 (log10 x)))

(define (20log10 x) (* 20 (log10 x)))

;;; sigmoid function
(define (logsig x)  (/ 1 (+ 1 (exp (- x)))))

;;; sign function
(define (sign x)
  (cond
    ((positive? x)  1)
    ((negative? x) -1)
    (else 0)
  ))

;;; inverse
(define (inverse x)  (/ 1 x))

;;; square
(define (square x)  (* x x))

;;;sinus cardinal
(define (sinc x)
  (if (= x 0.) 1.
      (/ (sin (* 3.1415927 x)) (* 3.1415927 x))))

;;; exact rounding

(define (exact-round x)   (inexact->exact (round x)))

(define (exact-floor x)   (inexact->exact (floor x)))

(define (exact-ceiling x) (inexact->exact (ceiling x)))

;;; float modulo
(define (fmodulo x y)
  (* y (- (/ x y) (floor (/ x y)))))

;;; floor relative to multiples of a float (complements fmodulo:
;;; ffloor+fmodulo = x)
(define (ffloor x y)   (* y (floor (/ x y))))

;;; fceiling = ffloor + y
(define (fceiling x y) (* y (ceiling (/ x y))))

(define (pos-lin x)
  (cond ((> x 0) x)
        (else
         (if (inexact? x) 0. 0))))

;;; lambda float modulo
(define (lambda-fmodulo y)
  (lambda (x)
    (* y
       (- (/ x y)
          (floor (/ x y))))))

(define (round-decimal num place) (/ (round (* num (expt 10 place))) (expt 10 place)))

;; eof