enigmaticape

<?php
	
    if( ($dir = session_save_path() ) == null ) {
        $dir = sys_get_temp_dir();
    }
    
    var_dump( $dir );
	
    if( $dir ) {
			

enigmaticape

;; expt is three characters too long on the REPL
;; I use on my iPhone
(define (^ x n) (expt x n))

;; Golden Ratio, phi and the conjugate, psi
(define psi (/ (- 1 (sqrt 5)) 2))
(define phi (/ (+ 1 (sqrt 5)) 2))

;; Linear recursive Fib
(define (fib n) 

enigmaticape

#!/usr/bin/python

# This is the python script I used to generate
# the table that illustrates my rambling answer
# to SICP exercise 1.13

import math

# Golden ratio and conjugate
phi = (1 + math.sqrt( 5 ) ) / 2

enigmaticape

;; Recursive function to compute the elements
;; of Pascal's triangle. Note the complete lack
;; of any sanity checks on the input. GIGO.

(define (pelem row col)
  (cond((= col 0) 1)
       ((= col row) 1)
       (else(+(pelem(- row 1)(- col 1))
              (pelem(- row 1) col) ) )))

enigmaticape

; f(n) = n if n < 3,
; f(n) = f(n - 1) + 2f(n - 2) + 3f(n - 3) if n > 3
;
; iterative (via tail recursion optimisation) 

(define (F-iter a b c count)
  (if (= count 0)
      c
      (F-iter (+ a (* 2 b) (* 3 c))
              a

enigmaticape

(define (fib n)
  (cond ((= n 0) 0)
        ((= n 1) 1)
        (else (+ (fib (- n 1))
                 (fib (- n 2))))))

enigmaticape

(define (fib n)
  (fib-iter 1 0 n))

(define (fib-iter a b count)
  (if (= count 0)
      b
      (fib-iter (+ a b) a (- count 1))))

enigmaticape

(define (F n)	
  (cond ( (< n 3) n)
        ( else (+ (F (- n 1)) 
                  (* (F (- n 2)) 2)
                  (* (F (- n 3)) 3)))))

enigmaticape

(define (A x y)
  (cond ((= y 0) 0)
        ((= x 0) (* 2 y))
        ((= y 1) 2)
        (else (A (- x 1)
                 (A x (- y 1))))))

enigmaticape

;; Recursively defined analogue of (h n) = (A 2 n)
(define (h-rec n)
  (cond ((= n 0) 0)
        ((= n 1) 2)
        (else (expt 2 (h-rec (- n 1))))))