Hi, I finally made a start on these tables... (there has been so much other stuff to explore with picolisp =)

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But I think I may have hit a dead-end right away for a 'pure' picolisp implementation; from the performance benefit point of view. At least for the two tables I cared most about.. multiplication and division. An idx, while impressively fast, comes nowhere near native multiplication. I'll try a table lookup implementation via a shared lib and see what overhead the function call would add. The time delta may also disappear for scientific tables (sin, cos, log, etc). In the meantime I thought I would share the code below for any thoughts or observations... demonstrates multiplication by table lookup and addition. This is the only instance I've run into where I have wanted some kind explicit array in picolisp... but I wouldn't trade a bit of the current functionality and performance of the platform for it. /Lindsay # 2 2 # ab = ( ((a + b) - (a - b) ) ) / 4 # # (let (A (rand 1 255) B (rand 1 255)) (= (* A B) (>> 2 (- (** (abs (+ A B)) 2) (** (abs (- A B)) 2))) ) ) # # For a restricted integer number range, using a table of 'squares' / 4 # reduces the multiplication to 3 additions (with two table lookups) # (let (A (rand 1 255) B (rand 1 255))(= (* A B) (- (cdr (lup *MULTBL (abs (+ A B)))) (cdr (lup *MULTBL (abs (- A B)))))) ) # Table of squares/4 (nil (setq *MULT (make (for N (** 2 9) (link (cons N (>> 2 (* N N )) )))))) (balance '*MULTBL *MULT) # Test functions (de MLup (A B) (- (cdr (lup *MULTBL (abs (+ A B)))) (cdr (lup *MULTBL (abs (- A B)))) ) ) # Multiplication by lookup (de mult-test2 () (bench (do (** 2 20) (let ( A (rand 1 255) B (rand 1 255) A+B (cdr (lup *MULTBL (abs (+ A B)))) A-B (cdr (lup *MULTBL (abs (- A B)))) ) (- A+B A-B) ) ) ) ) # Built-in multiplication (de mult-test1 () (bench (do (** 2 20) (let ( A (rand 1 255) B (rand 1 255) ) (* A B) ) ) ) ) : (mult-test1) 0.392 sec -> 14151 : (mult-test2) 1.507 sec -> 2249 : (= (* 13 41) (MLup 13 41)) -> T 2017-04-01 22:45 GMT+02:00 Lindsay John Lawrence < >> lawrence.lindsayj...@gmail.com>: >> >>> My next little picolisp project.. >>> >>> Picolisp's built-in functions for scaled arithmetic are brilliant once >>> you understand how they work. Still, it would be great to get more >>> scientific functions without have to link an external math lib, and get >>> 'real-time' performance when needed as well. >>> >>> http://wilsonminesco.com/16bitMathTables/ is a nice write-up (link >>> found on hacker news) of what you can do with fixed point, scaling and >>> lookup tables... Also has links to code to generate the tables. >>> >>> I think the concepts and technique will transfer quite nicely to >>> picolisp. We'll see... >>> >>> /Lindsay >>> >>> >> >