ZooMath - Glorified Adding Machine

advanced RPN superset calculator -- "I can do it in 16 keys"

[Related: 26+2 key alphanumeric key-entry]

I propose a 'minimal' 16-key data-and-control entry-pad to advance the state-of-the-art calculation-by-hand, consisting of--

The decimal digits, 0,1,2,3,4,5,6,7,8,9, decimal point, [.], the four arithmetic operations, +,-,×,/, and, the ZooM denoted # herein.

(#, is for website-font-commonality, alternatively understood 'not-unequal' or 'made equal', or depicturesque 'zoom' ¤, autc.)

And where--

The display consists of 10 decimal digits, 3 scale digits, 2 signs, and operational indicators: [and more advanced with multiple numbers]

Decimalpoint-numbers are precise to their significant digits, except, numbers with all-12 digits entered, are 'infinitely' precise (11-12th digits do not show but at the moment of appendation). The display rounds to 10 digits in integer, fixed-point, and engineering and electronics and scientific floating-point notations. Integers and scaled-integers -no decimal point- are also, 'infinitely' precise.

ZooMath calculates in 12 or more decimal digits to accumulate and retain precision for rounding, but shows only 10.

('Infinitely precise', has special meaning in calculation: Operations maintain significance, But once a number after operations falls out of 'infinitely precise', it does not resume 'infinitely precise' notation, n'even when seemingly infinitely precise; eg. 1.000000000:00 all digits calculated may not be an integer; This also applies in truncative functions where it has integer properties but not-definite-integer history ... the Entered tail-digit is assumed rounded, -but,- the Calculated tail-digit is truncate at 0-9 and appended with 0.5, as it averages 4.5-centered odd-symmetry: then crossover occurs as 5.5 rounds up and 4.5 rounds down.... An alternative interpretation assumes the last digit is repeating ad infinitum cf :29.999...= :30.000... like a vernier-9 scale. [See also Guarded Significant Figures])

During number-entry key-by-key, digits and decimalpoints can be removed by excess points; Holding the point key, rapidly deletes multiple digits. Simple scaling is achieved by holding the zero key and letting it enter multiple zero-digits quickly (up to 99): this is efficient also for quickly expressing the trailing zeros of 'infinitely' precise simple decimals.

Then, after keying the number,

  • "+" posits,
  • "-" negates,
  • "/" reciprocates,
    and so completes the number;
  • "×" posits, too, but also locks it for subsequent self-multiplicative exponentiation.

    A second number is supplied, and,

  • "+" adds,
  • "-" subtracts,
  • "×" multiplies,
  • "/" divides,
    the first by the second, if the first is not locked in which case second is as at first.

    Without the second number,

  • "+" locks for subsequent self-additive multiplication (scaling),
  • "-" negates (repeatably), but clears a lock,
  • "/" reciprocates (repeatably but affects precision), also clears a lock,
  • "×" locks for subsequent self-multiplicative exponentiation.

    Before supplying a succeeding number, a preceding "×" locks the prior number for (self-multiplicative) exponentiation by a power: completed by the next operation ... Further application of "×" again "early locks" its immediately preceding number: for enabling exponential towers, ABC, (but only three levels are allowed).

    Similarly, "+" after a number completed by any operation, locks it for (self-additive) multiplication by a scale factor ... a further application of "×" then early-locks its immediately preceding scale factor: for scaling by powers of a radix, implicitly radix-10 in "C+×N" implementing C×10N, explicitly any precise-number radix in "C+R×N" implementing C×RN, completed by its final operation.

    After the final number,

  • "+" posits power, decimal powers too,
  • "-" negates power,
  • "/" reciprocates power,
    but once finally as the stack is then fully evaluated to a completed number;
  • "×" posits power too, but the third fully evaluates to completion without locking up higher.

    (For simplicity ZooMath does not stack operations higher.)
    (Note also that doublet "++" locks for 'learners exponentiation'.)

    Note then, negative-reciprocal-power A-1/B equaling 1/A1/B is also accomplished by reciprocal-power reciprocal-result, "A×B//".


    (EQUIPPED BEGINNERS, NOTE, that ZooM-ZooM, ##, clear-empties the display.)
    (Also, Double-negative, "--", is the easiest way to clear a number-lockup on the baseline.)

    MEMORY, FUNCTIONS, RELATIONS, and CONSTANTS are accessible by the ZooM, #: each access comprised of a ZooM, #, before or after a cell or code number (not arithmetically completed), and an arithmetic operation or second ZooM for completion:
  • ZooM preceding, #M, writes to a memory/relation cell or code number, completed by operation, and clear-empties the display;
  • ZooM succeeding, M#, reads a memory/function/relation/constant to the display, even multi-previewably, before operation.

    (Writing to an unused or unlocked constant, edits it, allowing constants to be added, improved, or replaced ... a programming lock function keeps them more permanently; a recovery function can unlock and switch them with their original manufacture.)


    DEEPER EXAMPLES: ADVANCED EXAMPLES: (Special controls actuated by decimalpoint in the address) NOTES on clear, erasure, significance, display, power, stack, memory, functions, features: (Note the revision group-then-pointer is for visibility: group keys first, its subselection is visibly local; excess functions locate on adjacent key-caps ... cf if pointer keys first, cf contemporaries, key-caps are visibly more-uniform but spread one-per.)


    ZooM (Z∞M) is the most powerful concept to glorify the adding machine since the handcrank.

    A premise discovery under the title,

    Grand-Admiral Petry
    'Majestic Service in a Solar System'
    Nuclear Emergency Management

    © 1996,2000,2002,2008,2009 GrandAdmiralPetry@Lanthus.net