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Jan 19, 2021

IVT (IV-TINY) - A FORTH-programable Scientific RPN Calculator that fits in 8 kilobytes (Arduino, ATTINY85)

ivt

See a short video of IVEE at: https://youtu.be/VqkXdZuKv6A


PREAMBLE


IVT (IVEE-TINY) is the smallest member of the IV-calculator series (FORTH-like programable calculators). The name Ivee or IV stands for the roman number 4, which was the basis for naming FORTH (4th generation programming language).

The hardware is simple:

  • AVR ATTINY85 microcontroller (8192/512/512 bytes of FLASH/RAM/EEPROM)
  • OLED-display (128x32, I2C, SSD1306)
  • 16 keys touch sensitive keypad (TTP229-BSF, 2-wire)
  • CR2032 battery

IVT was made without making compromises to offer a complete FORTH-like programming environment and a maximum of mathematical functions (mostly written in FORTH itself). And it's amazing, how much calculating power fits into 8 kilobytes:

  • 80 intrinsic functions based on FORTH
  • A wide range of mathematical and scientific commands (DUP DROP SWAP ROT OVER / * - + PI SQRT POWER INV INT EXP LN SIN COS TAN ASIN ACOS ATAN GAMMA P>R R>P nPr nCr)
  • Statistics, line best fit and normal distibution (CDF/PDF)
  • Present value calculations
  • Programming: Up to 16 user definable programs with a total of 440 steps (< = <> > IF ELSE THEN BEGIN UNTIL)
  • A solver to find roots of user defined functions
  • A dictionary of all commands, words and programs
  • An user definable menu for fast access to all commands, words and programs
  • Storing of 10 numbers/constants (permanently)
  • Adjustable brightness of the display

Have fun! deetee


COMPILING


As IVT consumes 8190 bytes of flash memory (maximal 8192 bytes possible) compiling with proper settings is essential. Use the Arduino IDE, load the right library for the ATTINY85 and use the following settings:

  • Library: "attiny by Davis A. Mellis"
  • Board: "ATtiny25/45/85 (No bootloader)"
  • Chip: "ATtiny85"
  • Clock: "8 MHz (internal)"
  • B.O.D. Level: B.O.D. Disabled
  • Save EEPROM: "EEPROM retained"
  • Timer 1 Clock: "CPU (CPU frequency)"
  • LTO: "Enabled"
  • millis()/micros(): "Disabled"

KEYBOARD


ivt - keys

F(MENU) 7(SUM+) 8(PRG)  9(/)
E(SWAP) 4(DICT) 5(USR)  6(*)
N(ROT)  1(RCL)  2(STO)  3(-)
C(CA)   0(PI)   .(INT)  D(+)

LIMITS


As a microprocessor is primarily not made to do such complex things like performing a powerful calculator there are some limits in performance and resources. Most obvious is the limited precision of the intrinsic float format (IEEE 754, 32 bit). As four bytes only are used to represent a float respective double number the decimal digits of precision are limited to 6...7.

In addition the resources of a microcontroller are limited like the FLASH memory (holds the executable program code), the RAM memory (holds variables and data while running) and the EEPROM (holds permanent data like settings or user programs).

Due to the target of maximal calculating power IVT lacks on many "features of comfort". For example there is no error control - a division by zero results in a "non interpretable" display.

However IVT tries to offer a maximum of features, comfort and performance with a minimum of required resources.

LIMITS:
  24   ... Maximal data stack size
  7    ... Maximum number of displayed significant digits of a number
  10   ... Maximal amount of numbers saved permanently (0~9)
  16   ... Maximal number of user programs
  440  ... Maximal size (steps) of all user programs
  32   ... Maximal definable command slots of user menu

BROWSING MENUS


To navigate through the menu of some functions (MENU, DICT or USR) all selectable items are divided into four sections. Every section has its own up and down key (section I: E/N, section II: 4/1, section III: 5/2 and section IV: 6/3). To select one of the four presented items use the appropriate function key (F/7/8/9) or escape the menu with "C". There is some kind of hidden feature: If you leave the menu with the D-key the brightness of the display will be set (0~255, not permanent!).


COMMANDS


 BASIC KEYS:
  0~9.     ... Digits and decimal point
  EE N     ... 10-exponent (actually Y*10^X) and negate (change sign)
  D        ... DUP (push stack) or complete number input
  C        ... DROP top of stack or clear entry when in number input
  F        ... Shift to select function keys or double press for user menu

 FUNCTION KEYS:
  + - * /  ... Basic operations
  MENU     ... Browse (and select) the user menu
  SUM+     ... Enter X-data for statistics or X,Y-data for linear regression
  PRG      ... Edit program (00~15) - enter program number first
  SWAP     ... Swap the two top numbers of stack (1 2 -> 2 1)
  DICT     ... Browse (and select) the complete dictionary
  USR      ... Set dictionary entry to user menu
  ROT      ... Rotate stack (1 2 3 -> 2 3 1)
  STO RCL  ... Store/recall number - enter memory number first (0~9)
  CA       ... Clear stack and memories for statistics (5~7)
  PI       ... Push PI to stack
  INT      ... Integer value

 DICTIONARY (4 sections):
  F  7  8  9   ... F-key, numbers
  EE 4  5  6   ... 10-exponent, numbers
  N  1  2  3   ... NEGATE, numbers
  C  0  .  D   ... Clear/DROP, number, dot, DUP
  M  S+ PR /   ... MENU, SUM+, PRG edit, divide

  >< DC US *   ... SWAP, DICT, set USER menu, multiply
  RT RC ST -   ... ROT, RCL, STO, subtract
  CA PI IN +   ... CA (clear all), PI, INT, add
  IF EL TH PC  ... IF, ELSE, THEN, nPr/nCr
  <  =  <> >   ... LESSTHAN, EQUAL, NOTEQUAL, GREATERTHAN

  BE UN SO I   ... BEGIN, UNTIL, SOLVE, INV (1/X)
  c  t- E  LN  ... COS, ATAN, EXP, LN
  s  t  s- c-  ... SIN, TAN, ASIN, ACOS
  OV SQ yx !L  ... OVER, SQRT, POW (y^x), ln(GAMMA)
  PV ND P> R>  ... Present value, normal distribution, P->R, R->P

  S+ Sc x- LR  ... SUM+, SUMclr (clears memories 5~9), MEAN/STDEV, L.R.
  00 01 02 03  ... User programs
  04 05 06 07  ... User programs
  08 09 10 11  ... User programs
  12 13 14 15  ... User programs

PV, ND, P<>R, STAT


PV     ... Present value of given interest rate (ie. 0.08) and periods
ND     ... PDF (X) and CDF (Y) of standard normal distribution
P> R>  ... Polar/Rectangular conversion
STAT   ... Mean value (X) and standard deviation (Y).
           Note that the memories 5~9 (see RCL/STO) are used as statistic
           registers (Sxx, Sxy, n, Sx, Sy).
LR     ... Line best fit (y = X * x + Y)

PROGRAMMING


IVT is able to deal with up to 16 user programs (named 00-15) with a total number of 440 steps/commands. The maximal size per user program rises from 20 steps (program 00) to 35 steps (program 15). To edit a program, enter the program number (00-15) followed by PRG (F-8). The display shows P (for program), the program number (00-15), the program step number (vary with cursor keys E and N) and the command of this step. To insert a program step

  • press a key (number or DUP),
  • press a shifted key (press F twice to toggle) or
  • press DICT (F-4) to select a command from the dictionary. To delete a program step press ".". Leave and save the program with "C". To execute a program select the appropriate program number/name from DICT. Please note that the first user program (00) will be used by the solver.

SOLVER


To find a root of a function (programmed in user program 00) enter an appropriate start value and select the command SO from the dictionary.


POWER CONSUMPTION


As IVT provides a maximum of calculating power there where less resources for a good power management (i.e. idle, screen saver, auto power off) left. Merely the not needed timer1 and AD-convertes are set off to save approximately 0.9 mA. The power consumption of IVT depends mainly on the usage of the display. That's why per default the brightness of the display is set to minimum. Please note that you can (not permanently) set the brightness of the display with pressing D when in any menu (takes brightness value from stack). In total IVT consumes approximately 9 mA - so a a single battery (CR2032) which has a capacity of approximately 200 mAh should theoretically work at least 20 hours. Electrical current drawn by device (approximately):

  • ATTINY85 ... 5 mA
  • Keypad ... 2 mA
  • Display ... 1~4 mA (promt ~ display full of 8's)

PROGRAM EXAMPLES


  ABS:   DUP 0 LT IF NEG THEN
  FRAC:  DUP INT -
  SINH:  EXP DUP INV NEG + 2 /          ... sinh=(exp(x)-exp(-x))/2
  COSH:  EXP DUP INV + 2 /              ... cosh=(exp(x)+exp(-x))/2
  TANH:  2 * EXP DUP 1 - SWAP 1 + /     ... tanh=(exp(2*x)-1)/(exp(2*x)+1)
  ASINH: DUP DUP * 1 + SQRT + LN        ... asinh(x)=ln(x+sqrt(x*x+1))
  ACOSH: DUP DUP * 1 - SQRT + LN        ... acosh(x)=ln(x+sqrt(x*x-1))
  ATANH: DUP 1 + SWAP NEG 1 + / SQRT LN ... atanh(x)=ln(sqrt((1+x)/(1-x)))
  POW10: 1 SWAP EE
  LOG:   LN 1 0 LN /                    ... log(x)=ln(x)/ln(10)
  %: OVER / 1 0 0 *                     ... %=x/B*100%
  CHG%: OVER - OVER / 1 0 0 *           ... chg%=(x-B)/B*100%

  QE: OVER 2 / DUP * SWAP - SQRT SWAP 2 / NEG
  SWAP OVER OVER - ROT ROT +            ... x12=-p/2+-sqrt(p*p/4-q)

  DEG<>RAD: DUP PI * 1 8 0 / SWAP 1 8 0 - * PI /
  C<>F: DUP 1 . 8 * 3 2 + SWAP 3 2 - 1 . 8 /
  KM<>MI: DUP 1 . 6 0 9 3 4 4 DUP DUP ROT SWAP / ROT ROT *
  M<>FT: DUP 3 . 3 7 0 0 7 9 DUP DUP ROT * ROT ROT /
  CM<>IN: DUP 2 . 5 4 DUP DUP ROT SWAP / ROT ROT *
  KG<>LBS: DUP 2 . 2 0 4 6 2 3 DUP DUP ROT * ROT ROT /
  L<>GAL:  DUP 3. 7 8 5 4 1 2 DUP DUP ROT SWAP / ROT ROT *

  HMS2H: DOT 0 0 0 0 0 1 ADD // Round up to prevent leaps
  DUP DUP INT SWAP OVER - 1 0 0 * INT // hh mm
  ROT 3 PICK SUB 1 0 0 MULT OVER SUB 1 0 0 MULT, // ss
  3 6 0 0 / SWAP 6 0 / + + // ->s ->h

  H2HMS: DUP 3 6 0 0 * DUP ROT INT // h->s
  SWAP OVER 3 6 0 0 * - 60 DIV INT, // hh mm
  ROT OVER 6 0 MULT SUB 3 PICK 3 6 0 0 * - // ss
  1 0 0 0 0 / SWAP 1 0 0 / + + // hh.mmss

  nPr = n!/(n-r)! : OVER ROT ROT - 1 ROT ROT SWAP
  BEGIN SWAP ROT 1 ROT + DUP ROT * SWAP ROT OVER OVER SWAP LT UNTIL DROP DROP

  nCr = n!/(n-r)!/r! = nPr/r! : DUP ROT SWAP PERM 1 ROT
  BEGIN ROT ROT DUP ROT SWAP / ROT ROT 1 + SWAP OVER 1 - OVER SWAP LT UNTIL DROP DROP

ATTINY85 PINS


                      _____
  Analog0/Reset P5 H1|* U  |H8     Vcc
        Analog2 P3 H2|     |H7 P2  SCK/Analog1
        Analog3 P4 H3|     |H6 P1  PWM1/MISO
            GND    H4|_____|H5 P0  PWM0/AREF/SDA/MOSI

CIRCUIT DIAGRAM


 _________________
|   OLED-DISPLAY  |
|  128x32 SSD1306 |
|_GND_VCC_SCK_SDA_|
   |   |   |   |
           |   |
 __|___|___|___|__
| GND VCC P2  P0  |
|  AVR  ATTINY85  |
|_________P3__P1__|
           |   |
           |   |
 __|___|___|___|__
| VCC GND SCL SDO |
|Keypad TTP229-BSF|
|-----------------|
|  O O O O        |
|                 |
|  O O O O        |
|  O O O O        |
|      |          |... Solder to enable
|  O O O O        |    16-key-mode (TP2=0)
|                 |

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