Help Page for the ti5x app

Topics:

• Introduction
• Basic Operation
• Display Control
• Copy/Paste
• Additional Operations
• Memories
• Trigonometry
• Statistics Functions
• Program Entry
  • Transfer of Control
  • Comparisons
  • Flags
  • Looping
  • Other Control
  • User-Defined Keys
  • Key Codes
• Program Execution
• Library Programs
• Importing Data
• Printer Emulation
• Exporting Data
• Options Menu
• Additional Information

Introduction

ti5x is an emulator for the TI-58/58C/59 family of programmable scientific calculators which were manufactured by Texas Instruments from the late 1970s. It mostly tries to follow the original functionality; features marked “extension” are additions not present in the original.

Basic Operation

•  0 ,  1 ,  2 ,  3 ,  4 ,  5 ,  6 ,  7 ,  8 ,  9 , — number entry.
•  .  — decimal point. Also lets you continue mantissa entry after entering exponent.
• EE (during number entry) — enter exponent
• +/- — change sign of mantissa or exponent
• CE — clear current number without losing rest of calculation.
• CLR — clear entire current calculation.
•  + ,  - ,  ×  and  ÷  — four-function arithmetic operators with usual algebraic precedence.
•  ( ,  )  — lets you override normal arithmetic operator precedence.
•  =  — completes entire pending calculation, automatically supplying any missing closing parentheses.

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Display Control

• INV 2nd Fix or 2nd Fix 9 — switch display to default format. This uses up to 9 decimal places (trailing zeroes omitted) with no exponent displayed, provided the magnitude of the number is within [5.0 × 10^-9 .. 1.0 × 10¹⁰], otherwise it will show 8 figures with an exponent.
• 2nd Fix n (n ∈ 0 .. 8) — switch display to fixed point with exactly n decimal places, provided number is within the range above, otherwise 8 figures will be shown with exponent.
• EE (after a result has been computed) — round displayed number to only digits shown. Display will also switch to exponential format for subsequent results.
• INV EE — switch display to default format.
• 2nd Eng — switch display to engineering notation (with exponent that is always a multiple of 3).
• INV 2nd Eng — switch display to default format.

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Copy/Paste

If you long-tap the display, a context menu will appear with “Copy Number”, “Copy Full-Precision Number” and “Paste Number” options in it. Select “Copy Number” to copy the currently-displayed number to the Clipboard, or “Copy Full-Precision Number” to copy it with all significant figures intact, regardless of how many are being displayed. From here it may be pasted into other applications. Select “Paste Number” to enter a number from the Clipboard, perhaps copied from another application. If it is not a valid number, you will get an error message.

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Additional Operations

• 2nd — modify next key to perform function written just above it, rather than on key itself.
• INV — modify next key to perform “inverse” function (meaning depends on key).
• INV  ÷  — extension: remainder on division.
• y**x — raise number entered before to power of number entered after.
• INV y**x — raise number entered before to power of reciprocal of number entered after.
• lnx — replaces last-entered number with its log base e.
• INV lnx — replaces last-entered number with its antilog base e.
• 2nd log — replaces last-entered number with its log base 10.
• INV 2nd log — replaces last-entered number with its antilog base 10.
• x² — replaces last-entered number with its square.
• √x — replaces last-entered number with its square root.
• 1/x — replaces last-entered number with its reciprocal.
• x⇌t — interchanges contents of X (displayed number) and T registers.
• 2nd Op nn — performs various special operations, depending on the value of nn.
• 2nd Op 50 — extension: return the current time in seconds since 00:00:00 1st January 1970 UTC.
• 2nd Op 51 — extension: return a cryptographically-strong random value in [0.0 .. 1.0).

If you use both 2nd and INV, they can be pressed in either order. If you press one of these by mistake, just press it again to cancel it before pressing another key.

The following operations are mainly useful when writing programs:

• 2nd Int — replace the displayed number with its integer part.
• INV 2nd Int — replace the displayed number with its fractional part.
• 2nd |x| — replace the displayed number with its absolute value.
• 2nd Op 10 — signum: replace displayed number with 1 if positive, 0 if zero, or -1 if negative.
• 2nd Nop — does nothing. May be inserted in program sequences in place of deleted instructions to avoid changing the positions of following instructions.

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Memories

There are 100 memory registers available, numbered 00 to 99.

• STO nn — store current number into memory nn.
• RCL nn — replace current number with copy of memory nn.
• SUM nn — add current number to memory nn.
• INV SUM nn — subtract current number from memory nn.
• 2nd CMs — set all memories to zero.
• 2nd Exc nn — exchange current number and contents of memory nn
• 2nd Prd nn — multiply contents of memory nn by current number.
• INV 2nd Prd nn — divide contents of memory nn by current number.

The following operations are mainly useful when writing programs:

• STO 2nd Ind nn, RCL 2nd Ind nn etc — all the above memory operations on single registers are also available in indirect versions, where the contents of the specified memory register are taken as the number of the actual register to operate on.
• 2nd Op 2n — adds 1 to memory 0n.
• 2nd Op 3n — subtracts 1 from memory 0n.
• 2nd Op 52 — extension: returns the current register offset as nn (nn ∈ 00 .. 99).
• 2nd Op 53 — extension: sets the register offset to the current number nn (nn ∈ 00 .. 99).

The register offset is an adjustment to the numbering of all the memory registers: when the offset is set to nn, all references to register ii actually become references to register ii + nn (modulo 100). The purpose of this is to minimize register conflicts when one program calls another. For example, you might want to call two library programs that both use registers 01 .. 06; rather than move the registers one by one into different registers and then back again, simply change the register offset before calling one or both of them, to cause them to use different registers. You can also use this to give yourself more convenient numbering for your own register usage; thus, if you want to use 10 registers, but want to call a library routine that will use registers from 00 onwards, simply add 10 to the register offset before calling that routine, then subtract 10 back after it returns. That way your own code can use the register numbers 00 .. 09 without conflict.

The preferred way to make adjustments to the register offset is to always add to or subtract from the current value, never unconditionally set it to a new value. In the previous example, you might use a key sequence like  (  2nd Op  5   2   +   1   0   )  2nd Op  5   3  before invoking the routine, and  (  2nd Op  5   2   -   1   0   )  2nd Op  5   3  to restore the previous offset afterwards. The reason for this is to allow the same trick to be pulled on your routine to relocate its register usage by some other routine that wants to call it.

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Trigonometry

• 2nd π — enter π.
• INV 2nd π — extension: enter the equivalent of 1 radian in the current angle units (1 if in radians, 180 ÷ π if in degrees, 200 ÷ π if in gradians). Dividing an angle in the current angle units by this number converts it to radians; multiplying a value in radians by this number converts it to the current angle units. Many algorithms are easiest to express if all angles are in radians; at the same time, you can make your program more user-friendly if it accepts inputs and displays results in the current angle units.
• 2nd Deg — switches angle units to degrees (default).
• 2nd Rad — switches angle units to radians.
• 2nd Grad — switches angle units to gradians (100 gradians = 90°).
• 2nd Sin — sine of last-entered number.
• INV 2nd Sin — arcsine of last-entered number.
• 2nd Cos — cosine of last-entered number.
• INV 2nd Cos — arccosine of last-entered number.
• 2nd Tan — tangent of last-entered number.
• INV 2nd Tan — arctangent of last-entered number.
• 2nd P→R — polar-to-rectangular coordinate conversion; input angle in X register and magnitude in T register, output will be X-coordinate in T register and Y-coordinate in X register.
• INV 2nd P→R — rectangular-to-polar coordinate conversion: input X-coordinate in T register and Y-coordinate in X register, output will be angle in X register and magnitude in T register.

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Statistics Functions

Note these accumulate totals in registers 01 to 06 as follows:

• 01 — ∑y
• 02 — ∑y²
• 03 — N
• 04 — ∑x
• 05 — ∑x²
• 06 — ∑xy

so these need to be cleared before use. (The Master Library provides a function in Program 01 for doing this: 2nd Pgm 01 SBR CLR.)

• 2nd ∑+ — accumulate a data point; independent variable in T register, dependent variable in X register. T register automatically incremented for next entry.
• INV 2nd ∑+ — remove a data point. Can be used to undo an incorrect entry. Note that T still increments!
• 2nd mean(x) — compute sample mean: T = ∑x / N, X = ∑y / N.
• INV 2nd mean(x) — compute population standard deviation: T = sqrt(∑x² - (∑x)² / N(N - 1)), X = sqrt(∑y² - (∑y)² / N(N - 1)).
• 2nd Op 11 — compute sample variance: T = ∑x² / N - (∑x)² / N², X = ∑y² - (∑y)² / N².
• 2nd Op 12 — compute linear regression slope and intercept: T = m, X = ∑y - m * ∑x / N where m = (∑xy - ∑x∑y / N) / (∑x² - (∑x)² / N).
• 2nd Op 13 — compute correlation coefficient: X = m * sqrt(∑x² - (∑x)² / N(N - 1)) / sqrt(∑y² - (∑y)² / N(N - 1)) where m = (∑xy - ∑x∑y / N) / (∑x² - (∑x)² / N).
• 2nd Op 14 — compute estimated y from x: X = m * X + (∑y² - m * ∑x) / N where m = (∑xy - ∑x∑y / N) / (∑x² - (∑x)² / N).
• 2nd Op 15 — compute estimated x from y: X = (X - (∑y² - m * ∑x) / N) / m where m = (∑xy - ∑x∑y / N) / (∑x² - (∑x)² / N).

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Program Entry

Programs are stored as a sequence of 2-digit numbers that (mostly) correspond to the position of the keys on the keyboard. There are 960 program locations available for holding a user-entered program. These are numbered from 000 to 959.

• 2nd CP — in calculation mode, set all program locations to zero.
• LRN — toggle between calculation and program-entry modes.
• SST — in program-entry mode: skip to the following program location.
• BST — in program-entry mode: step back to the previous program location.
• 2nd Ins — in program-entry mode, insert a zero at the current location and move the following instructions down one.
• 2nd Del — in program-entry mode, delete the instruction at the current location and move the following instructions up one.

Other keys will enter keystrokes that will perform their function when executed.

Note that all register, flag and location operands allow indirection: simply enter 2nd Ind nn in place of the operand to specify the register which will supply the value of the operand.

Transfer of Control

Enter 2nd Lbl followed by just about any other key (except the above program-entry functions, the digit keys or Ind) to use that key to label the current location. The same label key can then be specified as the loc operand to any of the branch/call/loop instructions.

• GTO loc — unconditional transfer of control to loc.
• SBR loc — unconditional transfer of control to loc, until the next INV SBR instruction is executed, in which case control returns here to continue from the following instruction.
• INV SBR — return from the last subroutine entered.
• INV GTO loc — extension: put the address of loc into the display register.

Any of the preceding that take a loc operand may be prefixed by 2nd Pgm nn (or 2nd Pgm 2nd Ind nn) to refer to the specified location in library program nn (or the library program given by the contents of register nn) rather than the current program.

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Comparisons

• 2nd x=t loc — if X is equal to T, branch to location loc.
• INV 2nd x=t loc — if X is not equal to T, branch to location loc.
• 2nd x≥t loc — if X is greater than or equal to T, branch to location loc.
• INV 2nd x≥t loc — if X is less than T, branch to location loc.
• 2nd CP — when executed in a program, this just clears the T-register. It does not clear the program.

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Flags

There are 10 flags (numbered 0 to 9), each of which may be set, unset, or tested.

• 2nd St flg n — set flag n.
• INV 2nd St flg n — clear flag n.
• 2nd If flg n loc — if flag n is set, branch to location loc.
• INV 2nd If flg n loc — if flag n is unset, branch to location loc.
• 2nd Op 18 — if there is no error condition, set flag 7, otherwise leave it unchanged.
• INV 2nd Op 18 — if there is no error condition, clear flag 7, otherwise leave it unchanged.
• 2nd Op 19 — if there is an error condition, set flag 7, otherwise leave it unchanged.
• INV 2nd Op 19 — if there is an error condition, clear flag 7, otherwise leave it unchanged.

Stop on error: if flag 8 is set when an error condition occurs during program execution, execution immediately stops.

Trace execution: if flag 9 is set, the result of each calculation step will be printed on the printer.

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Looping

• 2nd Dsz n loc — decrement register 0n, and branch to loc if its new value is nonzero, otherwise continue with the following instruction.
• INV 2nd Dsz n loc — decrement register 0n, and branch to loc if its new value is zero, otherwise continue with the following instruction.

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Other Control

• 2nd Pause — pauses execution of the program just long enough for the user to see the displayed value before continuing.
• R/S — when this is encountered in a program, execution stops. The user may resume from that point by pressing R/S.

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User-Defined Keys

The keys  A , 2nd A´,  B , 2nd B´,  C , 2nd C´,  D , 2nd D´,  E  and 2nd E´ may be used as labels just like most other keys. They are special in that they can be invoked as subroutines without being prefixed with SBR. They are intended to behave as user-definable function keys.

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Key Codes

Note that some codes represent merged keystrokes. This not only saves space; some sequences cannot be represented unambiguously otherwise (Ind versus register 40).

Note also that INV is (usually) a separate keystroke, while 2nd is not.

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Program Execution

•  A , 2nd A´,  B , 2nd B´ etc — execute the subroutines with those labels.
• SBR followed by another key, or by 3 digits — execute the subroutine labelled by the following key, or starting at the specified location.
• GTO followed by another key, or by 3 digits — in calculation mode, set the current location to that labelled by the following key, or the specified number.
• R/S — in calculation mode, start execution at the current location, or stop execution if already running.
• SST — in calculation mode: execute one instruction.
• RST — clear all flags and the subroutine return stack, and set the current location to 000.
• INV RST — extension: close the current data-import and data-export files.

While a program is running, you can hold down the GTO/Pause key to slow down execution and see intermediate results appearing in the display. Release to resume full-speed execution.

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Library Programs

It is possible to load external library modules into the calculator. One module, the “Master Library”, comes preloaded with the calculator. A library module can provide up to 99 separate program banks, which can be selected for execution instead of program bank 00, which is where your user-entered program is kept. Only one library module can be loaded at a time.

• 2nd Pgm nn — select program bank nn from loaded library module (if nn in [01 .. 99]), or select user-entered program bank (if nn = 00). If the selected program bank has a label card, it will appear just under the display. If the program bank has a help page, it can be shown by tapping in the label card area.
• 2nd Op 09 — copies the currently-selected program bank into the user program area.

Extension: pressing LRN while a nonzero program number is selected will display the contents of the selected program, rather than the user-program-entry area. The program number additionally appears to the left of the program location number. Library programs cannot be edited.

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Importing Data

You can read numbers from a data file, instead of having to enter them manually. You choose a file to open from the “Import Data...” item in the Options Menu. The file must contain a sequence of numbers separated by newlines, whitespace or commas. Thereafter, you can read the next number into the display using INV 2nd Prt (either from the keyboard or in a program). An attempt to read past the last number will set flag 7 and leave the display unchanged. If a number was successfully read, flag 7 will be cleared.

The import file can also be immediately closed by INV RST.

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Printer Emulation

The app also includes emulation for a connected PC-100x dot-matrix printer capable of printing 20 text columns per line, from a limited character set. The printer output can be viewed by selecting the “Printer” item from the options menu.

• 2nd Prt — print the number currently being displayed.
• 2nd Op 00 — initialize the print register to all blanks.
• 2nd Op 01 — load the 10-digit integer part of the displayed value into the leftmost 5 columns of the print register.
• 2nd Op 02 — load the 10-digit integer part of the displayed value into the next-to-leftmost 5 columns of the print register.
• 2nd Op 03 — load the 10-digit integer part of the displayed value into the next-to-rightmost 5 columns of the print register.
• 2nd Op 04 — load the 10-digit integer part of the displayed value into the rightmost 5 columns of the print register.
• 2nd Op 05 — print the contents of the print register.
• 2nd Op 06 — print the number currently being displayed, followed by the last three characters in the print register.
• 2nd Op 07 — plot an asterisk preceded by n spaces, where n (which must be in [0 .. 19]) is taken from the integer part of the displayed number.
• 2nd Op 08 — print a listing of the names and locations of all labels in the user program.
• 2nd Op 40 — set flag 7 to indicate that a printer is attached.
• 2nd Adv — advance the paper by 1 line.
• 2nd List — print out the user program contents in mnemonic form, starting from the current program counter. Press RST first to ensure the listing starts from 000.
• INV 2nd List — print out the memory contents, starting from the register with the number showing in the display.

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Exporting Data

Calculation results can also be exported, in either of two ways:

1. The printer emulation can write text representations of every printed line to an output file. Every line sent to the printer, whether via 2nd Prt or any of the printer-related 2nd Op nn functions, will be written to the file. Note that characters with no obvious Unicode equivalent are ignored. The 2nd Adv function will write a blank line.

   Note this file typically cannot be re-imported by ti5x, since exponents are separated from mantissas by a space or nothing before a minus sign (instead of the more conventional e character). Other programs are also likely to have trouble reading such numbers.

2. Only numbers are exported, in standard exponential format; the current calculation result is written out every time the 2nd Prt key is pressed (or that function is invoked from a program). This file format can be re-imported by ti5x, and should also be readable by other programs.

To close the current export file, press (or execute in a program) INV 2nd Adv. It is also closed by INV RST.

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Options Menu

Pressing the Android Menu button brings up a menu with the following options:

• Calc Help — bring up this help page.
• Key Codes — toggle the display of program key codes next to the corresponding keys.
• Module Help — bring up the main help page for the currently-loaded library module, if any.
• Printer — bring up the virtual printer display. (Use the Back button to return to the main calculator display.)
• Load Program... — load a library module or saved program from a file on the SD card. The list to pick from is built from the contents of the “Programs” and “Download” directories.
• Feedback... — lets you choose what kind of feedback is used to indicate a button press; either a click (the default), a short pulse of the vibrator, or nothing.
• Save Program... — save the user-entered program to a file on the SD card. The file is saved in the “Programs” directory.
• Import Data... — lets you open a data file in the “Download” directory on the SD card to begin importing numbers from. (See Importing Data for more details.)
• Export Data... — lets you create a data file on the SD card (or append to an existing data file) to write exported data to. The file is saved in the “Download” directory. (See Exporting Data for more details.)
• About ti5x... — displays version and copyright information for the app.
• Off — simulate a complete power down and quit the app. This completely wipes all user program and memory contents. The next time the app is started, it will initialize as though freshly installed.

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Additional Information

Copies of the user manuals for the original products can be found at rskey.org and datamath.org.