Plus42 : An Enhanced HP-42S Calculator Simulator

Plus42 builds on Free42 and adds: A Larger Display, with 8 rows and 22 columns (131x64 pixels) by default, which the user may resize at will; Algebraic Expressions modeled after those used on the HP-27S and HP-17B/19B; attached Units and unit conversions modeled after those used on the HP-48/49/50 series; Directories for more organized storage of programs and variables; TVM and amortization tables; and two-dimensional Plotting of functions, with ability to zoom and pan, and find integrals and roots from points in the plot.

Plus42 is an Open Source project. The executables and source code are released under the terms of the GNU General Public License, version 2.
All third-party code used in Plus42 is either in the public domain, or licensed under terms compatible with GPLv2, or used with the authors' permission.

Project Status

If you're interested in what's been going on with Plus42, see the project history.
If you have questions or comments about Plus42, you may use the Free42 & Plus42 discussion group.
Alternatively, you can contact me, Thomas Okken, via email at thomasokken@gmail.com.

You can find answers to some frequently asked questions in the Plus42 FAQ.

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Documentation

Introduction

Plus42 is a calculator app for people who like the simplicity and ease of use of RPN keystroke-programmable calculators like the HP-42S, but also enjoy some of the advanced features of HP's RPL series. It is an evolution of Free42, which also continues to be maintained as a separate app. Plus42 is fully compatible with Free42 and the HP-42S.

Plus42 is not an attempt to re-create the RPL calculators in full. These machines have a very well-thought-out design of their own, and if you want all their functionality, before too long you are bound to find yourself replicating their entire user experience. But it is possible to borrow some of their functionality into an HP-42S-like calculator, without compromising the elegance, simplicity, and intuitiveness of the 42S design.

I started adding some advanced functionality to Free42 in 2019: SST→ and SST↑ for easier debugging of large programs; LSTO for creating local variables; a large RTN stack, which, in combination with LSTO, enables implementing recursive functions; FUNC, RTNERR, RTNYES, and RTNNO, which make it possible to write user-code functions which behave more like built-in ones; and finally, a dynamically growing RPN stack.

These new functions are rather unobtrusive: if you don't need them and aren't interested in them, you probably won't even notice they exist, and you can continue using Free42 as an HP-42S-compatible calculator, just like before. And if you do like them, you can use them to help with some of the more demanding programming tasks, in a way that fits seamlessly with legacy code.

But there were also some ideas for improvements, floating around in the HP calculator community, that would have much more of an impact on the user interface, not to mention requiring much more work to implement. In 2021, with time on my hands thanks to a certain global health crisis, I started work on a fork of Free42, with the goal of adding support for algebraic equations, attached units, directories, and a big display. And about a year later, Plus42 1.0 was done.

If you are familiar with RPN programmable calculators, you will find Plus42 easy and intuitive to use. If you are familiar with the HP-42S specifically, you'll be up and running almost immediately.

If you are not familiar with RPN calculators, I recommend starting by reading the first few chapters of the HP-42S manual. Plus42 is an HP-42S simulator at heart, and everything you read in that manual applies to Plus42 as well. And I also recommend reading the documentation section of the Free42 home page (link); this covers loading and saving programs, Copy and Paste, and loading and saving state files.

If you are interested in programming, you'll want to read the Extensions section of the Free42 home page (link); this covers the advanced programming features I mentioned above, and also some other functions not present in the original HP-42S, like functions for accessing the current time and date, and calculating with times and dates, and support for user-selectable word sizes for the BASE menu functions.

What follows is documentation for the features present in Plus42 that are not in Free42. Since much of this functionality is modeled after other HP calculators, specifically, the HP-17B/19B/27S and the HP-48/49/50 series, experience with those models will help, but it is not required.

Algebraic Equations

In addition to keystroke programming like on the HP-42S and in Free42, Plus42 supports algebraic equations. These can be used with the SOLVER, ∫ f(x), and PLOT application menus, and they can be embedded in programs; they can be stored in variables and on the stack, and evaluated from any of those contexts.

The Plus42 equations, their syntax and capabilities, and the equation editor, are all modeled after the Solver found on the HP-17B, 19B, and 27S calculators. The HP-17B manual, sections 11 and 13; the HP-19BII manual, sections 11, 12, and 13; the HP-27S manual, section 5; the HP-27S/19B Technical Applications book; and Martin Hepperle's "About The Solver in the HP Pocket Calculators" — these can all be used with the Plus42 solver, with only minor differences. The set of built-in functions provided by Plus42 is a superset of the aforementioned calculators, and the direct and iterative solvers are both implemented.

The heart of the Plus42 equation functionality is Equation Mode, which is the central place where you enter and edit equations, and perform calculations with them.
You enter Equation Mode by pressing the EQN key on the keyboard, or using the = key in the SOLVER, ∫ f(x), and PGMMENU menus. This takes you to the Equation List.

In the Equation List, the two rightmost menu buttons are ↑ and ↓ buttons. These are used to rearrange equations: they swap the current equation with the one just above or below in the list. If the display is set to show just two rows, ↑ and ↓ will briefly show the equation being swapped with, and then move to the new position in the list, so you are left looking at the same equation as before.
If you want to move through the list without rearranging it, use the familiar ▲ and ▼ buttons.

To add a new equation, you can press NEW and start typing, or Paste text from a different app. The new equation or equations will be inserted after the current one.
If you pressed NEW, you will see the familiar ALPHA menu for entering text. To move the cursor to a different position, press EXIT to go to the cursor movement menu; this has keys for cursor movement in all four directions, plus DEL to delete the character under the cursor (to delete the character to the left of the cursor, press the backspace key on the keyboard), and ALPHA to go back to the ALPHA menu. Pressing EXIT from the cursor movement menu will finish editing and return you to the Equation List.

To start editing an existing equation, select it using ▲ and ▼ and press EDIT. This puts you in the Equation Editor, just like NEW, except you start in the cursor movement menu, rather than the ALPHA menu.

Use DELET to delete the current equation. Use this with caution: once an equation has been deleted, it cannot be recovered!
When you press DELET, and some or all of the variables used by the equation exist, you will be offered the choice whether to delete just those variables, or just the equation, or both.

Last but not least, press CALC to start performing calculations with the currently selected equation.

The action of CALC depends on how you entered Equation Mode. If you used EQN, or = in the SOLVER menu, CALC performs EQNSLV and enters the SOLVER menu; and if you used = in the ∫ f(x) menu, CALC performs EQNINT and enters the ∫ f(x) menu. Once in these menus, you use them with the current equation, exactly like you would if you had selected a program.

You can change the action of CALC without leaving Equation Mode, by pressing Shift-7 or Shift-8 (SOLVER and ∫ f(x)). You will briefly see a message confirming the new action.

This is the complete list of all the keys that are active while in the list view:

CALC and ENTER Start calculating with the currently selected equation.
EDIT Start editing the currently selected equation. The equation editor is discussed in detail below.
DELET Delete the currently selected equation. Since this is a rather drastic operation, you will be asked for confirmation; also, if any of the variables used by the equations exist, you will be asked whether you want to delete those variables only, the equation and its variables, or the equation only. Deleting the variables only can be a convenient way of resetting your calculations.
NEW Start editing a new equation. The equation will be inserted in the list below the currently selected one.
↑ and ↓ Move the currently selected equation up or down in the list, swapping it with the equation just above or below.
Shift PLOT Exit equation mode and enter the PLOT menu, with the current equation selected as if using EQNPLOT.
STO Export the equation to the RPN calculator environment. You will be offered these options: X to push the equation onto the stack, placing it in the X register; PRGM insert it into the current program as an XSTR line; if the current program line is an XSTR line, you will be offered the choice of overwriting that line, or inserting a new XSTR after it; if the current program line is not an XSTR, the equation is always inserted after it; and ALPHA, which puts the equation in the ALPHA register. When storing in ALPHA, bear in mind that the ALPHA register can only hold up to 44 characters, and equations can be any length, so any given equation may not fit.
RCL Import an equation from the RPN calculator environment. You will be offered these options: X to get it from the X register; PRGM to get it from the current program line; and ALPHA to get it from the ALPHA register.
Shift MODES and Shift DISP The normal MODES and DISP menus; the settings in these menus affect the equation environment much like the RPN environment, so access to them is provided here, without having to leave equation mode.
▲ and ▼ Move the selection up or down one position in the list view. When pressed with Shift, jump directly to the beginning or end of the equation list.
Shift SOLVER Set SOLVE mode, so pressing CALC or ENTER will enter the SOLVER menu with the currently selected equation.
Shift ∫ f(x) Set INTEG mode, so pressing CALC or ENTER will enter the ∫ f(x) menu with the currently selected equation.
Shift PRINT Opens the PRINT menu. This menu is a bit different than the PRINT menu shown in the RPN environment. This menu is discussed separately, below.
EXIT Exit equation mode and return to the RPN environment.
Shift EXIT Exit the Plus42 app.

The PRINT menu in Equation Mode is accessible both in the List View and in the Equation Editor. It has different functions than the PRINT menu in the RPN environment:

EQ Prints the current equation.
LISTE Print the whole equation list.
VARS Prints the variables used by the current equation.
LISTV Print all variables.
PRST Print the RPN stack.
ADV Paper advance; prints a blank line.

The second row of the PRINT menu has the printer mode settings: PRON, PROFF, MAN, NORM, TRACE, and STRACE; these work the same as the third row of the RPN-mode PRINT menu.

When you press EDIT or NEW in the equation list view, you enter the Equation Editor.
This is a very basic text editor. It is similar to ALPHA mode, except in the equation editor, there is no 44-character length limit, and you can move the cursor around freely.

The two main menus in the equation editor are the cursor movement menu and the ALPHA menu. When you press EDIT, you will start with the cursor movement menu, and when you press NEW, you will start with the ALPHA menu, but you can switch between these two menus at any time: from the ALPHA menu, pressing EXIT will take you to the cursor movement menu, and from the cursor movement menu, pressing ALPHA will take you to the ALPHA menu.

The cursor movement menu exists in two variations, and which one you see depends on the current display size. The standard case is when the display has three or more rows, in which case the menu will look like

In two-line mode, there are no "up" and "down" arrows, since there is only one line of text being displayed; in other words, the view is like the equation is all on one line, no matter how long it may be. The <← and →> menu keys move left and right by one screenful at a time. And in both two-line and multi-line modes, pressing Shift with a cursor movement key moves as far as you can go in the given direction: to the top or bottom of the text, or to the left or right margin, or to the beginning or the end.

Because of their importance in equations, the characters ( ) [ ] . , = : are assigned to keys of their own in the equation editor, so you don't have to go through the ALPHA menu to type them.

The parentheses, ( and ), are used to control precedence, and to delimit lists of parameters passed to functions; [ and ] are used for indexing matrices and lists; . and , are used as the decimal, interchangeably and independent of RDX. / RDX, mode (note that thousands separators are not allowed in equations); =, when used at the top level of an equation, asserts the equality between the left-hand and right-hand sides of an equation, and in conditional contexts, is the equality test operator; and : is used as a separator, separating the elements in parameter lists, separating the indexes in two-dimensional matrix indexing, and separating the elements in Σ(), ∫ (), IF(), FOR(), and SEQ() expressions and matrix literals.

While in the equation editor, these menus are available: UNITS, the stack menu (R↓), MATRIX, STAT, BASE, CONVERT, hyperbolics (FLAGS), PROB, CUSTOM, PGM.FCN, PRINT, TVM, and CATALOG. The PRINT menu was discussed in the sub-section above; all the other menus only serve the purpose of allowing you to enter functions into equations without having to spell them out letter by letter. Most of these menus have slightly different contents than their RPN-mode counterparts, showing only those functions that can be used in equations, and, in some cases, functions that are available only in equations.

The syntax and semantics is closely modeled after the HP-17B and its siblings. In particular, all the functions listed in Martin Hepperle's "About The Solver in the HP Pocket Calculators" have been implemented.

In compatibility mode, the characters * / [ ] { } ! _ lose their special meanings, and can be used in identifier names. This mode is intended for compatibility with the HP-17B, 19B, and 27S calculators, where these characters have no special meaning and are commonly used in variable names. There are straightforward alternatives for most uses of these characters: instead of *, you can use ×; instead of /, you can use ÷; instead of A[B], you can use ITEM(A:B); instead of A != B, you can use A <> B; instead of A_"B", you can use UNIT(A:"B"); and instead of {A:B:C}, you can use APPEND(NEWLIST:A:B:C). On the other hand, the lack of [ ] means you cannot enter matrix literals, and will have to create empty matrices using NEWMAT, and then use code to populate them.

The equation language defines the following operators, shown in decreasing order of precedence:

`( ) [ ] { }`	Grouping; parameter passing; matrix and list indexing and literals
`^ ↑ _`	Exponentiation and unit attachment
`× * ÷ /`	Multiplication and division
`+ -`	Addition and subtraction; unary plus and minus
`= ≠ <> != < ≤ <= > ≥ >=`	Comparisons
`NOT`	Logical NOT
`AND`	Logical AND
`OR XOR`	Logical OR and XOR
`=`	Equality assertion (top level only)

Expressions operate on variables, number literals, string literals, and matrix literals.

Since equation variables correspond to Plus42 named variables, they can have any of the types that Plus42 variables can, including real numbers without units, real numbers with units, complex numbers, real and complex matrices, strings, and lists.
Matrices and lists can be indexed using square bracket notation or using the special ITEM() function. For matrices, one- or two-dimensional indexing can be used; for lists, only one-dimensional indexing is used. When a matrix is indexed using a single index, the matrix elements are numbered left-to-right and top-to-bottom.
Indexes start from 1, in both one- and two-dimensional indexing. And when lists are indexed for writing, they are resized as needed, so that the assignment succeeds. So, for example, when L(M[10]:5) is executed and M is a list, if it has fewer than 10 elements, it will be resized to 10, so the assignment can succeed. This automatic resizing is not performed while reading from a list, and it is never performed for matrices.

There are a few differences between the equation language of Plus42 and the equation language of the HP-17B and other HP calculators. For compatibility with the HP calculators, Plus42 has a compatibility mode, which can be turned on using the COMP setting in the MODES menu. The standard Plus42 mode is STD.

It may be desirable to mark certain equations for STD or COMP parsing regardless of the global STD/COMP mode setting, for example, if you have mosly STD-type equations where you make full use of Plus42 syntax, but also need to use a small number of COMP-type equations that were originally written for HP calculators, and would be inconvenient to adapt to Plus42 syntax.

To force an equation to be parsed in STD mode, regardless of the global STD/COMP mode setting, simply add :STD: between the function name and the function itself, or add :COMP: for functions that should always be parsed in COMP mode. For functions without names, add the :STD: or :COMP: at the beginning, for example: :STD:function or name:STD:function or name(x:y:z):STD:function, and similarly for :COMP:.

The equation language provides the following built-in functions:


`SIN(X) COS(X) TAN(X) ASIN(X) ACOS(X) ATAN(X)`	Trigonometric functions and their inverses
`SINH(X) COSH(X) TANH(X) ASINH(X) ACOSH(X) ATANH(X)`	Hyperbolic functions and their inverses
`DEG(X) RAD(X)`	Radians-to-degrees and degrees-to-radians conversions (RPN: `→DEG →RAD`)
`LN(X) LNP1(X) LOG(X) EXP(X) EXPM1(X) ALOG(X)`	Natural logarithm, natural logarithm of X+1, and base-10 logarithm, and their inverses (RPN: `LN LN1+X LOG E↑X E↑X-1 10↑X`)
`SQRT(X) SQ(X)`	Square root; square (RPN: `SQRT X↑2`)
`INV(X)`	Reciprocal (RPN: `1/X`)
`FACT(X) GAMMA(X)`	Factorial and Gamma functions (RPN: `N! GAMMA`)
`COMB(X:Y) PERM(X:Y)`	Number of combinations or permutations of Y elements from a set of X
`PI π`	The mathematical constant π
`RAN#`	Returns uniformly distributed pseudo-random numbers greater than 0 and less than 1 (RPN: `RAN`)
`ABS(X)`	Absolute value
`SGN(X)`	Sign function: for real numbers, returns +1 for positive numbers, 0 for zero, −1 for negative numbers, and z/\|z\| for complex numbers. Note that this is different from the RPN function `SIGN` in that the latter returns 1 for zero.
`INT(X) IP(X) FP(X)`	Round to integer toward negative infinity; round to integer toward zero; return fractional part of X, equivalent to X−IP(X)
`IDIV(X:Y) MOD(X:Y)`	Integer division and remainder
`RND(X:Y) TRN(X:Y)`	Round-to-nearest, or round-to-zero, the number X, to Y decimal digits (if Y nonnegative) or to −Y significant digits (if Y negative)
`DATE(X:Y)`	Calculate the date Y days after date X (RPN: `DATE+`)
`DDAYS(X:Y:C)`	Calculate the number of days between dates X and Y, using calendar C, where 1 = Gregorian Calendar, 2 = Calendar without leap days, and 3 = 30-day calendar (RPN: C=1 corresponds to the RPN function `DDAYS`)
`CDATE CTIME`	Returns the current date; current time (RPN: `DATE TIME`)
`HMS(X) HRS(X)`	Convert decimal hours to hours, minutes, seconds, and the reverse (RPN: `→HMS →HR`)
`HMSADD(X:Y) HMSSUB(X:Y)`	Add or subtract times or angles in hours, minutes, and seconds (RPN: `HMS+ HMS−`)
`SIZEC(X) SIZES(X) MROWS(X) MCOLS(X)`	Returns the size of a cash flow list; size of a regular list or the number of elements of a matrix; number of rows of a matrix; number of columns of a matrix
`DEC(X) OCT(X)`	Octal-to-decimal and decimal-to-octal conversions (RPN: `→DEC →OCT`)
`BNOT(X) BAND(X:Y) BOR(X:Y) BXOR(X:Y)`	Bitwise logical operations NOT, AND, OR, XOR (RPN: `NOT AND OR XOR`)
`BNEG(X) BADD(X:Y) BSUB(X:Y) BMUL(X:Y) BDIV(X:Y)`	Binary arithmetic operations (RPN: `BASE+/− BASE+ BASE− BASE× BASE÷`)
`INVRT(X) DET(X)`	Returns the inverse or determinant of the square matrix X
`TRANS(X)`	Returns the transpose of the matrix or vector X
`DOT(X:Y) CROSS(X:Y)`	Dot and cross product
`FNRM(X)`	Returns the Frobenius norm of the matrix or vector X
`RNRM(X)`	Returns the Row norm, or the row sum norm, of the matrix X (this is the maximum of the 1-norms of its rows)
`RSUM(X)`	Returns the vector of sums of each of the rows of the matrix X
`UVEC(X)`	Returns the unit vector for the complex number X, or if X is a vector or matrix, returns X/FNRM(X)
`NEWLIST NEWMAT(R:C)`	Create a new list, or a new matrix with R rows and C columns. Note that NEWLIST does not take any arguments; it always returns an empty list. Lists are resized as needed, whenever they are written to.
`NN→S(X) N→S(X) S→N(X) N→C(X) C→N(X) APPEND(X:Y:...) EXTEND(X:Y) HEAD(X) TAIL(X) LENGTH(X) POS(X:Y) POS(X:Y:Z) SUBSTR(X:Y) SUBSTR(X:Y:Z) REV(X)`	List and string functions. These simply correspond to the RPN functions with the same names, except for APPEND, HEAD, and TAIL. APPEND can take 2 or more parameters, with the first being a list and the remaining parameters being any type, and adds the second and subsequent parameters to the end of the list, each parameter being added as a separate element. HEAD(X) returns the first element of the list or string X, or `{}` or `""` if the list or string is empty. TAIL(X) returns the list or string X, with its first element or character removed, or `{}` or `""` if the list or string is empty.
`#T(X:Y) FLOW(X:Y)`	Return the Yth count or the Yth flow from cash flow list X
`ITEM(X:Y) ITEM(X:Y:Z)`	Return the Yth element from list or matrix X, or the element at row Y and column Z from the matrix X. Equivalent to X[Y] and X[Y:Z], but works even in compatibility mode.
`RCOMPLX(RE:IM) PCOMPLX(R:PHI)`	Construct a complex number using real part RE and imaginary part IM, or using magnitude R and angle PHI. Note that internally, complex numbers are always represented in rectangular form.
`RADIUS(RE:IM) RADIUS(Z) ANGLE(RE:IM) ANGLE(Z)`	Get the magnitude and angle of a complex number, which may be provided either as separate real and imaginary parts, or as a complex number object.
`XCOORD(R:PHI) XCOORD(Z) YCOORD(R:PHI) YCOORD(Z)`	Get the real and imaginary parts of a complex number, which may be provided either as a separate magnitude and angle, or as a complex number object.
`UNIT(X:Y)`	Construct a unit object from a real number X and a unit string Y. equivalent to X_Y, but works even in compatibility mode.
`UBASE(X)`	Converts X to its base unit.
`UVAL(X)`	Returns the value of X, discarding its unit, if any.
`ΣX ΣX2 ΣY ΣY2 ΣXY ΣN ΣLNX ΣLNX2 ΣLNY ΣLNY2 ΣLNXLNY ΣXLNY ΣYLNX`	Statistics sums, accumumated by the RPN Σ+ function (read-only)
`MEANX MEANY SDEVX SDEVY WMEAN`	Mean of X and Y; sample standard deviation of X and Y; weighted mean of X with weights Y; for the data accumumated by the RPN Σ+ function (read-only)
`CORR SLOPE YINT FCSTX(X) FCSTY(X)`	Correlation coefficient, slope, Y intercept, and backward and forward forecasting, using the statistics sums the RPN Σ+ function and the currently selected fitting model. CORR, SLOPE, and YINT are read-only; FCSTX and FCSTY behave like normal invertible functions.
`N(I%YR:PV:PMT:FV:P#YR:BEGIN) I%YR(N:PV:PMT:FV:P#YR:BEGIN) PV(N:I%YR:PMT:FV:P#YR:BEGIN) PMT(N:I%YR:PV:FV:P#YR:BEGIN) FV(N:I%YR:PV:PMT:P#YR:BEGIN)`	TVM: Calculate N, I%YR, PV, PMT, or FV, in terms of the other four, with P#YR the number of payments per year, and BEGIN=1 for payments at the beginning of the period, and BEGIN=0 for payments at the end.
`SPPV(I:N) SPFV(I:N) USPV(I:N) USFV(I:N)`	Present and future value of a unit, with interest rate I and N periods, for Single Payment or Uniform Series.
`REGX REGY REGZ REGT LASTX STACK[N]`	Read-only access to the RPN stack
`MIN(X1:X2:...) MAX(X1:X2:...)`	Return the smallest or largest of its arguments. Any number of arguments is allowed.
`REAL?(X) CPX?(X) MAT?(X) CPXMAT? STR?(X) LIST?(X) EQN?(X) UNIT?(X) TYPE?(X)`	Test whether X is a real number, a complex number, a matrix (real or complex), a complex matrix, a string, a list, an equation, or a number with an attached unit; return an integer indicating the type of X, like the RPN TYPE? function
`Σ(VAR:FROM:TO:STEP:EXPR)`	With the variable VAR going from FROM to TO in steps of STEP, calculate the sum of evaluating EXPR once for each value of VAR.
`∫(EXPR:VAR:LLIM:ULIM:ACC)`	Integrates the expression EXPR with integration variable VAR going from LLIM to ULIM, with relative accuracy ACC. The ACC parameter is optional; if omitted, the value of the variable ACC will be used, if it exists, or otherwise, the integral will be calculated with maximum precision.
`IF(A:B:C)`	If A is 'true', returns B, else C.
`FOR(INIT:COND:NEXT:EXPR:...) BREAK CONTINUE`	After evaluating the initialization expression INIT, starts executing these steps in a loop: first, evaluate COND, and if it returns 'false', exit the loop; evaluate EXPR and any additional expressions that follow; evaluate NEXT; repeat. When it finishes, FOR returns the value returned by the last EXPR to be evaluated, or the value returned by INIT if the loop body was never executed at all, that is, if COND returned 'false' the first time it was called. Within the list of expressions `EXPR:...`, the special expressions BREAK and CONTINUE may be used. BREAK ends the FOR loop immediately, and CONTINUE ends the current execution of the `EXPR:...` list, proceeding to NEXT and the next iteration.
`SEQ(EXPR1:EXPR2:...)`	Evaluates EXPR1, EXPR2, etc., in sequence, and returns the value that was returned by the last expression. This may be used when multiple expressions need to be evaluated in a context that normally allows only one.
`XEQ(NAME:X1:X2:...)`	Calls the user code program starting with LBL "NAME". The parameters X1, X2, etc., will be assigned to the MVAR parameters declared by the program, or pushed onto the stack if the program has no MVAR declarations. The return value will be whatever is left in the X register when the program returns.
`EVALN(NAME:X1:X2:...)`	Calls the equation stored in the variable named "NAME". The parameters X1, X2, etc., will be assigned to the equation's declared parameters.
`FunctionName(X1:X2:...)`	Calls the equation named FunctionName in the equation editor's list. The parameters X1, X2, etc., will be assigned to the equation's declared parameters.
`STOP(X)`	Inserts a STOP in the generated code. Meant for debugging. In terms of function evaluation, it simply returns its argument unchanged, and it is invertible.
`L(NAME:VALUE) G(NAME)`	Assign the value VALUE to the variable named NAME, or get the value of the variable named NAME. In `STD` mode, this works on all variables, including the local variables created by Σ() and when calling named equations; in `COMP` mode, L() and G() only work on global variables. NAME may be an array element, so you can say things like L(A[B]:C). Note that when writing to a list in this way, the list will be expanded, as needed, to make sure index B exists.
`S(NAME)`	Returns 'true' if the function is being called by SOLVE and NAME is the variable being solved for; returns 'false' in all other situations.

You may have noticed that equations are stored in the EQNS list in parsed form, but how and when do functions actually get parsed?

The answer is that equations are always parsed before being stored in EQNS, and, if necessary, they are parsed again by CALC.

Equations can be stored in EQNS in three ways: by exiting the equation editor without cancelling; by pasting into the equation list; and by inserting an equation into the equation list using RCL. In each of those cases, Plus42 will attempt to parse the equation, and if successful, it will store the resulting equation object in EQNS. If the parse is not successful, it will not report an error, but instead simply store the equation as an unparsed string, so you can revisit and correct it later.

When CALC is pressed, and the currently selected equation is an unparsed string, it will then attempt to parse the string, and if successful, store it in EQNS; if the parse fails, an error will be reported, since CALC absolutely needs a parsed equation in order to proceed.

If the currently selected equation is a parsed equation object, it is used as is. However, there is one additional case, where the equation will be parsed again, even though it had already been parsed successfully, and that is the case where the global compatibility mode setting has changed (STD or COMP in the MODES menu; see the section about Compatibility Mode, above). This behavior ensures that equations without embedded :STD: or :COMP: tags will always behave in accordance with the current STD or COMP mode setting when used by CALC, while also making sure that equations aren't parsed any more often than necessary. This last consideration is significant because equation objects include not just the equation text, but also associated data structures and generated code. This means they are rather heavyweight data structures, and they should be reused and shared whenever possible.

When equation objects are copied (using ENTER, DUP, STO, RCL, etc.), the copies actually all point to the same internal data structures, so once an equation object is created by PARSE, creating additional copies of it is a very inexpensive operation. But if an equation string is parsed again and again, each parse operation creates a brand new equation object, and there is no sharing in that case. Thus, it makes sense to parse an equation as soon as possible and then copy the parsed equation object as necessary, and the behavior of EQN with regards to parsing is designed with this in mind.

When SOLVE is used with equations, it will try to apply the direct solver first. The direct solver works by rearranging the equation, so that the variable to be solved for is isolated by itself on one side of the equals sign.

This works by using substitutions like these (assuming the variable to be solved for is X):

This approach only works if the variable to be solved for occurs only once in the equation, and if all the functions that have to be inverted have explicit inverses, and if no divisions by zero occur during the rearrangement.

If the direct solver can't be used, SOLVE will fall back on using the numeric solver instead. This is the same solver that is used for solving programs. The HP-27S and HP-17B/19B manuals refer to it as the iterative solver.

You may force SOLVE to always use the numeric solver, by setting NUMERIC mode in the MODES menu. To allow the direct solver to be used, set DIRECT mode instead. (DIRECT mode is the mode that is initially set, when the calculator is first turned on.)

Equations can be named with parameter lists: FUN(X:Y):X^2−2*X*Y+Y^2. Such equations can be called like functions from other equations.

Functions may return complex results, depending on the HP-42S REALRES/CPXRES mode setting.

NOTE: Programs, whether they have MVARs or not, must not change or drop anything that's on the stack, apart from consuming their parameters and leaving their return values. They will be called in NSTK mode, and the stack will contain whatever intermediate results exist from the evaluation of the current expression. Programs with MVARs should take their parameters only from their named parameters, and programs without MVARs should consume only as many levels from the stack as they need parameters, and leave the rest alone; and all programs, whether with MVARs or without, should leave only one result on the stack.

Future versions of Plus42 may include logic to protect the stack from undisciplined programs, but for the time being, programs called from equations using XEQ() must be well-behaved, or else the outcome of equation evaluation will be undefined.

Equations can be shared with the RPN (HP-42S-based) environment using STO and RCL in the list view. STO will offer to write the current equation to the X register, ALPHA register, or current program location, and RCL can retrieve equations from those same places.

In the RPN environment, equations may be used in much the same way programs can, using a parallel set of functions: EVALN instead of XEQ, EQNSLV and EQNINT instead of PGMSLV and PGMINT, EQNMENU and EQNMNU1 instead of VARMENU and VARMNU1, and EQNVAR instead of PGMVAR (formerly PRMVAR, the function that prints all of a program's associated variables).

You can also play with equations without ever using the equation editor: first, create the equation as a string using XSTR, or by pasting the text from a text editor; then use PARSE to convert the string in the X register to an equation object. EVAL evaluates the equation object in the X register, and is exactly equivalent to EVALN ST X.

Note that XSTR will only let you enter up to 50 characters when you use it interactively, but when created by pasting text, XSTR commands in programs can be up to 65535 characters long, and string objects (on the stack and in variables) don't have a length limit at all.

Units and Conversions

Plus42 supports numbers with attached units. For exampe, the quantity of two and a half kilometers can be represented as 2.5_km, with number and unit joined together. When calculations are performed with such number-unit pairs, the necessary conversions take place automatically, and if an operation is impossible because the units are incompatible — such as when trying to add a length to an area — an error message is shown.

You can access units by pressing the UNITS key, or by selecting the UNITS catalog in the CATALOG menu. The two are equivalent; the UNITS key is just a shortcut to access the units catalog with fewer keystrokes.

The units catalog is divided into 16 sections, each containing units of similar quantities: LENG for units of length, POWR for units of power, ELEC for various electrical units, and so on.

You use the units in the units catalog by applying them to the number in the X register. The X register must contain either a simple real number without a unit, or a number that already has a unit; you cannot attach units to complex numbers, matrices, or other types. To apply a unit to the number in the X register, simply press its key. For example, if you're in the LENG section and the X register contains the number 2.78, pressing cm applies the centimeter unit, and the result is 2.78_cm.

You can combine units; for example, to enter "five Newton-meters", type 5 FORCE N EXIT LENG m, to get 5_N*m. To divide by a unit instead of multiplying, press Shift: to enter "55 volts per meter", type 55 ELEC V EXIT LENG Shift m, to get 55_V/m. And you can enter powers of units by entering them multiple times: to enter "9.80655 meters per second squared", type 9.80655 LENG m EXIT TIME Shift s Shift s, to get 9.80655_m/s^2.

The real power of attached units lies in the fact that you can perform calculations with them. The result of the calculation will have the appropriate unit, and any necessary conversions will be performed automatically. For example, 25_m 3_s ÷ gives 8.3333_m/s.

When adding or subtracting, the result of the operation will have the same unit as the number provided in the X register. So, for example, the result unit of adding one foot and one meter depends on the order of the operands: 1_m 1_ft + gives 4.2808_ft, while 1_ft 1_m + gives 1.3048_m.
This behavior can be used to convert numbers to different units, by adding zero with the desired unit attached. For example, to convert 12 miles to kilometers: 12_mi 0_km +, to get 19.3121_km.

When units are combined in multiplication or division, the resulting unit is simplified by combining or cancelling identical units, but no conversions are performed. This means that m^2 divided by m gives m, but yd divided by ft gives yd/ft: while yards and feet are compatible units, they are not identical, so they are not cancelled against each other automatically. Of course, if you happen to know the unit of the result, you can use conversion to force the unit to be normalized; for example, if you already know that yd/ft is dimensionless, you can simply add zero: 1_yd/ft 0 + gives 3, or 1_acre*ft 0_gal + gives 325852.7320_gal.
Other ways of normalizing units are discussed below.

The UNIT.FCN menu contains a few functions that can be useful when working with units, particularly when using units in programs, but also when using units in manual calculations:

CONVERT Converts the number in the Y register to the unit in the X register. Only the unit part of the number in the X register is used; the value part is ignored.
In practice, it will usually be more convenient to add zero with the desired unit, rather than use the CONVERT function.

UBASE Converts the number in the X register to its base unit. All units defined in Plus42 are defined in terms of these base units: m, s, kg, mol, K, A, r, sr, and cd, and every derived unit can be expressed as some unique combination of these base units. UBASE finds this unit and converts the number in X to it.

UVAL Returns the value part of the number in X, discarding its unit. No conversions are performed.

UFACT Factors out the unit in X from the number in Y. Only the unit part of the number in the X register is used; the value part is ignored.
Use this function if you want a unit to be expressed in terms of a specific other unit. For example, say you have a speed in mph, and you want to see it in terms of meters: 15_mph 0_m UFACT, to get 11.176_m/s.

→UNIT Applies the unit in X to the dimensionless number in Y. Only the unit part of the number in the X register is used; the value part is ignored. For example: 3.16 125_m →UNIT, gives 3.16_m.

UNIT→ Splits the number in X into its value (the same value that is returned by UVAL) and its unit, attached to 1. For example, 40076_km UNIT→, gives 40076 in Y and 1_km in X. It is valid to apply this to a number without a unit, in which case 1 will be returned in X.

UNIT? Tests whether the object in the X register is a number with a unit or not. This is a do-if-true conditional, meaning it displays Yes or No, as appropriate, when executed from the keyboard, or it either does not, or does, skip the next instruction, while running a program.

Instead of using the UNITS catalog, you can also enter units by typing them directly, letter by letter. This is only possible during number entry, and is convenient primarily when using Plus42 on computers with a full keyboard.

To attach a unit to a number being entered, press Shift .. An underscore will be appended to the number, which may be hard to spot at first because the number entry cursor is also an underscore. Once you do this, the ALPHA menu will be activated, and you can then enter the unit letter by letter. Bear in mind that units are case-sensitive, so don't type KM when you mean km.

If you want to cancel entering the unit, you can backspace until you're back at the number part, or press EXIT to remove the unit all in one go. When finished entering the unit, press ENTER; this only ends number entry, but does not perform the usual RPN duplication of the X register.

You can define your own units, and use them just like the pre-defined ones. These user-defined units can be derived units, that is, defined in terms of pre-defined units and/or other user-defined units; or they can be base units, not defined in terms of anything else, and not touched by UBASE.

To define a derived unit, simply create a number that represents the value of 1 of that unit, and then store it as a variable, giving it the name you want to use for the unit.

For example, to define "pond", a customary Dutch unit equal to half a kilogram, do 0.5_kg STO "pond". To see that this works, try converting 15 pond to kilograms: 15_pond 0_kg +, to get 7.5_kg.

You may define dimensionless constants by using the unit one, which simply represents the number 1. For example, to define tau, a constant sometimes used to represent 2π, do 2_one π × STO "tau".

For easier entry, you can assign user-defined units to the CUSTOM menu. This works like any other assignment: ASSIGN "pond" TO 01, ASSIGN "tau" TO 02, etc. When a unit is assigned to CUSTOM, you can multiply by that unit by simply pressing its key, or divide by that unit by pressing Shift followed by its key. And you can convert to that unit as you would with any other unit, by attaching it to 0 and then adding.

To define a base unit, store the special value 0_one. User-defined base units behave just like pre-defined base units. For example, let's define a base unit named USD, to represent U.S. Dollars: 0_one STO "USD", and then calculate the cost of 10 yards of fabric, sold at a price of 5 dollars per foot: 5_USD/ft 10_yd ×, gives 50_USD*yd/ft; normalize: UBASE, gives 150_USD.

Note that since user-defined units are simply variables, a user-defined unit only works as long as it is visible. This means you'll probably want to store your user-defined units in the HOME directory, or in a directory that is included in the PATH list. See the section on directories for more information about directories and variable lookups.

Units work with arithmetic (including STO and RCL arithmetic), 1/X, X^2, SQRT, and Y^X (integer and 1/integer exponents only), %, %CH, IP, FP, RND, ABS, SIGN, MOD, SOLVE, INTEG, and PLOT. They cannot be stored in matrices or numbered registers, but they can be stored in named variables and lists.

With Y^X with 1/integer exponents and SQRT, all the units must have powers divisible by the exponent, since units with non-integral exponents are not allowed, unlike on HP calculators. Also, SIN, COS, TAN, →REC, and COMPLEX in POLAR mode will recognize angles with angular units and treat them appropriately, ignoring the current angle mode.

Units are supported in equations. The syntax is slightly different from units in normal RUN and PRGM modes, in that the units must be enclosed in double quotes. So, instead of 16_oz, you write 16_"oz". What's going on here is that the units are actually string literals, and _ is a multiplicative operator that creates a unit object from a number on its left and a string on its right.
In compatibility mode, _ is an identifier character, so it's not available to use as an operator; in this case, the syntax UNIT(16:"oz") can be used instead.

Directories

In Plus42, internal storage is organized in directories. A directory can contain programs, variables, and other directories. There is always at least one directory, called HOME, which is created when the app creates a new state, and which cannot be deleted.

Because of the importance of directories, the path of the currently active directory is always displayed at the top of the screen. Initially, it will say { HOME }, but when you create and change directories, it will show a list of directories, always starting with HOME and ending with the name of the current directory, with the chain of ancestor directories in between.

Use DIRS to navigate the directory hierarchy. DIRS actually opens a special section of CATALOG, which you can also reach using the CATALOG menu. The DIRS catalog provides a view of the current directory; it allows you to move between directories, in addition to showing you the programs and variables that are in the current directory.
Unless you're looking at the HOME directory, the DIRS catalog always starts with .., which moves to the parent directory of the current directory; the HOME directory is at the top of the directory hierarchy, so it has no parent.
Following the .., also shown on black keys, are the current directory's sub-directories, if there are any. Next, shown on white keys, are the programs in the current directory; this is the same list that you see when you press GTO. And last, shown on black keys, are the variables that exist in the current directory; this is the same list that you see when you press RCL.

When you press a directory key, the selected directory becomes the current directory; when you press a program key, an XEQ to the corresponding LBL or END is performed; and when you press a variable key, that variable is RCLed. And when you press Shift followed by a directory, program, or variable key, a Reference to that item is created and placed on the stack; references and their uses are discussed later in this section.

Directories are manipulated using commands found in the DIR.FCN menu. It contains these functions:

CRDIR (or MKDIR) Creates a new directory. This directory will become a child of the current directory.

CHDIR Changes into a subdirectory. The selected directory will become the new current directory. This is also the action that is performed when you press a directory key in the DIRS catalog.

UPDIR Changes into the current directory's parent directory. This is also the action that is performed when you press the .. key in the DIRS catalog.

HOME Changes into the HOME directory. Remember, HOME is the un-deletable and un-renameable top of the directory hierarchy.

PATH Returns the path to the current directory, as a string formatted like HOME:FOO:BAR:BAZ, in which BAZ is the current directory, BAR is the current directory's parent, FOO is BAR's parent, and so on until HOME.

RENAME Renames a directory. To rename the directory FOO, located in the current directory, to BAR, place the string "BAR" in the ALPHA register, and then perform RENAME "FOO". Note that moving a directory to a different directory requires a different function; this is discussed later in this section.

PGDIR (or RMDIR) Deletes ("purges") a directory. This will delete the named directory and all its contents, including sub-directories, so use this with caution!

PRALL Prints a summary of all directories and their contents, in a hierarchical, indented format. Programs are shown with their sizes, and variables are shown with their types, and, in the case of matrices and lists, also their sizes, but the contents of programs and variables are not shown.

All operations that access programs or variables operate primarily within the current directory, but programs and variables in ancestor directories will also be found, for operations that don't modify or delete their targets. So, for example, if no variable named "A" exists in the current directory, RCL "A" will look for it in the ancestor directories as well, and similarly, XEQ "Q" will look for LBL "Q" in ancestor directories if it isn't found in the current directory. But STO "A" will always create or update the variable "A" in the current directory; even if "A" does not exist in the current directory but does exist in an ancestor directory, STO "A" will create a new variable "A" in the current directory, leaving the "A" in the ancestor directory alone.

Operations that read and modify their targets will only work when their targets are in the current directory. So, for example, attempting to edit a program that isn't in the current directory will result in a Restricted Operation message, and attempting to modify a variable that isn't in the current directory will result in a Variable Not Writable message. Specifically, Variable Not Writable will happen with STO+, STO−, STO×, STO÷, X<>, ISG, DSE, and HEAD.

Sometimes, you may want to move items from one directory to another, or create copies. Plus42 supports these kinds of operations using Reference objects.

In the DIRS catalog, pressing Shift followed by a directory item generates a "reference" object. This is a type of object that contains no data of its own, but only acts as a pointer to something else. This is similar to a "shortcut" or "symbolic link" in desktop environments.

Creating a reference object while there is a reference in the X register already causes a list object to be created, with both reference objects inside. Creating further reference objects adds them to this list. This is to make it convenient to create sets of references, so you can move or copy a group of items all at once. Note that you can even add references to objects from multiple directories to the same list, so this is a very flexible and powerful means of creating selections.

These reference objects, and lists containing only reference objects, serve one and only one purpose: they can be fed to the new REFMOVE, REFCOPY, and REFFIND functions.
(Actually, that is not quite true; directory references are also used in the PATH list. This is covered later in this section.)

REFMOVE Moves the referenced objects into the current directory. In case of a list, the objects are added in the order in which they appear in the list, and they are added in front of the already existing objects. Note that it is possible to move objects within a directory as well, which can be useful if you want to change the order in which they appear in the catalogs.

REFCOPY Works like REFMOVE, except it copies items instead of moving them. However, directories and variables within the current directory are never copied, always just moved. (Programs are copied.)

REFFIND Finds the real object referenced by the reference in X. (This only works when X contains a single reference object, not a list.) It changes to the referenced directory, and moves to the referenced program or VIEWs the referenced variable.

For convenience, the REFMOVE, REFCOPY, and REFFIND commands are mapped to the keyboard when objects of the appropriate types are in the X register; REFMOVE is −, REFCOPY is ×, and REFFIND is ÷.

For example, let's say you have variables A, B, and C, which you want to move from directory FOO to directory BAR, and both FOO and BAR are children of HOME. Here is how you could accomplish this: DIRS, then press .. until you're at HOME, then press FOO to go to the FOO directory; Shift A Shift B Shift C (there will now be a 3-item list in the X register); .. BAR (to go to the BAR directory); − (REFMOVE, to move the three items to BAR).

A few more words about the reference objects themselves:
References are created by pressing Shift followed by a DIRS menu item. Pressing a directory item causes a directory reference to be created, and pressing a LBL or END item causes a program reference to be created, and pressing a variable item causes a variable reference to be created. Pressing Shift .. is special: it causes a reference to the current directory to be created, not to the parent directory as you might expect.

Reference objects can only be used as input for REFMOVE, REFCOPY, and REFFIND, as mentioned above, but the way they are displayed is designed to at least make it reasonably obvious to the user just what they are referring to. This works as follows:

Directory references look like Dir[2] "HOME". The word Dir indicates the type of reference, and the number in square brackets is the directory ID. This ID is assigned to a directory when it is created, and it never changes, even if the directory is moved or renamed. The name that is shown after the Dir[ID] part is the current name of the directory with that ID; the name is not actually a part of the reference object. So, if you create a directory reference, and then rename that directory, the reference object will be displayed with the updated name.

(Note: directory ID 2 is the HOME directory. All other directories will have numbers greater than 2. The number 1 is used internally to represent an invisible directory, where generated code for equations is stored; and numbers ≤ 0 are used internally to represent levels on the RTN stack where local variables are stored.)

Program references look like Pgm[5:1] "FOO". The word Pgm indicates the type of reference; the first number in square brackets is the ID of the directory where the program is located, and the second number in square brackets is the index of the program within that directory. The name that is shown after the Pgm[ID:Index] part is the first global label found in that program; for programs that don't contain any global labels, END or .END. is shown instead.

As with the directory names shown in directory references, the global label names shown in program references are only shown for the convenience of the user. They aren't actually part of the reference objects themselves. Also, note that when you insert or delete programs, references to programs with higher indexes within that same directory will end up pointing at other programs. Unlike directory IDs, which never change, program indexes simply represent the positions of programs in their containing directories, and those positions can change.

Variable references look like Var[5:"A"]. The word Var indicates the type of reference; the number is the ID of the directory of the variable is located, and the name is simply the variable's name. Unlike with directory and program references, where the directory or label names aren't actually part of the reference objects and only shown for the convenience of the user, the names in variable references are part of the reference; these names are how they are represented to the user and how the system keeps track of them internally. This is the reason why the variable names are shown inside the brackets, to highlight the fact that they are a part of the reference objects themselves.

As was mentioned earlier, operations that perform read-only access to programs and variables, like GTO and RCL, will look for their targets in the current directory first, but if they don't find them there, will also try the current directory's ancestors, up to and including HOME.

For programs and variables that you want to be able to access from anywhere, you can use the PATH variable. This is a list, which the system looks for in the HOME directory, containing references to directories. If a program or variable was not found in the current directory or its ancestors, the directories in PATH are tried next, from first to last. (If PATH contains items that aren't directory references, they are simply ignored.)

(Note: Actually, the above isn't the whole story. When a running program performs a GTO or XEQ to a global label, and it isn't found during the search of the current directory and its ancestors, the next step is to look for it in the directory where the currently running program resides, and its ancestors. Only when that second search has also failed to find the label, will the PATH list be searched.
Note that this only applies to label searches, and only from running programs.)

Many functions, including GTO and RCL but also most other functions that access global labels or named variables, will pop up a menu of eligible labels or variables for the user to choose from, so they don't have to be spelled out each time. In Plus42, these menus will show eligible items from the current directory on black menu buttons, and any eligible items from ancestor directories, or from directories referenced by the PATH list, using white menu buttons. Note that the list of eligible items will depend on the operation being performed, so RCL may show items from ancestor directories, but STO or CLV never will.

The current program is the program you'll see when you enter PRGM mode, and that will execute when you press R/S or SST. The current directory is where functions like GTO and RCL will start looking for global labels and named variables.

What can be confusing is that the current program isn't necessarily in the current directory. When you change directories using CHDIR, the current program does not change along with it, and conversely, when the current program is changed by GTO or XEQ, the current directory does not change along with it, either.

You can tell when the current program is not in the current directory when you switch to PRGM mode. If the triangle that indicates the current program line is solid black, the current program is in the current directory; if it is a hollow triangle, the current program is not in the current directory. The distinction matters, because you can only edit programs that are in the current directory.

If you are looking at a program and are unable to edit it because it isn't in the current directory, performing GTO . . will change the current directory to the program's directory. You can see the effect because the hollow triangle will turn solid black, and the directory shown in the header will change. Or, approaching it from the other side, when you perform GTO "label" while not in PRGM mode, the current directory will automatically be set to the directory where the target LBL was found.

Note: It is possible to step into generated code, that is, programs that are created by Plus42 when it parses equations. For example, if you execute a program fragment like XSTR "A+B*C" PARSE EVAL, the PARSE will translate the equation to an RPN program, and store it in the invisible directory with ID 1, and EVAL will call that generated code, somethat like XEQ. When you SST the EVAL, you will next find yourself single-stepping the generated code.

This is perfectly legal and safe, but you will not be able to use the GTO . . trick to make directory 1 the current directory, and start editing the generated code. When in generated code, GTO .. simply does what it usually does, which is to create a new empty program at the end of the current directory, and make that the current program.

Big Display

When Plus42 creates a new state, by default it now creates a display with 8 rows by 22 columns.
The DISP menu contains several functions for adjusting and querying the display size. They are:

ROW+ and ROW− Increase or decrease the number of rows. The minimum number of rows is 2 and the maximum is 99.

COL+ and COL− Increase or decrease the number of columns. The minimum number of columns is 22 and the maximum is 999.

GETDS and SETDS Get or set the display size. GETDS returns the number of rows in Y and the number of columns in X, and SETDS sets the display size. The number of rows passed to SETDS must be between 2 and 99, and the number of columns must be between 22 and 999. Unlike ROW+, ROW−, COL+, and COL−, GETDS and SETDS are programmable.

WIDTH and HEIGHT Get the display size, in pixels. The main use of these functions is to make programs that use PIXEL and AGRAPH resolution-independent: instead of hard-coding the display width as 131 and the display height as 16, as you would when programming Free42 or the real HP-42S, use WIDTH and HEIGHT, and you can make your programs work regardless of the screen size that happens to be in effect. This kind of modification works perfectly with the DPLOT program from the HP-42S Owner's Manual, for example.

HEADER This function turns the information header on or off. The header shows the current directory, and also the BEGIN/END and P/YR mode, while the TVM menu is active, and the word size and signed/wrapped modes, while the BASE menu is active. It is only shown when the number of rows is set to 4 or greater, but it can be disabled altogether using this function, to free up even more room for stack or program display.

1LINE and NLINE These functions control how matrices and lists are displayed, when they are in the X register and the number of display rows is set to 3 or greater. In 1LINE mode, matrices and lists are shown in compact format, that is, like [ 25x1 Matrix ] or { 3-Elem List }, which is the format used in Plus42 before release 1.0.17. In NLINE mode, they are shown expanded, so you can actually see their contents without needing to print them or having to use EDIT.
Note that objects in the other stack registers / levels are always displayed in compact format, and everything is shown in compact format when the display is set to 2 rows.

Financial Functions

Plus42 has a TVM menu, containing functions for Time Value of Money calculations, and to calculate and print amortization schedules. This functionality is closely modeled after the TVM menu found on the HP-17B, but should also be familiar to anyone who has used the HP-19B or its variants.

N, I%YR, PV, PMT, and FV The standard functions for compound interest. Entering a number and pressing one of these keys stores the number, while pressing one of these keys right after another one calculates the quantity from the other four.

A simple example: If you borrow $10,000 at 5% annual interest, and make monthly repayments of $100, how long will it take to pay off the loan?

Shift DISP FIX 02 Shift TVM
5 I%YR 10000 PV −100 PMT
(note: PV is positive because it is money you receive, and PMT is negative because it is money you pay; you could change the sign of both numbers, performing the calculation from the point of view of the lender)
0 FV N

BEGIN and END Select whether payments are made at the beginning or at the end of each period.

With the amortization menu, you can calculate and print amortization schedules, where you can see how much of your payments go toward interest and how much toward the principal, and see the remaining balance. The calculations can be performed in steps of one or more periods. The initial values for the calculation are taken from the I%YR, PV, and PMT settings from the main TVM menu, taking the same P/YR and BEGIN/END settings into account.

For example, to calculate an amortization schedule for the same $10,000 loan used in the example above:

This is the summary from before any repayments have been made. On the top line, #P indicates the number of payments that will be calculated at the next step, and PMTS indicates which payments have been made at the previous step. The payments are numbered starting at 1, so 0-0 indicates that no payments have been made yet.
Pressing NEXT calculates one step, that is, one sequence of #P payments:

You can see that with each payment, the amount that goes towards interest is a bit less than the payment before, reflecting how the principal is gradually getting smaller.

The INT, PRIN, and BAL keys let you recall the current Interest, Principal, and Balance, so you can use them in calculations. You may also need them if you are using a skin that displays fewer than 4 rows, since Plus42 won't be able to display all three of these numbers simultaneously then.

To generate a printed amortization table, press TABLE. Then, use FIRST, LAST, and INCR to specify the first and last payments to tabulate, and the number of payments to calculate together at each step. Then, press GO to generate the table, which will appear in the Print-Out window. (Note that printing must be enabled! Use PRON in the PRINT menu if this not the case.)

Note that the FIRST may be greater than 1; in this case, the payments before FIRST are not printed, but they are taken into account in the remainder of the calculation.

To conclude with an amortization table for the same loan as above, printed in steps of one year:

Note how the balance changes sign at the end, since before the last payment, the remaining balance is actually less than the value of PMT. The calculation does not take this into account, and will just keep going, even after the balance has been paid in full.

Function Plotting

Plus42 offers a simple built-in two-dimensional function plotter. You use this to make XY function plots, that is, plot how the value Y of a given function varies as the independent variable X traverses a given range. The PLOT menu has five functions for configuring the function to be plotted, plus the PLOT function itself, which performs the actual plot, and then segues into the plot viewer, where you can take sample points, find roots, and calculate integrals. This section will cover all functions in the order in which they appear in the main PLOT menu, which is also the order in which you will use them to go from selecting a function to viewing the actual plot.

First, enter the PLOT menu by pressing Shift PLOT. The first two functions in the menu are for selecting the program or equation to plot:

PGMPLOT (abbreviated PGM): select a program to plot. When you press PGMPLOT, you will be presented with a menu of global LBLs; this will include LBLs with MVAR declarations, but also those without, both kinds are supported.

EQNPLOT (abbreviated EQN): select an equation to plot. When you press EQNPLOT, you will be presented with a menu of equations stored as named variables. Note that the equations you keep in Equation Mode are stored separately, in a list named EQNS, and these are not available for selection with EQNPLOT, but you can select them for plotting as well, in two ways. One is to use STO in Equation Mode to store the equation in the X register, and then, in normal mode, use EQNPLOT ST X; the other, more convenient, is to select the equation to be plotted in Equation Mode, and then simply press PLOT. This will select the equation for plotting, and leave Equation Mode and enter the PLOT menu, all in one step.

You can review which program or equation you have selected, at any time, by pressing Shift-PGM or Shift-EQN. Both have the same effect, you don't have to remember whether you had selected a program or an equation. If you had selected a program, Shift-PGM and Shift-EQN will show the label name, in double quotes; if you had selected an equation, they will show you the equation. In addition, the label name or equation will be placed in the X register.

PARAM The next step is to specify the independent and dependent variables, referred to as the X Axis and the Y Axis, or simpy X and Y, in the following. The PARAM menu lets you configure these. Press PARAM and you will enter a new menu, with two functions: XAXIS and YAXIS, and the currently defined parameters will be shown at the top of the screen. By default, both will be set to use the stack: X:<STK> Y:<STK>.
Note: you may review the PARAM settings without entering the PARAM menu, by pressing Shift-PARAM.

If the currently selected program or equation has no named parameters, then there is nothing to choose; the parameter will be passed to the program or equation in the X stack register, indicated by X:<STK>, and the return value will also be expected in the X stack register, indicated by Y:<STK>.

If the program or equation does have named parameters, then pressing XAXIS and YAXIS let you specify which one should be plotted on the X axis and which one should be plotted on the Y axis. It is possible to specify a named parameter for X, and take the result from the stack, or to specify named parameters for both X and Y, but it is not allowed to provide the parameter on the stack while using a named parameter for the result. When X is set to <STK> and you press YAXIS, the message Restricted Operation is shown to indicate that this is not allowed, and conversely, whenever you set X to <STK>, Y is automatically set to <STK> as well.

Note that setting a named parameter for Y means PLOT will have to use SOLVE. That is, if you set Y:A, for example, PLOT will call SOLVE "A" for every point it plots. For starting values, it will pass YMIN and YMAX to SOLVE each time.

CONST For programs with MVAR declarations, and for equations with named parameters, you should set values for all parameters that are held constant during the plot, that is, that are not assigned to either the X or the Y axis. Pressing CONST presents a menu of all parameters, which you can use to store or review these values.

Pressing Shift-CONST will print all parameters, with their current values, without entering the CONST menu. This is equivalent to using the PGMVAR or EQNVAR functions.

VIEW This is where you specify the plotting range. You must specify the range for the independent variable, that is, set XMIN and XMAX. For the dependent variable, you may enter YMIN and YMAX by hand, or you may press SCAN, which will evaluate the function at every 10th point, to estimate the required plot range.

You can press Shift-XMIN, Shift-XMAX, etc., to review the current setting of each of the four limits; this displays them and also recalls them to the stack. Or you may press Shift-SCAN, to view all four limits at once.

PLOT This starts the plot. For most functions, the plot should finish within seconds, but functions using SOLVE or INTEG, or both, may plot a lot slower. If you find the plot speed to be too slow, try setting ACC to limit INTEG precision and make it return faster. (You can't control SOLVE accuracy, but SOLVE is typically pretty fast; INTEG is the real CPU hog.)

Note that PLOT is present in the main PLOT menu, and also in the VIEW sub-menu. They are the same, it doesn't matter which one you use. PLOT in the VIEW menu is there for convenience, so you can tweak the plot range without having to switch between the PLOT and VIEW menus every time you make a change.

Once the plot has finished, you are in Plot Viewer mode. While in this mode, the following key assignments are in effect:

7/8/9/4/6/1/2/3: move crosshair cursor around the screen. If the cursor is hard against an edge and you try to move it even further, the plot view will jump in that direction by 1/4 the screen size.
5: re-center the plot on the current crosshair location.
ENTER: mark the coordinates of the current crosshair position, and also place them in the X register, as a complex number.
0: change the plot rectangle to the one spanned by the two marks
Shift SOLVER: find a root, with the two marks as starting values
Shift ∫ f(x): integrate the function between the two marks
+ or −: zoom in or out by a factor of 2, keeping the coordinates of the center of the screen constant. (To zoom in on a particular spot, move the crosshairs to that spot, then press 5 to re-center the plot, then press + to zoom in.)
Shift PRINT: print the current plot.
← or EXIT: Leave the Plot Viewer
Shift OFF: Exit the app, without leaving the Plot Viewer.

Functions for Generated Code

When PARSE parses an algebraic equation, it converts it to an equivalent RPN program. This program is what's executed by EVAL, or when an equation is called by SOLVE, INTEG, or PLOT.

Many of the functions that can be used in equations can be trivially translated to RPN programs, but certain constructs are a bit harder to deal with. To help with those, Plus42 includes a set of functions that were designed specifically to allow more efficient code to be generated. They are documented here for the sake of completeness, but also because it isn't inconceivable that they may even come in handy in hand-written RPN code in some cases.

GTOL and XEQL GTO and XEQ to Line Number. These work like the regular GTO and XEQ, except the destination is not a LBL, but a line number in the current program. Note that these functions are not updated when the program they are in is edited, so you won't want to use these functions in code that isn't in its final form yet. Also, GTO and XEQ are just as fast as GTOL and XEQL, since they all cache the destination's absolute memory address when first executed, so there's really not much reason for using GTOL and XEQL in hand-written code.

GSTO and GRCL These are variants of STO and RCL that only work with global variables. They are used to emulate the semantics of variable access in L() and G() on the original HP calculators.

SVAR Test whether the variable named by the string in the X register is currently being solved for. The string is consumed, and 1 is returned if the variable is currently being solved for, and 0 is returned otherwise.
This is used to implement the S() function.

GETITEM and PUTITEM Single-element access for matrices and lists. GETITEM expects the name of a matrix or list variable in Y, and a linear index in X; or, for matrices only, a name in Z, a row index in Y, and a column index in X. Consumes all arguments and returns the element.
PUTITEM expects the name of a matrix or list variable in Z, a linear index in Y, and a value in X; or, for matrices only, a name in T, a row index in Z, a column index in Y, and a value in X. Consumes all arguments and stores the value in the element.
All indexes are 1-based.

=, ≠, <, >, ≤, and ≥ Relational tests. The left-hand operand is taken from Y and the right-hand operand is taken from X; both are consumed, and the result is returned to X. The result is 1 if the test was true and 0 if it was false.

&&, ||, ^^, and ! Boolean operators. &&, ||, and ^^ consume two arguments from X and Y, and return the Boolean 'and', 'or', or 'exclusive or', respectively. Arguments that are zero are considered to be 'false' and arguments that are non-zero are considered to be 'true'; the returned value is 1 for true and 0 for false. The ! function is a single-argument function that performs logical 'not', using the same parameter and return conventions.

IF? Execute the next line if X is nonzero, and skip it otherwise. In other words, like the X≠0? function, except X is consumed. This is meant to be used in conjunction with the relational and Boolean operators, above.

TRUNC Truncation. Works like RND, i.e. it rounds according to the current display mode, except while RND rounds to nearest, TRUNC rounds toward zero.

DDAYSC Calculates the number of days between two dates, according to the specified calendar. The first date is taken from Z, the second from Y, and the calendar number from X. The calendar may be one of: Gregorian calendar (1), equivalent to the RPN DDAYS function; 365-day calendar without leap years (2); or 360-day calendar with 30-day months (3).
This function is used to implement the DDAYS() function in equations.

GETEQN Gets an equation by name, from the EQN list. The equation name is taken from X, and is replaced by the named equation, if it exists. If no equation is found for the given name, the function returns a Nonexistent error.

→PAR This function sets up parameters in preparation for calling an equation or program. The equation object, or the program name, is taken from X, and the parameter count is taken from Y. The parameters themselves are taken from Z and up.
If the equation has named parameters, or the program has MVAR declarations, the parameters are stored in local variables with matching names. If the equation has no named parameters, no parameters are passed. If a program has no MVAR declarations, the parameters are passed on the stack.
This function may only be called in NSTK mode.

FDEPTH Returns the "frame depth," that is, the number of items that have been pushed onto the stack since FUNC was called. This is used to implement the REGX, REGY, REGZ, REGT, and STACK[n] special variables, for accessing the RPN stack from equations.

FLASTX Returns the LASTX that was saved by the most recent FUNC call. This used to implement the LASTX special variable, used to access the RPN LASTX from equations.

RAISE Raises an error. The argument is interpreted like the argument to RTNERR, which is documented in the Programming Utilites section of the Free42 home page, here.

Complete list of functions in Plus42 that are not in Free42

Equations:
PARSE UNPARSE STD COMP DIRECT NUMERIC EVAL EVALN EQNSLV EQNINT EQNVAR EQNMENU EQNMNU1 EQN? EQN EQN.FCN

Directories:
CRDIR PGDIR RENAME CHDIR UPDIR HOME PATH REFMOVE REFCOPY REFFIND PRALL DIRS DIR.FCN

Big Display:
ROW+ ROW− COL+ COL− GETDS SETDS WIDTH HEIGHT HEADER 1LINE NLINE
(Actually, WIDTH and HEIGHT exist in Free42 as well, but they always return 131 and 16 there, since its display is not resizable. It has those functions only for compatibility with Plus42.)

Financial:
N I%YR PV PMT FV CLEAR P/YR BEGIN END RESET #P INT PRIN BAL NEXT FIRST LAST INCR GO SPPV SPFV USPV USFV $N $I%YR $PV $PMT $FV TVM AMORT

Function Plotting:
PGMPLOT EQNPLOT XAXIS YAXIS XMIN XMAX YMIN YMAX SCAN PLOT LINE PLOT.M PARAM CONST VIEW.P

Statistics:
ΣX ΣX2 ΣY ΣY2 ΣXY ΣN ΣLNX ΣLNX2 ΣLNY ΣLNY2 ΣLNXLNY ΣXLNY ΣYLNX

Generated Code:
GTOL XEQL GSTO GRCL SVAR GETITEM PUTITEM = ≠ < > ≤ ≥ && || ^^ ! IF? TRUNC DDAYSC GETEQN →PAR FDEPTH FLASTX RAISE

Frequently Asked Questions

If you can't find what you're looking for here, please check the Free42 FAQ, since most of the information provided there applies to Plus42 as well.

Why am I getting Restricted Operation when I try to edit a program?

Plus42 allows you to run programs that aren't in the current directory (if they are in one of the ancestors of the current directory, or in one of the directories in the PATH list). However, it will only allow you to edit programs that are in the current directory, and if the current program is not in the current directory, you will get a Restricted Operation error message when you try to edit it.
When this happens, you can use GTO . . while in PRGM mode to change the current directory to the directory containing the current program. You will see the current-line indicator change from a hollow to a solid triangle to indicate that you are now able to edit the program.

The keyboard is too cluttered!

If you're using Plus42 mainly as a Free42 replacement with a bigger display, you may not be interested in the additional keyboard rows of the standard Plus42 skins. (Of course there may be other reasons for not wanting the extra rows as well, and the Plus42-specific functionality is accessible even without them, through the CATALOG menu.) If this describes you, you may be happy to hear that you can use skins designed for Free42 in Plus42 as well. The display area will stretch as necessary to accommodate the big display, just as it does with the standard Plus42 skin; DIRS and UNITS move to the first row of CATALOG to keep them easy to reach, and of course EQN can be reached using the = soft key in the SOLVER and ∫ f(x) menus.

Why is the top row of the keyboard acting weird?

The top row of the standard Plus42 skins is actually mapped like the top row of the original Free42 and HP-42S keyboard. This means that when there is no active menu, the top row performs the same functions as the third row of the Plus42 standard keyboard. This is not a bug.

Can I adjust the display contrast?

No, Plus42 does not offer a contrast adjustment setting. However, there are high-contrast versions of the standard skins available in the Plus42 Skins section in this web site, here, and you can download them using the built-in skin loader in the Android, iOS, and Mac versions.

	Android Get it at Google Play. Requires Android 4.0 or later.
	iOS (iPhone, iPad, iPod touch) Get it from the App Store. Requires iOS 11.0 or later.
	Windows Download: Plus42Windows.zip (32-bit) Requires Windows Vista or later. If Plus42 does not run as is, you will also need to download and install the Latest supported Visual C++ Redistributable.
	MacOS Download: Plus42Mac.zip Requires MacOS 10.13 (High Sierra) or later.
	Linux Download: Plus42Linux.tgz Built in Ubuntu 14.04, with libc 2.19, libstdc++ 4.8.4, and GTK+ 3.10.8. It should work on any Linux (x86_64) with those or similar libraries.
Additional Downloads
	Skins Some skins to use instead of the faceplates built into Plus42.
	HP-42S/Free42/Plus42 programs A small collection of HP-42S/Free42/Plus42 programs.
	rom2raw A C program that converts user code from HP-41 ROM images, from ROM or MOD files, to Free42/Plus42/Emu42 compatible "raw" program files. Download rom2raw.zip; source code and Win32 console executable included.
	Plus42 Source Code Get it from GitHub: https://github.com/thomasokken/plus42desktop Package for GTK only, for building Linux packages: upstream. I cannot keep track of exactly which combinations of tools do and don't work for building Plus42, but for what it's worth, these are the ones I use: For the MacOS version, I always use the latest Xcode. For the Windows version, I use Microsoft Visual Studio 2022. I have built the GTK version in many different Linux distros, and also in FreeBSD and Solaris. What I typically need to install are: the standard set of build tools (called 'build-essential' in Ubuntu), libgtk-3-dev, libasound2-dev, and, if 'make' is not GNU Make, also 'gmake'. Note that libasound2-dev is optional; you just need it if you want BEEP and TONE to sound nice.

Plus42 : An Enhanced HP-42S Calculator Simulator

What it is

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Android

iOS (iPhone, iPad, iPod touch)

Windows

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Additional Downloads

Skins

HP-42S/Free42/Plus42 programs

rom2raw

Plus42 Source Code