db48x/help/db48x.md

Overview

DB48X on DM42

The DB48X project intends to rebuild and improve the user experience of the legendary HP48 family of calculators, notably their "Reverse Polish Lisp" (RPL) language with its rich set of data types and built-in functions.

This project is presently targeting the SwissMicro DM42 calculator and leveraging its built-in software platform, known as DMCP. This is presumably the calculator you are currently running this software on. You can also try it in your browser.

Table of contents

• Using the on-line help
• Quickstart guide
• State of the project
• Design overview
• Keyboard interaction
• Soft menus
• Differences with other RPLs
• Built-in help
• Acknowledgements and credits
• Release notes
• Performance

State of the project

This is currently SEMI-STABLE software, meaning that the implemented features appear to work somewhat reliably, but that some features are still being added with each new release. This is NOT PRODUCTION READY and should not be used for any mission-critical computation.

At this point in time, you should only installing this if you are interested in contributing to the project, whether it is in the form of code, feedback or documentation changes. Please refer to the web site of the project on GitHub or GitLab for details and updates. The best way to report an issue, request an improvement or submit a proposed change is on the project's GitHub page.

The implementation status section categorizes all the RPL commands in the HP50G and in DB48X into "implemented", "not implemented" and "DB48X only" lists.

Design overview

The objective is to re-create an RPL-like experience, but to optimize it for the existing DM42 physical hardware. Ideally, DB48X should be fully usable without a keyboard overlay. though one is being worked on.

Compared to the original HP48, the DM42 has a much larger screen, but no annunciators (it is a fully bitmap screen). It has a keyboard with dedicated soft-menu (function) keys, but only one shift key (whereas the HP48 has two), lacks a dedicated alpha key, does not provides left or right arrow keys (only up and down), and has no space key (SPC on the HP48).

Keyboard interaction

The keyboard differences force us to revisit the user interaction with the calculator compared to the HP48:

• When running DB48X on the DM42, the single yellow shift key cycles between three states, Shift (shown in the documentation as 🟨), Right Shift (shown in the documentation as 🟦), and no shift. This double-shift shortcut appears necessary because RPL calculators like the HP48 have a rather full keyboard even with two shift keys.

• A first press on the shift key is shown as 🟨 in the documentation, and activates functions shown in yellow in the keyboard overlay. A second press is shown as 🟦 in the documentation, and activates functions shown in blue in the keyboard overlay. On the screen, the shift state is indicated in the header area. When a soft menu is visible on the screen, the selected row of functions is highlighed.

In the rest of this document, the shift key is referred to as 🟨, and pressing it twice is referred to as 🟦, irrespective of the appearance of the physical shift key on your particular hardware. While running the firmware, this will display in the annunciator area as follows:

Other aspects of the keyboard interaction are fine-tuned for RPL usage:

• Since RPL uses alphabetic entry (also called Alpha mode) a lot more frequently than on RPN models like the HP41 or HP42, making it quickly accessible seems important, so there are three distinct ways to activate it.

• The ▲ and ▼ keys move the cursor left and right while editing instead of up and down. These cursor movements are much more useful for a text-based program editing as found in RPL. In the rest of this document, they are described as ◀︎ and ▶︎ respectively.

• Using 🟨 ◀︎ and 🟨 ▶︎ moves the cursor up and down. When not editing, ◀︎ and ▶︎ behave like ▲ and ▼ on the HP48, i.e. ◀︎ enters the interactive stack (not yet implemented) and ▶︎ edits the object on the first level of the stack.

• Long-pressing arrow keys, the ← (also known as Backspace) or text entry keys in Alpha mode activates auto-repeat.

• Long-pressing keys that would directly trigger a function (e.g. SIN), including function keys associated with a soft-menu, will show up the built-in help for the corresponding function.

Alpha mode

Entering alphabetic characters is done using Alpha mode. These alphabetic characters are labeled on the right of each key on the DM42's keyboard.

When Alpha mode is active, an ABC indicator shows up in the annunciator area at the top of the screen. For lowercase entry, the indicator changes to abc.

There are three ways to enter Alpha mode:

• The first method is to use 🟨 ENTER as indicated by the ALPHA yellow label on the DM42 ENTER key. This cycles between Alpha ABC, Lowercase abc and Normal entry modes.

• The second method is to hold 🟨 for more than half a second. This cycles between Alpha ABC and Normal entry modes, and cannot be used to type lowercase characters.

• The third method is to hold one of the arrow keys ◀︎ or ▶︎ while typing on the keyboard. This is called transient alpha mode because Alpha mode ends as soon as the arrow key is released. Using ◀︎ enters uppercase characters, while ▶︎ uses lowercase characters.

There is no equivalent of the HP48's "single-Alpha" mode. Alpha mode is either transient (when you hold one of the arrow keys) or sticky (with 🟨 ENTER or by holding 🟨).

Alpha mode is cancelled when pressing ENTER or EXIT.

Since the DM42's alphabetic keys overlap with the numeric keys (unlike the HP48), as well as with operations such as × and ÷, using 🟨 in Alpha mode brings back numbers. This means 🟨 cannot be used for lowercase, but as indicated above, there are two other methods to enter lowercase characters.

Using 🟨 or 🟦 in combination with keys other than the numeric keypad gives a variety of special characters.

Key mapping

The layout of keys on DB48X was carefully chosen to offer a good compromise between immediate applicability for calculations and giving access to numerous advanced functions through menus.

DB48X keyboard overlays for DM-42 and DM-32 SwissMicros calculators are already available.

In the rest of this document, keys bindings will usually be described using the alphabetic key, to make it easier to locate on the keyboard, followed by the standard label on the DB48X layout. For example, the assignment for the sin function will be described as J (SIN). The shifted functions of the same key will be described as 🟨 J (SIN⁻¹) or 🟦 J (HYP) respectively.

In some cases, the label between parentheses may refer to another calculator model, which will be indicated as follows. For example, the A key can be described as A (⚙️, DM-42 Σ+, DM-32 √x).

However, if you are using DB48X on a DM42, it is possible to do it without a keyboard overlay, because great care was taken to have the DB48X keboard layout remain close to that of the DM42, in order to preserve muscle memory. New features were positioned on the keyboard at positions that are close to what is familiar in the original DM42 firmware.

A few keys that have little use in RPL are reassigned to features that you should be able to quickly remember. For example, the DM-42 RCL key is used for the DB48X VAR key, which invokes the VariablesMenu.

Note that the LOG and e^x keys are swapped relative to the DM-42. The HP42 has LOG and LN with shifted 10^x and e^x. DB48X has e^x and LN with shifted 10^X and LOG, so that the more frequently used mathematical functions are available without shifting. Note that in the future, full keyboard remapping similar to the HP41 or HP48 will allow you to change that if you prefer.

Here are a few of the interesting RPL-specific key mappings:

• A (⚙️, DM-42 Σ+, DM-32 √x) is used to invoke a context-sensitive ToolsMenu, which select a softkey menu based on what is on the stack and other context.

• 🟨 A (←MENU, DM-42 Σ-, DM-32 x²) selects the LastMenu command, which displays the previously selected menu.

• 🟦 A (MAIN, DM-32 PARTS) selects the MainMenu, a top-level menu giving indicrect access to all other menus and features in DB48X (see also the Catalog feature).

• F (' (), DM-42 XEQ, DM-32 Σ+) opens an algebraic expression, i.e. it shows '' on the command-line and switches to equation entry. If already inside an equation, it inserts a pair of parentheses. This can be used to evaluate expressions in algebraic mode instead of RPN.

• 🟨 G (CPLX, DM-42 COMPLEX, DM-32 CMPLX) lets you work with complex numbers. It opens the ComplexMenu, which can be used to enter complex numbers in rectangular or polar form, and perform common operations on these numbers. The same menu can be accessed without shift using A (⚙️) when there is a complex number on the stack.

• H (VAR, DM-42 and DM-32 RCL) opens the VariablesMenu showing user variables in the current directory.

• I (STK, DM-42 and DM-32 R↓) will open the StackMenu, giving access to stack operations.

• 🟨 I (CONST, DM-42 π, DM-32 HYP) shows a ConstantsMenu giving access to various constants. You can provide your own constants in a config/constants.csv file on disk.

• M (X⇆Y) executes the RPL Swap function

• 🟨 M (LAST, DM-42 LAST x, DM-32 MEM) is LastArg, which recalls the arguments of the last command.

• 🟦 M (Undo, DM-32 X⇆) restores the previous state of the stack. This is like Last Stack on the HP48, but on DB48X, it is a real command that can be used in programs.

• N (+/-) executes the equivalent RPL Negate function. While editing, it changes the sign of the current number on the command-line.

• O (×10ⁿ, EEX or E depending on keyboard labeling, referred to as ×10ⁿ in the rest of this document) is used to enter the exponent of a number in scientific notation. However, when not entering or editing values, it invokes the Cycle command, which cycles between various representations of a number, for example polar and rectangular for a complex number, or fraction and decimal for a decimal number.

• EXIT (DM-32 ON) corresponds to what the HP48 manual calls Attn, and typically cancels the current activity. It can also be used to interrupt a running program.

• 🟨 EXIT (OFF) shuts down the calculator. The state of the calculator is preserved.

• 🟦 EXIT (SAVE) saves the current state of the calculator to disk. This state can be transferred to another machine, and survives system reset or firmware upgrades.

• 🟨 0 (SETUP) shows the firmware's SystemMenu, for example to load the original DM-42 or DM-32 program, activate USB disk, and to access some calculator preferences.

• The R/S keys inserts a space in the editor, an = sign inside equations, and maps to Evaluate otherwise.

• 🟨 R/S («PROG», DM-42 and DM-32 PRGM) inserts the delimiters for an RPL program, « and », while 🟦 R/S ({LIST}) inserts the list delimiters, { and }.

• 🟨 + (CAT, DM-42 CATALOG, DM-32 LBL) shows a complete context-sensitive catalog of all available functions, and enables auto-completion using the soft-menu keys. Note that the + key alone (without shift) activates the catalog while in Alpha mode. When inside text, the catalog presents alternates for the character at the left of the cursor, providing a convenient way to select diacritics and accents..

• 🟦 + (HELP, DM-32 RTN) activates the context-sensitive help system.

Soft menus

The DM42 has 6 dedicated soft-menu keys at the top of the keyboard. Most of the advanced features of DB48X can be accessed through these soft menus. Soft menu keys have no label on the physical calculator, but in this documentation, they may sometimes be referred to as F1 through F6.

All built-in soft-key menus are named, with names ending in Menu. For example, the VariablesMenu is the menu listing global variables in the current directory. Unlike HP RPL calculators, menus cannot be accessed by number, but they can be accessed by name. In a future version of the firmware, a Menu special variable will return the name of the current menu. The LastMenu command selects the previous menu.

Menus are organized internally as a hierarchy, where menus can refer to other menus. A special menu, MainMenu, accessible via the 🟦 A, contains all other menus.

Menus can contain up to 18 entries at once, 6 being directly accessible, 6 more being shown when using the 🟨 key, and 6 more with 🟦. Three rows of functions are shown on screen, with the active row highlighted.

A long press on a function key invokes the on-line help for the associated function.

When a menu contains more than 18 entries, then the F6 function key turns into a ▶︎, and 🟨 F6 turns into ◀︎. These keys can be used to navigate across the available menu entries. This replaces the NXT and PREV keys on HP calculators.

The VariablesMenu is used to access global varibales. It is invoked using the H key, which is labeled RCL on SwissMicros hardware. This menu is special in the sense that:

• Selecting an entry evaluates that menu entry, for example to run a program

• The 🟨 function recalls its name without evaluating it.

• The 🟦 function stores into the variable.

Differences with other RPLs

Multiple implementations of RPL exist, most of them from Hewlett-Packard. A good reference to understand the differences between the various existing implementations from HP is the HP50G Advanced User's Reference Manual.

There are a number of intentional differences in design between DB48X and the HP48, HP49 or HP50G's implementations of RPL. There are also a number of unintentional differences, since the implementation is completely new.

User interface

• DB48X features an extensive built-in help system, which you are presently using. Information for that help system is stored using a regular markdown file named /help/db48x.md, stored in the calculator's flash storage.

• DB48X features auto-completion for commands while typing, through the CAT key (a Catalog of all commands).

• Many RPL words exist in short and long form, and a user preference selects how a program shows. For example, the Negate command, which the HP48 calls NEG, can display, based on user preferences, as NEG, neg, Neg or Negate. In the help, it will be shown as Negate (NEG).

• The DB48X dialect of RPL is not case sensitive, but it is case-respecting. For example, if your preference is to display built-in functions in long form, typing inv or INV will show up as Invert in the resulting program. This means that the space of "reserved words" is larger in DB48X than in other RPL implementations. Notably, on HP's implementations, DUP is a keyword but you can use DuP as a valid variable name. This is not possible in DB48X.

• The saving of the stack arguments for the LastArg command is controled independently by two distinct settings, SaveLastArg and SaveLastArgInPrograms. The first one controls if LastArg is saved for interactive operations, and is enabled by default. The second one controls if LastArg is saved before executing commands while running a program or evaluating an expression, and is disabled by default. This impacts commands that evaluate programs, such as ROOT. On the HP48, LastArg after running ROOT interactively gives arguments used by some operation within ROOT, whereas on DB48X with the default settings, it returns the arguments to ROOT.

• When parsing the Σ (sum) function (as well as the ∏ (product) function which the HP calculators do not have), all arguments are separated by semi-colons like for all other functions. HP calculators have a special syntax in that case, where an = sign separates the index and its initial value. In other words, where an HP calculator would show Σ(i=1;10;i^2), which corresponds to the 4-argument sequence i 1 10 'i^2' Σ, the DB48X implementation shows and requires the Σ(i;1;10;i^2) syntax. Note that an = sign may appear inside an expression, but it always denotes equality.

Evaluation

• Local names are evaluated on DB48X, unlike in the HP versions of RPL. This makes it easier to use local subprograms in larger programs as if they were normal operations. In the less frequent case where you do not want evaluation, you need to use RCL like for global variables.

• Lists do not evaluate as programs by default, like on the HP28, but unlike on the HP48 and later HP models. This can be controlled using the ListEvaluation setting. Note that a list can be converted to a program using the Cycle command, which makes it easy to build programs from lists.

• The case statement can contain when clauses as a shortcut for the frequent combination of duplicating the value and testing against a reference. For example, case dup "A" = then "Alpha" end can be replaced with case "A" when "Alpha" end.

• There are no compiled local variables. The a program like → ←x « Prog » might perform incorrectly if Prog attempts to access ←x. Compiled local variables are a rather obscure feature with a very limited use, and might be replaced with true closures (which have a well-defined meaning) if there is enough demand.

Numbers

• DB48X has several separate representations for numbers: integers, fractions and decimal. Notably, it keeps integer values and fractions in exact form for as long as possible to optimize both performance and memory usage. This is closer to the HP50G in exact mode than to the HP48. Like the HP50G, DB48X will distinguish 1 (an integer) from 1. (a decimal value), and the TYPE command will return distinct values.

• Integer and fraction arithmetic can be performed with arbitrary precision, similar to the HP50G. The MaxNumberBits setting controls how much memory can be used for integer arithmetic.

• DB48X has true fractions. From a user's perspective, this is somewhat similar to fractions on the HP50G, except that fractions are first-class numbers, whereas the HP50G treats them like expressions. On the HP50G, 1 3 / TYPE returns 9., like for 'A + B'. On DB48X, the TYPE for fractions is different than for expressions. Fractions can be shown either as MixedFractions or ImproperFractions.

• On HP50G, decimal numbers often outperform integers or fractions, and benchmark code will contain 1. instead of 1 for that reason. On DB48X, arithmetic on integers and fractions is generally faster.

• Like the HP Prime, DB48X displays a leading zero for decimal values, whereas HP RPL calculators do not. For example, it will display 0.5 and not .5.

• DB48X has two distinct representations for complex numbers, polar and rectangular, and transparently converts between the two formats as needed. The polar representation internally uses fractions of pi for the angle, which allows exact computations. By contrast, HP RPL implementations always represent complex numbers in rectangular form internally, possibly converting it to polar form at display time.

• DB48X features arbitrary-precision decimal floating-point. The Precision command (in the DisplayModesMenu) can be used to select the precision for numerical operations. In addition, it supports 32-bit and 64-bit hardware-accelerated binary floating-point.

• Based numbers with an explicit base, like #123h keep their base, which makes it possible to show on stack binary and decimal numbers side by side. Mixed operations convert to the base in stack level X, so that #10d #A0h + evaluates as #AAh. Based numbers without an explicit base change base depending on the Base setting, much like based numbers on the HP48, but with the option to any base between 2 and 36. In addition to the HP-compatible trailing letter syntax (e.g. #1Ah), the base can be given before the number (e.g. 16#1A), which works for all supported bases.

Representation of objects

• The storage of data in memory uses a denser format than on the HP48. Therefore, objects will almost always use less space on DB48X. Notably, the most frequently used functions and data types consume only one byte on DB48X, as opposed to 5 nibbles (2.5 bytes) on the HP48. A number like 123 consumes 2 bytes on DB48X vs. 7 on the HP50 and 10.5 on the HP48.

• Numerical equality can be tested with =, whereas object equality is tested using ==. For example, 0=0.0 is true, but 0==0.0 is false, because 0 is an integer whereas 0.0 is a floating-point.

• Because of differences in internal representation that would require expensive computations to mimic the HP50G behaviour with limited benefit, Size returns 1 for integers, algebraic expressions and unit objects.

• The Type command can return HP-compatible values that are sometimes imprecise (e.g. it cannot distinguish between polar and rectangular complex values), or numerical values that distinguish all the types in DB48X. This is controlled by the CompatibleTypes setting. The TypeName command is a DB48X-only extension that returns more precise textual information, and should be preferred both for readability and future compatibility.

• DB48X has a dedicated data type to represent multi-variate polynomials, in addition to the classical RPL-based algebraic expressions.

Alignment with SwissMicros calculators

• DB48X will borrow to the DM-42 the idea of special variables for settings, which are variables with a special meaning. For example, the Precision special variable is the current operating precision for floating point, in number of digits. While there is a Precision command that sets the value, it is also possible to use 'Precision' STO to set it, and 'Precision' RCL to fetch the current value. This does not imply that there is an internal Precision variable somewhere. This applies to all settings and flags. Additionally, binary settings can be set with SF and CF, and queried with SF? and CF?. For example, 'HideDate' CF will clear the HideDate flag, meaning that the date will show in the header.

• The DB48X also provides full-screen setup menus, taking advantage of the DM42 existing system menus. It is likely that the same menu objects used for softkey menus will be able to control system menus, with a different function to start the interaction.

• The whole banking and flash access storage mechanism of the HP48 will be replaced with a system that works well with FAT USB storage. It should be possible to directly use a part of the flash storage to store RPL programs, either in source or compiled form. As an example, using a text argument to STO and RCL accesses files on the USB disk, e.g. 1 "FOO.TXT" STO stores the text representation of 1 in a file named DATA/FOO.TXT on the USB flash storage.

List operation differences

The application of a same operation on arrays or matrices has never been very consistent nor logical across RPL models from HP.

• On HP48 and HP50, { 1 2 3 } 4 + gives {1 2 3 4}. However, { 1 2 3} 4 * gives a type error on the HP48 but applies the operation to list elements on the HP50, yielding { 4 8 12}.

• For arrays, [ 1 2 3 ] 4 + fails on both the HP48 and HP50, but [ 1 2 3 ] 4 * works.

• The HP50 has a MAP function, which works both for list and matrices. [ 1 2 3 ] « 3 + » will return [ 4 5 6 ], and { 1 2 3 } « 3 * » will return { 3 6 9 }. That function has no direct equivalent on the HP48.

DB48X considers lists as bags of items and treat them as a whole when it makes sense, whereas arrays are focusing more on the values they contain, and will operate on these items when it makes sense. Therefore:

• { 1 2 3 } 4 + gives { 1 2 3 4 }, { 1 2 3 } 2 - gives { 1 3 } (not yet implemented), and { 1 2 3 } 3 × gives { 1 2 3 1 2 3 1 2 3 }. The ÷ operator is equivalent to the ListDivide function, and partitions a list in chunks of the given size and returns the number of partitions so generated (the last partition being possibly shorter), i.e. { 1 2 3 4 5 } 2 ÷ will generate {1 2} {3 4} {5} 3 on the stack (this is not yet implemented).

• [ 1 2 3 ] 4 + gives [ 5 6 7 ], [ 1 2 3 ] 2 - gives [ -1 0 1 ], [ 1 2 3 ] 3 × gives [ 3 6 9 ] and [ 1 2 3 ] 5 ÷ gives [ 1/5 2/5 3/5 ].

• Two lists can be compared using lexicographic order. This also applies to the Min and Max functions, which compares the entire lists, whereas on HP50G, it compares element by element (element-wise comparison applies to arrays).

Vectors and matrices differences

• On DB48X, vectors like [ 1 2 3 ] are very similar to lists. The primary difference is the behavior in the presence of arithmetic operators. On lists, addition is concatenation, e.g. { 1 2 3} { 4 5 6} + is { 1 2 3 4 5 6 }, whereas on vectors represents vector addition, e.g. [1 2 3] [4 5 6] + is [5 7 9]. However, unlike on the HP original implementation, a vector can contain any type of object, so that you can do [ "ABC" "DEF" ] [ "GHI" "JKL" ] + and obtain [ "ABCGHI" "DEFJKL" ].

• Size enforcement on vectors only happens during these operations, not while you enter vectors from the command line. It is legal in DB48X to have a non-rectangular array like [[1 2 3] [4 5]], or even an array with mixed objects like [ "ABC" 3 ]. Size or type errors on such objects may occur if/when arithmetic operations are performed.

• In particular, a matrix is nothing but a vector of vectors. DB48X also supports arrays with dimensions higher than 2, like [[[1 2 3]]].

• As a consequence, The GET and GETI functions work differently on matrices. Consider a matrix like [[ 7 8 9 ][ 4 5 6 ][ 1 2 3 ]]. On the HP48, running 1 GET on this object gives 7, and the valid range of index values is 1 through 9. On DB48X, that object is considered as an array of vectors, so 1 GET returns [7 8 9]. This is intentional. The behavior of { 1 1 } GET is identical on both platforms, and is extended to multi-dimensional arrays, so that [[[4 5 6]]] { 1 1 2 } GET returns 5.

• Matrices and vectors can contain integer values or fractions. This is closer to the HP50G implementation than the HP48's. In some cases, this leads to different results between the implementations. If you compute the inverse of [[1 2 3][4 5 6][7 8 9] on the HP48, you get a matrix with large values, and the HP48 finds a small, but non-zero determinant for that matrix. The HP50G produces a matrix with infinities. DB48X by default produces a Divide by zero error.

• DB48X accept matrices and vectors as input to algebraic functions, and returns a matrix or vector with the function applied to all elements. For example, [a b c] sin returns [ 'sin a' 'sin b' 'sin c' ].

• Similarly, DB48X accept operations between a constant and a vector or matrix. This applies the same binary operation to all components of the vector or matrix. [ a b c ] x + returns [ 'a+x' 'b+x' 'c+x' ]. Consistent with that logic, inv works on vectors, and inverts each component, so that [1 2 3] inv gives [1/1 1/2 1/3].

• The Min and Max operations on arrays apply element by element, in a way similar to how these operations apply to lists on the HP50G (which seems to be undocumented).

Mathematics

• The Σ operation behaves differently between the HP48 and the HP50. On the HP48, I A B 'I^3' Σ gives an expression, Σ(I=A;B;I^3), and an empty range like I 10 1 'I^3' Σ gives 0 as a value. On the HP50, this sum is simplified as a polynomial expression, so that you get a negative value if A>B. The HP50G behaviour seems surprising and undesirable. DB48X follows the HP48 approach.

• The ↑Match and ↓Match operations return the number of replacement performed, not just a binary 0 or 1 value. In addition, the patterns can identify specific kinds of values based on the first letter of the pattern variable name, e.g. i or j for positive integers, or u and v for unique terms, i.e. terms that are only matched once in the expression.

Unicode support

DB48X has almost complete support for Unicode, and stores text internally using the UTF-8 encoding. The built-in font has minor deviations in appearance for a few RPL-specific glyphs.

Overall, a text file produced by DB48X should appear reliably in your favorite text editor, which should normally be GNU Emacs. This is notably the case for state files with extension .48S which you can find in the STATE directory on the calculator.

The Size operation when applying to text counts the number of Unicode characters, not the number of bytes. The number of bytes can be computed using the Bytes command.

The Num and Chr commands (also spelled Char→Code and Code→Char) deal with Unicode codepoints, and do not use the special HP characters codes. In addition, Num return -1 for an empty string, not 0. 0 is only returned for a string that begins with a NUL codepoint.

The Code→Char command can also be spelled as Code→Text, and take a list of Unicode codepoints as input. Conversely, Text→Code will generate a list of all the codepoints in a text.

Help

The DB48X project includes an extensive built-in help, which you are presently reading. This help is stored as a help/db48x.md file on the calculator. You can also read it from a web browser directly on the GitHub page of the project.

The Help command makes it possible to access the built-in help in a contextual way. It is bound to 🟦 +. If the first level of the stack contains a text corresponding to a valid help topic, this topic will be shown in the help viewer. Otherwise, a help topic corresponding to the type of data in the stack will be selected.

The DB48X help viewer works roughly similarly to the DM42's, but with history tracking and the ability to directly access help about a given function by holding a key for more than half a second.

To navigate the help on the calculator, use the following keys:

• The soft menu keys at the top of the keyboard, references as F1 through F6, correspond to the functions shown in the six labels at the bottom of the screen.

• While the help is shown, the keys ◀︎ and ▶︎ on the keyboard scroll through the text.

• The F1 key returns to the Home (overview).

• The F2 and F3 keys (labels Page▲ and Page▼) scroll the text one full page at a time.

• The F4 and F5 keys (labels Link▲ and Link▼) select the previous and next link respectively. The keys ÷ and 9 also select the previous link, while the keys × and 3 can also be used to select the next link.

• The F6 key correspond to the ←Menu label, and returns one step back in the help history. The ← key achieves the same effect.

• To follow a highlighted link, click on the ENTER key.

Acknowledgements and credits

DB48X is Free Software, see the LICENSE file for details. You can obtain the source code for this software at the following URL: https://github.com/c3d/db48x.

Authors

This software is (C) 2022-2023 Christophe de Dinechin and the DB48X team.

Additional contributors to the project include:

• Camille Wormser (complex number fixes)
• Jeff, aka spiff72 (keyboard overlay)
• Conrado Seibel (help file fix)

• Kjell Christenson (simulator fix)
• Václav Kadlčík (documentation fix)
• Franco Trimboli (WASM port)

The authors would like to acknowledge

• Hewlett and Packard
• The Maubert Team
• Museum of HP calculators
• HPCalc
• The newRPL project
• The WP43 and C47 projects
• SwissMicro's DMCP

This work was placed by Christophe de Dinechin under the patronage of Carlo Acutis

Hewlett and Packard

Hand-held scientific calculators changed forever when Hewlett and Packard asked their engineers to design and produce the HP35, then again when their company introduced the first programmable hand-held calculator with the HP65, and finally when they introduced the RPL programming language with the HP28.

Christophe de Dinechin, the primary author of DB48X, was lucky enough to meet both Hewlett and Packard in person, and this was a truly inspiring experience. Launching the Silicon Valley is certainly no small achievement, but this pales in comparison to bringing RPN and RPL to the world.

The Maubert Team

Back in the late 1980s and early 1990s, a team of young students with a passion for HP calculators began meeting on a regular basis at or around a particular electronics shop in Paris called "Maubert Electronique", exchanging tips about how to program the HP28 or HP48 in assembly language or where to get precious technical documentation.

It started with Paul Courbis, who carefully reverse-engineered and documented the internals of RPL calculators, encouraging his readers to boldly cut open these wonderful little machines to solder IR receivers acting as makeshift PC connection tools, or to waste countless hours debugging video games.

There were more serious efforts as well, notably the HP48 Metakernel, which completely reinvented the HP48 user interface, making it both much faster and better. It is fair to see DB48X as a distant descendent from such efforts. The Metakernel was the work of many now well-known names in the HP community, such as Cyrille de Brébisson, Jean-Yves Avenard, Gerald Squelart and Étienne de Foras. Many of these early heroes would go on to actually change the history of Hewlett-Packard calculators for the better.

The original author of DB48X, Christophe de Dinechin, was part of this loose team, focusing on cross-development tools, which he used at the time to write several games for the HP48, notably PacMan or Lemmings clones. If DB48X exists, it's largely because of that community.

HP Museum

The HP Museum not only extensively documents the history of RPN and RPL calculators, it also provides a very active forum for calculator enthusiasts all over the world.

HPCalc

Much of the work from early enthusiasts can still be found on hpcalc.org to this day.

Back in the 1990s, long before Internet was widely available, HP48 programs were busily swapped over floppy disks, or propagated from machine to machine using the built-in infrared ports. This may have been the first case of large-scale viral distribution of software. This is probably the reason why all this software. which originated from all over the world, can still be downloaded and used today.

newRPL project

newRPL is a project initiated by Claudio Lapilli to implement a native version of RPL, initially targeting ARM-based HP calculators such as the HP50G.

DB48X inherits many ideas from newRPL, including, but not limited to:

• Implementing RPL natively for ARM CPUs
• Adding indicators in the cursor to indicate current status
• Integrating a catalog of functions to the command line

A first iteration of DB48X started as a branch of newRPL, although the current implementation had to restart from scratch due to heavy space constraints on the DM42.

WP43 and C47 projects

The DB48X took several ideas and some inspiration from the WP43 and C47 projects.

Walter Bonin initiated the WP43 firwmare for the DM42 as a "superset of the legendary HP42S RPN Scientific".

C47 (initially called C43) is a variant of that firmware initiated by Jaco Mostert, which focuses on compatibility with the existing DM42, notably with respect to keyboard layout.

DB48X borrowed at least the following from these projects:

• The very idea of writing a new firmware for the DM42
• The idea of converting standard Unicode TrueType fonts into bitmaps (with some additional contributions from newRPL)
• How to recompute the CRC for QSPI images so that the DM42 loads them, thanks to Ben Titmus
• At least some aspects of the double-shift logic and three-level menus
• The original keyboard layout template and styling, with special thanks to DA MacDonald.

SwissMicros DMCP

SwissMicros offers a range of RPN calculators that emulate well-known models from Hewlett-Packard. This includes the DM42, which is currently the primary target for the DB48X firmware.

Special thanks and kudos to Michael Steinmann and his team for keeping the shining spirit of HP RPN calculators alive.

The DM42 version of the DB48X software relies on SwissMicro's DMCP SDK, which is released under the following BSD 3-Clause License:

Copyright (c) 2015-2022, SwissMicros All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

• Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Introduction to RPL

The original RPL (Reverse Polish Lisp) programming language was designed and implemented by Hewlett Packard for their calculators from the mid-1980s until 2015 (the year the HP50g was discontinued). It is based on older calculators that used RPN (Reverse Polish Notation). Whereas RPN had a limited stack size of 4, RPL has a stack size only limited by memory and also incorporates programmatic concepts from the Lisp programming language.

The first implementation of RPL accessible by the user was on the HP28C, circa 1987, which had an HP Saturn processor. More recent implementations (e.g., HP49, HP50g) run through a Saturn emulation layer on an ARM based processor. These ARM-based HP calculators would be good targets for a long-term port of DB48X.

DB48X is a fresh implementation of RPL on ARM, initially targetting the SwissMicros DM42 calculator. This has implications on the design of this particular implementation of RPL.

The RPL stack

The RPL stack can grow arbitrarily in size.

By convention, and following RPN usage, this document gives the names X, Y, Z and T to the first four levels of the stack. This is used to describe the operations on the stack with synthetic stack diagrams showing the state of the stack before and after the operation.

For example, the addition of two objects in levels 1 and 2 with the result deposited in stack level 1 can be described in synthetic form using the following stack diagram:

Y X ▶ Y+X

The duplication operation Duplicate (DUP) can be described in synthetic form using the following synthetic stack diagram:

X ▶ X X

Algebraic mode

Unlike earlier RPN calculators from Hewlett-Packard, RPL calculators from HP includes complete support for algebraic objects written using the standard precedence rules in mathematics. This gives you the best of both worlds, i.e. the keyboard efficiency of RPN, requiring less keystrokes for a given operation, as well as the mathematical readability of the algebraic notation. Better yet, it is possible and easy to build an algebraic expression from RPN keystrokes. These nice properties are also true for DB48X.

In RPL, algebraic expressions are placed between ticks. For example, '2+3×5' will evaluate as 17: the multiplication 3×5, giving 15, is performed before the addition 2+15, which gives 17. An algebraic expression can also be symbolic and contain unevaluated variables. For example, 2+x is a valid algebraic operation. If, having this expression on the stack, you type 3 and then hit the × key, you will end up with (2+x)×3, showing how the algebraic expression was built from RPN keystrokes.

Algebraic expressions are not evaluated automatically. The R/S key (bound to the Evaluate function) will compute their value as needed. On the DB48X keyboard overlay, this key is also marked as = for that reason.

Rich data types

Since introducing the first scientific pocket calculator, the HP-35, in 1972, and with it the reverse polish notation (RPN), Hewlett-Packard perfected its line-up for decades. This led to such powerhouses pocket computers such as as the HP-41C series, or tiny wonders of pocket efficiency such as the HP-15C. Many of these calculators, including the models we just cited, were capable of advanced mathematics, including dealing with complex numbers, matrix operations, root finding or numeric integration.

Then in 1986, everything changed with the HP-28C, which introduced a new user interface called RPL. While the most evidently visible change was an unlimited stack, what instantly made it both more powerful and easier to use than all its RPN predecessors was the introduction of data types. Every value on the stack, instead of having to be a number, could be a text, a name or an equation. This made operations completely uniform irrespective of the data being operated on. The same + operation that adds numbers can also add complex numbers, vectors, matrices, or concatenate text. The exact same logic applies in all case. This solved a decade-long struggle to extend the capabilities of pocket calculators.

For example, whereas the HP-41C had some support for text, with an "Alpha" mode and an alpha register, text operations were following their own logic, with for example ARCL and ASTO dealing with at most 6 characters at a time, because they were artificially fitted in a register designed to hold a numerical value. Dealing with complex numbers on the HP-41C was similarly clunky. Even the HP-15C, which had built-in support for complex numbers, remained a bit awkward to use in "complex mode" because its display could only show one half of a complex number, e.g. the real or imaginary part. Similarly, matrix or statistic operations had non-obvious interactions with numbered data registers.

All this was solved with RPL, because now a complex number, a matrix or a text would occupy a single entry on the stack. So whereas adding two integers would require a sequence like 1 ENTER 2 + like in RPN, a very similar sequence would add two texts: "ABC" ENTER "DEF" +, and the exact same logic would also add two vectors in [1 2 3] ENTER [4 5 6] +.

DB48X adopts this extremely powerful idea, with a focus on making it as efficient as possible for interactive calculations as well as for custom programmed solution.

Quickstart guide

This quickstart guide will rapidly give you an overview of the capabilities of DB48X, and show you how to use it efficiently. Make sure that you have installed the latest version.

The ON / EXIT button is at the bottom left of the calculator. It can be used to power the calculator on, but also to exit operations, for example aborting a data entry.

DB48X is a RPL calculator, which means that:

• It inherits the stack-based "reverse polish" approach to operations that has been a central feature of practically all Hewlett-Packard scientific calculators since the HP-35. You enter arguments to a functions by pushing them on the stack, and the operation removes its arguments from the stack before putting its result(s). Unlike earlier HP calculators, the RPL stack is practically unlimited.

• Unlike simpler calculators, it uses a command line for data entry, with advanced text editing capabilities, and a rich text-based command language. One way to access the hundreds of available commands is by simply typing their name.

Arithmetic operations

Let's compute the area of a room made of a main section that is 6 meters by 8.3 meters, with an additional smaller section that is 3.5 meters by 2.8.

A first way to do it is to use the reverse polish stack-based approach, by typing the following sequence of keys: 6, ENTER, 8, ., 3, ×, 3, ., 5, ENTER, 2, ., 8, ×, +. The result, 59.6, shows on the stack. Prior to pressing the + key, the intermediate results for the two multiplications, 49.8 and 9.8, could be seen on the stack.

RPL also supports the standard algebraic notation. Begin the computation with the '() key. The editor contains quotes, '' with the cursor between them. The cursor shows the latter A, indicating algebraic entry. Type 6, ×, 8, ., 3, +, 3, ., 5, ×, 2, ., 8. At this point, the text editor should show the whole expression, '6·8.3+3.5·2.8' or '6×8.3+3.5×2.8'. Press ENTER and the expression shows up on the stack. Hitting the = / EVAL / SPC key (located between the . and + keys) evaluates the expression, to get the result 59.6.

Algebraic and reverse-polish computations are equivalent, and can be mixed and matched during computations. Using one or the other is stricly a matter of preference. Algebraic data entry makes it easier to view the entire expression. Reverse-polish makes it easier to see intermediate results.

Fractions

Let us now compute how many pies we need to feed 22 kids if we divide each pie in 8 slices. Using the RPL approach, we would type 2, 2, ENTER, 8, ÷. Using the algebraic notation, we would type '(), 2, 2, ÷, 8, ENTER and then use the = to perform the computation.

With the default settings, you should see a mixed fraction, 2 ³/₄. Unlike many calculators, DB48X by default perform exact computations on fractions instead of using approximate decimal numbers.

You can convert that fraction to a decimal value and back using the Cycle command, which is bound to the ×10ⁿ key. A first press will show 2.75, and a second press will show the value again as fraction 2 ³/₄.

Mathematical functions

DB48X features a number of mathematical functions. Some of the functions are directly available on the keyboard.

We can compute the length of the diagonal of a rectangle with sides 2m and 3m using the Pythagorean theorem, and display it in millimeters.

In RPL, we can type the following sequence: 2, x² (🟨 C), 3, x², +, √x (C), 1, 0, 0, 0, ×. The decimal result, 3 605.55127 546, is shown on the stack. The digits in the whole part of the decimal number are grouped 3 by 3, while the digits in the fractional part are grouped 5 by 5.

In algebraic mode, we can type the following sequence: '(), 1, 0, 0, 0, ×, √x, 2, x² (🟨 C), +, 3, x², ENTER. The mathematical expresssion shows up on the stack graphically. It can then be evaluated using the = key, and shows the same result as for RPL mode.

Mixing algebraic and reverse-polish operations

In the algebraic expression, we have multiplied by 1000 first, whereas in the RPL case, we multiplied by 1000 last. We can also multiply by 1000 last in algebraic mode. There are at least two ways to do it.

A first method is to use the arrow key to exit the parentheses around the argument of the square root function, as follows: '(), √x, 2, x², +, 3, x², ▶︎, ×, 1, 0, 0, 0, ENTER. The expression with the multiplication is then shown on the stack, and can then be evaluated with the = key.

A second method is to mix and match algebraic and RPL, by typing the following sequence: '(), √x, 2, x², +, 3, x², ENTER. At this point, the expression without the multiplication is on the stack. We can then multiply it by 1000 by typing 1, 0, 0, 0, ×. The expression with the multiplication is then shown on the stack, and can then be evaluated with the = key.

Trigonometric functions

Consider that we need to build a plank ramp. We can ask a number of questions, like:

• If the plank is 5 meters in length, and the slope is 10 degrees, how high will it reach?

• If we need to reach 60 cm above ground, what is the required slope?

In RPL, can answer the first question by typing 1, 0, SIN, 5, ×. The result is shown in scientific format as 8.68240 88833 5×₁₀⁻¹. In algebraic mode, we would type '(), 5, ×, SIN, 1, 0, ENTER and then evaluating the expression with =. This shows the same result.

We can answer the second question using RPL by typing 6, 0, ENTER, 5, ENTER, 1, 0, 0, ×, ÷, sin⁻¹ (🟨 J). The result is shown as 6.89210 25793 5 °. This is an example of unit object: the value is associated with a unit, in that case the ° symbol indicating that we use degrees. DB48X supports three other angle modes, radians, grads and fractions of pi (piradians).

Answering the same question using algebraic mode introduces a new little keyboard trick. Type '(), sin⁻¹, 6, 0, ÷, '(), 5, ×, 1, 0, 0, ENTER, and then evaluating the expression with the = key. Observe how the second use of the '() key, which inserts parentheses when used inside an expression.

Selecting display modes

The scientific notation may not be the most readable in that case. How do we display this result with three digits? We will use a menu for that. Menus are an essential component of the DB48X user interface.

Let us type 🟨 O (Disp). This shows the DisplayModesMenu. The menu occupies three rows at the bottom of the screen, with six columns. Menus can give a quick access to 18 functions directly, six more with a single shift 🟨, and yet another six with the second shift 🟦. Hitting the shift key 🟨 repeatedly will highlight the different rows of the menu.

On the lower row of the menu, the second entry from the left is labeled Fix. The Fix display mode shows a fixed number of digits after the decimal separator. There are other modes, Sci to display in scientific notation, Eng to display with engineering multiples (the exponent is a multiple of three), and Sig to display at most a given number of digits.

We can type 3, F2, where F2 is the second key from the left on the top row of the keyboard. This activates the Fix 3 mode, which shows three digits after the decimal separator. The display changes to 0.868 for the answer to the first question, and 6.892 ° for the answer to the second question.

Displaying the on-line help for a function

Since the number of available commands in DB48X is quite high, it is useful to be able to consult the built-in help. In order to get help on a command, simply hold the corresponding key until the help shows up. For instance, to get help about the command under the Std label, simply hold the F1 key.

This also works for normal keyboard operations. For instance, if you hold the SIN key, you will get the help about the sine command.

You should refer to the on-line help whenever you have a question about a specific command.

Angle operations

The sin⁻¹ command we used previously returns an angle which was shown in degrees, the default angle mode for DB48X. When applied to angles, the Cycle command on the ×10ⁿ key cycles between various angle units: degrees, radians, grads and pi-radians, i.e. a number of radians shown as a multiple of π.

The function also alternates between decimal and fractional representations of angles.

In order to access angle-related functions, we can use the Tools key ⚙️ which invokes the ToolsMenu command. That command picks up a menu that is suited for the value on the stack. For angles, this shows the AnglesMenu, which can be used to perform angle conversions directly.

We can select the →Deg command to convert an angle to degrees by hitting the 🟨 F1 key while the AnglesMenu is active, and similarly for →Rad with 🟨 F2, and so on. To convert the angle to a Degrees/Minutes/Seconds (DMS) representation, we can select the →DMS using the 🟦 F1 key, since that function is on the second level of the menu.

There is a quick way to manually enter angles in DMS format by using the . more than once during data entry. For example, to enter 10°20′30″, you simply need to type 1, 0, ., 2, 0, ., 3, 0, ENTER.

On the command-line, this shows up as 10°20′30_hms. Once you hit the ENTER key, this shows on the stack as 10°20′30″.

Using . more while on the command-line lets you add fractions of a second, for example 1, 0, ., 2, 0, ., 3, 0, ., 4, 0, ., 5, 0, ENTER, which will show on the stack as 10°20′30″4/5.

You can add or subtract angles directly using normal arithmetic functions. For example, hitting the + key will add angles, correctly adjusting the angle units as necessary.

Complex number operations

DB48X support complex numbers both in rectangular and polar (phasor) form. For example, in our effort to build a plank ramp, we may need more than one plank. How far and how high can you reach if you have a 5 meter plank with a slope of 10 degrees, followed by a 3 meters plank with a slope of 30 degrees?

We can add two complex numbers in phasor form to answer that question. In order to enter the complex number representing the first plank, we need the ComplexMenu, which is activated with the CPLX key (🟨 G). The F1 key will be used to enter complex numbers in rectangular form, and the F2 key to enter complex numbers in polar form.

To solve our problem, we simply need to enter CMPLX (🟨 G), then 5, F2, 1, 0, ENTER to enter the first complex number. The stack shows the complex value as 5∡10°. We can enter the second complex number using 3, F2, 3, 0, and add the two values using the + key. The result shows as 7.522+2.368ⅈ, which means that we can reach about 7.5 meters ahead and 2.3 meters above ground.

Unit conversions

If you are living in the United States, having the results in meters might not be convenient. You can use the DB48X built-in units in order to convert the result above into feet, yards or inches.

Select the UnitMenu with 🟨 5. This shows a catalog of unit categories. We can select the Length category using the F4 key. In order to indicate that our result is in meters, we select the m unit by hitting F1. Our result now shows as 7.522+2.368ⅈ m We can then convert that result in yards by selecting the →yd command with the 🟨 F2 key.

You can convert to other units in the Length units menu the same way. This menu is too large to fit on the screen, so the F6 key can be use to select the next page in the menu with more units, such as in or mm. Note that DB48X does not have a NXT key unlike HP calculators. Instead, when necessary, the NXT and PREV features appear in the menu itself as F6 and 🟨 F6.

Operations on whole numbers

Entering whole numbers

Arithmetic on integers

Changing the sign of a number with +/-

Exact division

Computing on large numbers: 2^40, 25!

Separators to make large numbers more readable

Built-in functions: example of 1/x

Using the shift key

Primary function: 1/x

First shifted function: y^x and square

Second shifted function: Help

The shift annunciator

Invoking the on-line Help

Long-press on a function key

Moving up and down

Following links

Navigating back to a previous topic

Exiting the on-line help

Contextual help

The annunciator area

Battery level

USB vs. battery power

Showing or hiding the date and time

Current state file name

Future direction

Decimal values

Entering a decimal number

Entering a number in scientific notation with ×10ⁿ

Arithmetic on decimal values

Arithmetic on fractions

Cycling between decimal and fraction with ×10ⁿ

Separators for the fractional part

Live separators during number editing

Soft keys and menus

Soft keys

The DISP menu

Effect of shift state on the menu

Submenus

Menu history (Last Menu)

Displaying decimal values

Standard display mode

FIX display mode

Switching to scientific mode

Digits to show for small values

SCI display mode

ENG display mode

SIG display mode

Emulating HP48 standard display

Scientific functions

Square and power

Square root and xroot

Exponential and Log

Exponential and log in base 10

DM42 layout difference: EXP LN instead of LOG LN

Trigonometric functions and their inverse

Functions in menus: example of hyperbolic functions

Using an infinite stack

Showing multiple stack levels

Result vs. other levels

When a result is too large

An example of complicated calculation - The Mach number benchmark

How to proceeed with that computation

Correcting an error in the middle

Saving results for later with Duplicate

Dropping results and cleaning up with Drop

LastArg to recall last arguments

Undo to restore previous stack state

The command line

Editing an object on the stack with Right key

Moving left and right on the command line

Repeating keys: Insert, left, right, delete

Inserting characters in the middle

Deleting characters left and right

Space key on R/S

Command line: entering three numbers at once

The editor menu

Selecting the editor menu

Moving word by word

Moving to beginning and end

Selecting text

Cut, copy and paste

Incremental search

Search and replace

Command line history

Recalling a previous command line

Optimization of command-line space

Exiting the command line

Entering letters and symbols

Alpha mode with Shift Enter

Alpha mode with Long Shift

Transient Alpha mode, upper and lowercase

Shift on digits and operations while in Alpha mode

Shifted characters

2nd shifted characters

White cursor for Alpha mode

C and L cursor indicators in text

Entering names

Executing a command by typing its name

Catalog with + key

Auto-completion

Example: VERSION

What happens if the name is not a command

Multi-line text editor

Multi-line Text editor

Up and down by shifting

Repeat up and down by holding key

Entering text

Entering text with 2nd shift ENTER

The C and L cursors

Mixed operations, e.g. adding text

Multiplying text by a number

Entering an algebraic expression

The ' () key

Entering an expression

Evaluating an expression with =

Cursor in algebraic mode

Comparing the sin key in direct and algebraic mode

Entering parentheses

Automatic elimination of parentheses

Symbolic algebraic expressions

Performing RPN operations on algebraic expressions

Automatic simplification of 0+x, 1*x, etc.

The Tools menu

Tools menu on empty stack

Tools menu for a decimal value

Tools menu for an integer

Tools menu for a text

Tools menu for an expression

Computations on complex numbers

The complex menu

Entering numbers in rectangular form

Entering numbers in polar form

Switching between polar and rectangular with Cycle key

Arithmetic on complex numbers

Exact angles and exact computations: 2<45 * 3<90 ^ 8

Functions on complex numbers, e.g. sin and log.

Effect of angle mode on display in polar form

Computations on vectors

Entering a vector

The M cursor

Adding and subtracting vectors

Component-wise multiplication and division

Operations between vector and a constant

Component-wise functions: 1/x

The tools menu on vectors

Computing the norm of a vector

The Matrix menu

Computations on matrices

Entering a matrix

Adding and subtracting matrices

Multiplication and division by a constant

Multiplying square matrices

Multiplying a matrix and a vector

Computing a determinant

Computing an inverse with 1/x

Advanced matrix operations

Matrix of complex numbers

Symbolic matrix

Inverse and determinant of 2x2 symbolic matrix

Entering data in lists

Entering a list

Adding elements to a list

Applying a function to a list

Repeating a list (multiply)

Lists containing lists

Computations with based numbers

Entering based numbers

Entering hexadecimal directly with A-F

Logical operations

Setting the word size

Changing to common bases (2, 8, 10, 16)

Changing to an arbitray base

Entering number in arbitrary base

The tools menu on based number

Binary operations

Emulating a 16-bit or 256-bit CPU

The Cycle key on based numbers

Adding a suffix to force a base (DM32 only)

Unit objects

Entering a value with a unit

The units menus

Applying a unit

Converting to a unit

Dividing by a unit

Entering a program

Computing a VAT

Evaluating a program with Evaluate

Modifying a program with LastArg

Modifying a program with Undo

Modifying a program with command-line history

The three roles of the R/S key: Space, =, EVAL

Storing values in global variables

Storing a value in a new variable 'VATRate'

Evaluating a variable

Case insensitivity

Naming a variable on the command line

Using quotes to avoid evaluation

Overwriting a variable value

Expressions containing variables

Storing and modifying programs

Creating a new VAT command

Evaluating a program by name

Evaluting a program from variables menu

Taking input and computing output

The variables menu

Showing the variables menu

Evaluating a variable with F1

Recalling a variable with shift F1

Storing in an existing variable with xshift F1

Rationale for the difference with HP48

Using variables menu while editing a program

Menus with too many entries

Adding more variables overflows

Going from 6 to 7 entries

No next key, using F6 and shift F6 for next and previous

Saving your state to disk

The system menu

Saving the calculator state

Restoring another state

Merging states

Returning to the calculator

Saving state quickly with xshift-EXIT

Plotting a function

Plotting a wave function sin(x * a) * cos(x * b)

Plotting a polar function

Plotting a parameteric function

Drawing two functions on the same screen

Changing line width

Changing line patterm

The numerical solver

Solving an equation

Expressions that must be zero

Equations A=B

Solving for different variables

Numerical integration

Integrating x^2 from 0 to 1 (exact results)

What happens with 0.0 to 1.0

Integration 1/x from 2 to 22

Comparing with LN(2) - LN(2)

Symbolic expression manipulation

Collecting terms

Expanding terms

General expression rewriting facility

Local variables

Why use local variables

Inserting local variables in a program

Inserting local variables in equations

Localized number display preferences

Changing the decimal separator

Changing the spacing for numbers

Changing the character used for spacing

User interface preferences

Square and rounded menu styles

3-level, 1-level and flat menu styles

Changing result font size

Changing stack font size

Changing editor font size

Changing multi-line editor font size

Comparisons and tests

Truth: True, False, 0, 1

Equality tests

Differences between = and ==

Relational operators

Logical operations (AND, OR, NOT)

More sophisticated programming

Testing with IF THEN ELSE END

Conditional expression with IFTE

Counted loop with START NEXT

Stepping loop with START STEP

Named loop with FOR NEXT

Named loop with FOR STEP

WHILE conditional loop

UNTIL conditional loop

Enjoy the calculator!

Installation

Downloading the software

You can download pre-built versions of the firmware from the releases page of the project (https://github.com/c3d/db48x/releases), or alternatively, you can download the source code and build it yourself.

The pre-built firmware for the DM-42 is split into two components, db48x.pgm and db48x_qspi.bin. The built-in help is stored in a file called db48x.md.

In addition, a file called Demo.48s contains a few sample RPL programs to illustrate the capabilities of this new firmware, two comma-separated values files units.csv and constants.csv, which define the units and constants respectively.

Connecting the calculator to a computer

The DM-42 calculator connects to your computer using a standard micro-USB cable.

System menu

The Setup menu is displayed by using 🟨 0. This key combination is the same on the stock DM42 firmware and on the new DB48X firmware, and it contains similar entries. However, the setup menu entries are not necessarily in the same order.

On the stock firmware, you need to successively select:

• System

• Enter System Menu

• Reset to DMCP menu

On the DB48X firmware, the required options are both directly available from the Setup menu.

Exposing internal storage as a USB disk

The Activate USB Disk option enables the calculator's USB disk mode, and exposes 6MB of its internal storage as a regular flash disk that you can access from your computer as an external disk.

Copying DB48X installation files

The files should be copied as follows:

• db48x.pgm and db48x_qspi.bin in the root directory of the calculator's USB disk.

• db48x.md should be placed in a directory called help.

• units.csv and constants.csv should be placed in a directory called config. You can customize these files to add your own units and constants.

Copying DM42 installation files

Refer to the SwissMicros installation instructions to install or reinstall the original calculator firmware.

Installing the DB48X QSPI file

To install the QSPI file, select the system menu and then select the Load QSPI from FAT menu entry.

The QSPI in the menu label refers to the file ending with _qspi.bin. When upgrading, you should load the new QSPI file first, and only then load the program file.

Installing the DB48X program file

To install the program file file, select the system menu and then select the Load program menu entry.

After loading the DB48X program, the firmware loaded asks you to press a key, and the new firmware automatically runs.

Switching between DM42 and DB48X

Early releases of the DB48X firmware produced a QSPI image file that was capable of running the stock DM42 program file. Unfortunately, this is no longer the case due to space constraints.

Unfortunately, the installation procedure for the QSPI file erases the file from the flash storage. This makes it relatively inconvenient to switch back and forth between DB48X and original firmware, since that requires copying the _qspi.bin file from your computer every time.

Saving and restoring DB48X state

The DB48X Setup menu is displayed by using 🟨 0. It contains a State menu entry to manage the DB48X state, which includes variables, programs and preferences.

The State submenu includes the following options:

• Load state
• Save state
• Clear state
• Merge state
• Activate USB Disk
• Show Disk Info

Types

DB48X, like HP RPL, supports a wide variety of data types.

Integers

The DB48X version of RPL distinguishes between integer values, like 123, and decimal values, like 123. Integer values are represented internally in a compact and efficient format, saving memory and making computations faster. All values between -127 and 127 can be stored in two bytes. All values between -16383 and 16383 in three bytes.

Integers can be as large as memory permits.

Big integers

The DB48X version of RPL can perform computations on arbitrarily large integers, limited only by available memory, enabling for example the exact computation of 100! and making it possible to address problems that require exact integer computations, like exploring the Syracuse conjecture.

Decimal numbers

Decimal numbers are used to represent values with a fractional part. DB48X supports three decimal numbers, using the 32-bit, 64-bit and 128-bit binary decimal representation. In memory, all decimal numbers use one additional byte: a 32-bit decimal number uses 5 bytes, a 128-bit binary decimal number uses 17 bytes.

The 32-bit format offers a 7 digits mantissa and has a maximum exponent of 96. The 64-bit format offers a 16 digits mantissa and has a maximum exponent of 384. The 128-bit format offers a 34 digits mantissa and a maximum exponent of 6144.

The Precision command selects the default precision.

Note that a future implementation of DB48X is expected to feature variable-precision decimal numbers similar to newRPL.

Based numbers

Based numbers are used to perform computations in any base. The most common bases used in computer science, 2, 8, 10 and 16, have special shortcuts. The Bases Menu list operations on based numbers.

Like integers, based numbers can be arbitrary large. However, operations on based numbers can be truncated to a specific number of bits using the WordSize setting. This makes it possible to perform computations simulating a 16-bit or 256-bit processor.

Boolean values

DB48X has two boolean values, True and False. These values are typically returned by operations such as tests that return a truth value.

In addition, numerical values are interpreted as being False if the value is 0, and True otherwise. This applies to conditional tests, conditional loops, and other operations that consume a truth value.

Complex numbers

Complex numbers can be represented in rectangular form or polar form. The rectangular form will show as something like 2+3ⅈ on the display, where 2 is the real part and 3 is the imaginary part. The polar form will show as something like 1∡90° on the display, where 1 is the modulus and 90° is the argument. The two forms can be mixed and matched in operations. The calculator typically selects the most efficient form for a given operation.

Available operations on complex numbers include basic arithmetic, trigonometric, logarithms, exponential and hyperbolic functions, as well as a few specific functions such as conj or arg. These functions are available in the Complex Menu.

Expressions

Algebraic expressions and equations are represented between quotes, for example X+1 or A+B=C. Many functions such as circular functions, exponential, logs or hyperbolic functions can apply to algebraic expressions.

An expression that contains an equal sign, e.g. sin X + 1 = cos X, is called an equation. It can be given as an argument to the solver.

Lists

Lists are sequence of items between curly braces, such as { 1 'A' "Hello" }. They can contain an arbitrary number of elements, and can be nested.

Operations such as sin apply to all elements on a list.

Vectors and matrices

Vector and matrices represent tables of numbers, and are represented between square brackets, for example [1 2 3] for a vector and [[1 2] [3 4] for a 2x2 matrix.

Vector and matrices follow their own arithmetic rules. Vectors are one-dimensional, matrices are two-dimensional. DB48X also supports tables with a higher number of dimensions, but only offers limited operations on them.

DB48X implements vector addition, subtraction, multiplication and division, which apply component-wise. Multiplication and division are an extension compared to the HP48.

DB48X also implements matrix addition, subtraction, multiplication and division. Like on the HP48, the division of matrix A by matrix B is interpreted as left-multiplying A by the inverse of B.

As another extension, algebraic functions such as sin apply to all elements in a vector or matrix in turn.

Units

Unit objects represent values with an associated unit. They are represented using the _ operator, e.g. 1_km/s, although on display this operator is shown as a thin space, e.g. 1 km/s.

Units as implemented in DB48X are modernized compared to what the HP48 implements, and differ from the HP RPL implementation in the following ways:

• Add recent SI prefixes, Z (zetta), Y (yotta), R (ronna) and Q (quetta) for large scale, z (zepto), y (yocto), r (ronto) and q (quecto) for small scale.

• Take into account the impact on unit conversions of the revised 2023 definition of the foot.

• Use exact (fraction-based) conversions wherever possible. This notably matters for the conversions of pre-2023 US Survey units, where the ratio is 1_ft = 1200/3937_m, which is not well represented using decimal values.

• Add computer-related units, like the byte, the bit, the baud, as well as a menu supporting these units.

• In order to support the computer-related units better, also recognize the power-of-two variants, e.g. 1_kiB is 1024_B. Also recogize the K prefix in addition to k.

Units file

The built-in units can be overriden by your own set of units, which is defined in a CSV file called config/units.csv in the calculator. CSV stands for "Comma separated values, and is a common interchange format for spreadsheet data.

Here is an example of file that would let you have a units menu called Money to convert between various monetary units:

"Money"
"USD", "1_USD"
"EUR", "1.07_USD"
"GBP", "1.24_USD"
"CAD", "0.73_USD"
"AUD", "0.65_USD"
"CHF", "1.11_USD"

• All values must be placed between quotes. Separators between text values are mostly ignored.

• Rows in a file containing a single value denote unit menus, unless the value begins with an = sign.

• Rows in a file containing two ore more values denote unit menu entries, which will be added to the previous menu.

• The first column in these rows give the name of the unit as shown in the menu.

• The second column in these rows gives the definition of the unit.

• The definition should be reduced to = if the first column contains what would be a valid unit expression. For example, to place km/h in a menu, use "km/h", "=" since km can be deduced from existing unit m using the standard "kilo" unit prefix, and h is an existing unit.

A unit where the value is 1 of the same unit is a base unit. This is the case for USD in the example above, which is considered the base units for monetary exchanges. Units that refer to the same base unit can be converted with one another. For example, you can convert between GBP and AUD because they both have the same USD base unit.

The commands ShowBuiltinUnits and HideBuiltinUnits indicate if the built-in uits should be shown after the units loaded from the file. The default is that when a units file is present, the built-in units are hidden. This only affects the menus. Built-in units can always be used in expressions if they are typed manually. However, units loaded from file will be looked up first, so that a built-in unit can be overriden by the units file, which can be useful if a definition changes like the US Survey foot changed on January 1st, 2023.

If you build a units file, it is recommended that you do not exceed 17 unit submenus so that all unit categories fit on a single screen.

Cycle command customization

The menu name "=Cycle" is reserved to define sequences of units that the Cycle command (bound to the ×10ⁿ key) will recognize as special. For example, you can ensure that mm and in convert to one another as follows:

"=Cycle"
"in", "mm"
"mm", "in"
"USD", "EUR"
"EUR", "CHF"
"CHF", "USD"

If you do provide a Cycle customization for a unit, other normal behaviours of the Cycle command for units are disabled, notably conversion between various relevant scales and conversion between fractions and decimal. To force a particular conversion to happen in decimal, you can override the definition of the corresponding unit in the units file, for example:

"in",   "25.4_mm"

Constants

Constant objects represent named values like Euler's constant e, the ratio between circumference and diameter of a circle π, or the speed of light c. They are represented by a name, and have an associated value.

Like units, there are some built-in constants, and additional constants can be provided by a config/constants.csv file, which has the same format as for the units file.

On the command-line, constant names are prefixed with CST, which is a way to distinguish them from normal symbols.

You can edit the constants catalog by recalling its content on the stack using "config:equations.csv" RCL, editing the values, and then storing the content back to disk using "config:equations.csv" STO.

Infinite results

Some operations such as 1/0 or tan 90 ° are said to produce an infinite result. Like HP calculators, DB48X can either generate an error or produce a special result in these cases.

• If the InfinityValue (-22) flag is clear, corresponding to the InfinityError setting, then the operation generates a Division by zero error. Note that the text of the error is different than for Hewlett-Packard calculators, which generate an Infinite result error.

• If the InfinityValue flag is set and NumericalConstants (-2) flag is clear, corresponding to the SymbolicConstants setting, then the operation generates the ∞ (infinity) constant with the appropriate sign for the result, and the InfiniteResultIndicator (-26) flag is set.

• If the InfinityValue flag is set and NumericalConstants flag is set, then the operation generates the numerical value associated to the ∞ constant with the appropriate sign for the result, and set the InfiniteResultIndicator flag.

By default, the numerical value of the ∞ constant is set to 9.99999E999999, which is significantly smaller than what would actually cause a numerical overflow, but is easy to read. This value can be changed in the config/constants.csv file.

Overflow and underflow

There is a maximum representable value for decimal numbers. This value is significantly larger than on HP calculators. Whereas HP RPL implementations could not represent decimal numbers with an exponent bigger than 499 or smaller than -499, DB48X supports exponents ranging from -2^60 to 2^60 (±1 152 921 504 606 846 976).

An overflow happens if the result would have an exponent higher than the maximum. An underflow happens if the result would have an exponent lower than the minimum. Like HP calculators, DB48X can either generate an error or produce a special result in these cases.

• If the UnderflowValue (-20) or OverflowValue (-21) is clear, corresponding to the UnderflowError or OverflowError setting, then the operation generates a Positive numerical underflow, Negative numerical underflow or Numerical overflow error depending on the computation. Note that the text of the error is different than for Hewlett-Packard calculators, which generate an Overflow, Positive Underflow or Negative Underflow error.

• If the UnderflowValue or OverflowValue is set, and NumericalConstants (-2) flag is clear, corresponding to the SymbolicConstants setting, then overflowing operations generate the ∞ (infinity) constant with the appropriate sign for the result, and underflowing operations generate a zero value. The operation also sets the NegativeUnderflowIndicator (-23), PositiveOverflowIndicator (-24) or OverflowIndicator (-25) flag.

• If the UnderflowValue or OverflowValue is set, and NumericalConstants flag is set, then overflowing operations generate the numerical value associated to the ∞ constant, and underflowing operations generate a zero value. The operation also sets the NegativeUnderflowIndicator (-23), PositiveOverflowIndicator (-24) or OverflowIndicator (-25) flag.

Undefined

Some operations such as 0/0 are undefined, meaning that there isn't a single possible answer.

If the UndefinedValue flag is set, such operations return the constant ?, and further operations on the value will keep returning the same undefined result.

If the UndefinedValue flag is is clear, which corresponds to UndefinedError being set, such operations will generate an Undefined operation error.

Library

The Library is a catalog of frequently used and rarely modified objects that are stored on disk in the config/library.csv file.

You can edit it by recalling its content on the stack using "config:library.csv" RCL, editing the values, and then storing the content back to disk using "config:library.csv" STO.

Equations Library

The equations library is a catalog of common equations that are stored on disk in the config/equations.csv file.

You can edit it by recalling its content on the stack using "config:equations.csv" RCL, editing the values, and then storing the content back to disk using "config:equations.csv" STO.

Release notes

Release 0.7.16 "Clean" - New commands

The focus of this release is on new commands, notably for matrix and vector operations. This release also ships with a DM48X-specific keymap, which fixes a problem with teh file selector on the DM32. The equation library has been extended with numerous equations, but they are not fully validated yet.

Features

• con, idn and ranm matrix generation commands
• Array→ and →Array commands to convert array to/from stack
• dot product and cross product commands for vectors
• DispXY styled text rendering command
• DupDup command duplicating top item twice
• Add a large number of equations to equation library

Bug fixes

• Fix decimal::to_bignum for small magnitudes
• Return angle unit for atan2 and arg commands
• The for loop on lists no longer ends leaving the debugger active
• Interactive stack DropN command returns to level 1
• Fix file selector's "New file" on DM32 so that ENTER terminates it
• A few fixes in equations in the equation library

Improvements

• Improve graphical rendering of expressions such as multiplication operators
• doc: Update status
• font: Fix v glyph vertical placement, add dot and cross glyphs
• ttf2font: Add additional verbose info about source data
• Add CONSTANTS as an alias for ConstantsMenu
• Replace documentation references to EEX with ×10ⁿ
• Optimize parsing of real numbers in parentheses

Release 0.7.15 "Teaching" - Bug fixes notably on iOS

This release mostly focuses on issues exposed by the iOS releases. It's a bug-fixes only release.

Bug fixes

• ios: Fix a screen refresh bug delaying the display of computation results
• ios: Increase user-accesssible memory for DB50X to match the DM32
• files: Avoid opening two files when a loaded file contains units/constants
• units: Restrict unit expressions further, e.g. forbid 1_km^s
• build: Do not add unwanted macOS-specific files in release tar files
• build: Remove irrelevant help file from releae tar file
• constants: Fix numerical value for G constant
• tests: Rename M demo helper to D, since we use M in symbolic tests
• makefile: Add mv echo to targets doing image comparison
• units: Use pi constant in definition of radians unit
• parser: Detect syntax error on (inv(x)) in non-expression mode
• units: Avoid infinite loop for bad unit exponents
• files: Avoid crash in file_closer if file does not exist
• tests: Add DMS/HMS operations to math demo
• tests: Add keyboard shortcuts to launch the demos

Release 0.7.14 "Kids" - Equation-related bug fixes

This release fixes a number of issues that were discovered primarily through the Columns and Beams equations.

Features

• trigonometrics: Add conversion from non-standard angles, so that cos(1_turn) gives the correct result.
• debug: Debug on error with DebugOnError and KillOnError settings. This makes it easier to debug an RPL program, by making it possible to single-step around the instruction that generated the error.
• tests: Add three 30 second demo of DB48X features. These are to generate marketing videos for the iPhone version on the Apple store (to be done).

Bug fixes:

• ui: Keep a GC pointer in draw_object to avoid a memory crash
• equations: Add missing units in some equations, e.g. I and A in second equation of Coilumns and Beams
• equations: Add explicit radian unit in Eccentric Columns cos, which ensures we get the correct result from the HP50G manual even when in Degrees mode.
• units: Correctly factor out non-integral powers, so that we can compute 1/sqrt(epsilon_0*mu_0) and get the correct result.
• catalog: Display commands that begin with selection first, so that FORE shows Foreground before AlphaForeground.
• stats: When computing a sum, evaluate the expression on all terms. The result for Variance with single variables was wrong because the first term was computed incorrectly due to a misguided optimization.
• graphics: Error out in RGBPattern for negative input. The negative values were generating an error, but it was not reported, so the next command was likely to report it.
• help: Render shift keys correctly in the color version. The bitmap was interpreted as containing color data. Colorize it instead.

Improvement

• ui: Select orange as background color during search. The previous setting of showing seardch using white foreground on a white background was probably pushing the notion of "blind search" a bit too far.

Release 0.7.13 "Murderers" - Solver improvements

This releases focuses on improvements to the solver, with the completion of the Columns and Beams section from the HP50G equation library.

Features

• equations: Add remaining equations from "Columns and Beams"
• loops: For loops on lists and arrays
• menus: Add R→D, D→R, →Polar and →Rectangular
• menus: Automatically select tools menu for library equations
• units: Allow ubase to work on expressions
• units: Graphic rendering of units

Bug fixes

• 48calc.org: Fix mouse click position
• #ABC #DEF - now correctly produces a based number with >64-bit wordsize
• conditionals: Parse and evaluate IFTE correctly
• equations: Fix Elastic Buckling
• files: Avoid crash in file_closer if file was not open
• istack: Enable Swap feature on top two levels
• menu: Update SolvingMenu when updating VariablesMenu
• parser: Deal with negation more "normally", parse -a² correctly
• solver: Compute units correctly for inputs
• solver: Do not change unit when storing in a solver variable
• solver: Emit correct error message in EvalEq if missing variables
• solver: Preserve errors reported by underlying function
• units: Do not evaluate/render units with names
• units: No longer read variables m and s while processing 1_m/s
• units: Simplify units that convert to real numbers

Improvements

• Update .gitignore
• build: Add BMP files to the distribution
• complex: Optimize exit conditions for parentheses
• solver: Add test for equation library
• solver: Add tests for solving with units
• solver: Improve behaviour of EvalEq
• solver: Keep units and constants as-is in equation
• solver: Make precision relative to equation sides magnitude
• stack: Show vectors vertically by default
• ui: Do not persistently hide stack with current equation
• units: Keep power integral, i.e. avoid getting 1_m^2.0/s
• units: Strip tags from unit conversion functions
• units: The EvalEq command should not evaluate dates
• wasm: Add logos to the repository

Release 0.7.12 "Multiply" - Multiple equations

This release focuses on the equation solver, notably in interaction with the equation library. The goal is to get one step closer to the equation library in the HP50G, including the ability to have graphical illustration and multiple equations.

Features

• doc: Add documentation for the equation library
• doc: Add images from HP50G equation library (to be used later)
• doc: Some help for the elastic buckling equations.
• equations: Accept lists of equations in library
• help: Add documentation for the various constants
• help: Do not exit help when opening URLs or missing topics
• lists: Add a setting to evaluate list as programs
• menu: Add menu entries for solver imprecision and iterations
• solver: Add support for multiple equation solving
• ui: Add settings to hide/show empty menus and clear menu on EXIT
• units: Add flow units (per user request) in Fluid section of units

Bug fixes

• blitter: Adjust the right margin
• blitter: Base horizontal adjust on scanline, not width
• characters: Display correct content for built-in menus
• constants: Close current file while parsing values
• constants: Update some outdated values
• doc: Show help for equations and constants
• help: Do not try to load PNG images
• rewrites: Avoid contradictory rules when reordering constants
• solver: Work correctly with units (when in variables but not equation)

Improvements

• build: Shorten the size of the version abbrev
• config: Use config files only for user configuration
• doc: Record performance data about unit conversion
• help: Avoid slowing down when scrolling through pages of help
• help: Record position for history even without a \n
• simulator: Add tweak to show RPL object details
• tests: Increase wait time for tests with blinking cursor
• units: Do not simplify while in unit mode

Release 0.7.11 "Rest" - Refine interactive stack, graphics in help

This release is a refinement minor release. The primary focus is the interactive stack, which now lets you edit items, sort either according to memory representation or by value, display information about objects, and jump directly to a given stack level using digits.

The simple random number generator implemented in 0.7.10 was replaced with an additive congruential random number generator (ACORN), which can be configured in number of bits and number of iterations. A side effect is that there is now regression testing for single-variable statistics.

The history feature was also improved by automatically enabling the EditMenu when selecting history, and then having the (unshifted) word left and word right commands automatically cycle through history if used at beginning or end of the editing buffer.

Features

• help: Add ability to display BMP images in help files
• images: Convert help images to BMP
• ui: Add Edit feature to interactive stack
• ui: Add history menu entries to EditMenu
• ui: Accept UNDO while in interactive stack mode
• ui: Have word previous/next cycle through history
• ui: Accept digits to select stack level in interactive stack
• random: ACORN random number generator

Bug fixes

• editor: Fix spacing after number followed by - sign
• ui: Do not set the editing field from interactive stack
• ui: Replace interactive stack "Edit" with "Echo"
• ui: Block user input while using interactive stack
• ui: Do not draw menu markers when displaying interactive stack
• runtime: Avoid crash running above allocated memory in move_globals

Improvements

• ui: Reorganize code handling interactive stack keys
• help: Adjust help area to new height for menus

Release 0.7.10 "Hospitality" - Interactive stack

This release primarily adds the "interactive stack" feature of HP calculators.

Features

• stack: Interactive stack and associated menu
• functions: Very basic random number generator
• demo: Add CountPrimes and RandomPlot examples

Bug fixes

• menus: Do not execute if-then-else and similar
• expressions: Avoid error testing for zero/one in power operator
• condidionals: Avoid infinite loop evaluating condition
• menu: Insert iferr-then-else correctly from menu
• constants: Skip menu entries

Improvements

• menus: Reorganize stack menu to put Dup and Drop on first page
• menu: Add error functions to Debug menu

Release 0.7.9 "Just Asleep" - Online WASM simulator

This release includes a number of bug fixes, facilitates build from scratch by third-parties, and delivers a WASM-based simulator that runs on the https://48calc.org web site.

Features

• menu: Add Purge to the ClearThingsMenu
• purge: Add support for lists
• units: Accept units for sqrt, cbrt and xroot
• wasm: Add variant for 48calc.org
• wasm: Implement WASM support

Bug fixes

• complex: Give Syntax error for phasor without an angle
• dms/hms: Parse empty numbers in DMS entry
• dms/hms: Protect display against bad input
• editor: Make sure we reposition after shift-up and shift-down
• parser: Parse degrees as an angle unit in phasors
• simulator: Avoid high CPU usage when a timer is active
• simulator: Use the correct color for firmware text
• ui: Compute the correct refresh rate even when nothing is displayed
• ui: Create a non-empty dirty rectangle when clearing annunciators
• ui: Do not refresh beyond LCD size
• ui: Ensure we redraw the shift region to clear busy
• units: Disable simplification during unit definition evaluation

Improvements

• build: Fix the clean build
• object: Remove defaults for as_uint32 and similar
• parser: Cache parser::length when possible
• parser: Merge the parser::end and parser::length fields
• parser: Optimize integer parsing early exit
• simulator: Avoid Cancel in file save dialog
• simulator: Use https as a protocol for git submodules
• tests: Add support for degrees sign
• tests: Add test for polar angle conversion.
• units: Add factoring variable to limit simplifications
• wasm: Add link to deployed WASM simulator in the README
• wasm: Add script to add COOP / COEP headers
• wasm: Run the RPL thread in a separate thread

Release 0.7.8 "Mustard" - Constants in equations

This release keeps marching towards full support for an equation library. The primary focus was support for constants in equations, including constants with units like the speed of light, as well as fixing various user-reported issues.

Features

• cycle: Apply to value of tagged object
• equations: Add units to built-in equations
• equations: Adjust menu label to remove units
• equations: Strip units but not constants when rendering
• expressions: Treat 2X as an implicit product
• solver: Strip units from constants
• units: Unit prefix should preserve the tag

Bug fixes

• clearlcd: Fix erasure of screen when not in graphics mode
• constants: Count number of menu entries correctly for builtin menus
• decimal: Accept leading . or , for decimal values
• expressions: Parse negation after parentheses
• sum: Do not accept a non-name in a sum or product
• type: Return a type value for decimals
• ui: Fix insertion/editing of infix with alphabetic names
• units: Do not read units from variable if they exist
• xroot: Reverse xroot arguments in algebraic parsing

Improvements

• editor: Shuft-up returns to beginning of line if on first row
• errors: Add error_save class, use it in constant::value
• expressions: Use the SaveAutoSimplify class in simplify_products
• units: Split Eng to Elec and Visc

Release 0.7.7 "Forgiving" - Units in equations

This release keeps marching towards full support for an equation library. The primary focus was support for units in equations.

New features

• solver: Accept equations in solver menu
• solver: Add shortcut to solve an equation from the library
• solver: Display the current equation above the stack
• solver: Solve expressions containing units
• solver: Add units for solver variables when entering them
• equations: Add option to list variables with units
• programs: Enforce numerical values for solver / plotter
• constants: Implement programmatic lookup
• fonts: Add support for fixed-width digits
• keyboard: Interpret ASN as AsNumber (convert to decimal)
• complex: Allow insertion of angle while entering phasors
• complex: Implement auto-complex promotion
• graph: Render abs(X) with bars (e.g. |X|)
• functions: Automatic simplification of expressions

Bug fixes

• arithmetic: Avoid null-dereference in complex operations
• help: Close help file if topic not found
• solver: Do not store tag for tagged values
• graph: Gracefully fallback if fraction integral part does not render
• units: Avoid null-dereference if unit simplification fails
• units: Count parentheses while parsing units
• put: Fix null-dereference checking the index
• fractions: Do not render two negative signs in graphical mode

Improvements

• cycle: Update behaviour for several data types
• menu: Replace abs with |z| in complex menu
• ui: Micro-optimization to avoid reading object type twice
• parser: Accelerate and improve object parsing
• recorder: Add recorder entries for evaluation
• build: Remove any leftover references to Intel decimal library
• tests: Add ▶ entry in tests
• tests: Increase default wait time to 1000ms
• tests: do not error out if teval takes less than 100ms
• equations: Rename PerfectGas equation to IdealGas
• menus: Adjust size of menus to make descenders visible
• solver: Replace SolverPrecision with SolverImprecision

Release 0.7.6 "United" - Equation Solving Menu

This release is primarily about implementing a dynamic solving menu that makes it easier to solve equations with multiple variables. This is roughly equivalent to the "Solve Equation" application in the HP50G.

New features

• solver: Implement solving menu
• tag: Graphic rendering for tagged objects
• lists: Implement lname and xvars commands
• arithmetic: Implement div2 command
• variables: Implement vars and tvars commands

Bug fixes

• render: Avoid errors while rendering / graphing
• expressions: Avoid consuming stack levels for invalid expressions
• symbols: Avoid ignoring the list of bad characters in symbols
• command: Fix for x! parsing
• stack: Correctly set clipping for stack index
• doc: Fix typo in release note

Improvements

• menus: Add PixOn, PixOff, Pix? and PixC? to GraphicsMenu

Release 0.7.5 "Perfect Joy" - Polynomials and symbolic rewrites

This release contains a lot of groundwork in preparation for future work on symbolic expressions, symbolic solving and symbolic integration, as well as to improve compatibility with HP calculators. In particular, rewrite has been replaced with the HP equivalents, ↑Match and ↓Match, allowing top-down and bottom-up replacement, as well as support for conditions. Also, these commands return the number of replacements performed instead of just 0 or 1.

THe other major user-visible new feature is the addition of a polynomials data type, which does not exist on HP calculators, exposing polynomial features in a way that is more consistent with the spirit of RPL. For example, Euclidean division of polynomials can be achieved using the regular / operation on polynomials instead of requiring a dedicated DIV2 command.

New features

• Support for polynomials as a data type, including Euclidean division
• Arithmetic operations on polynomials, including sq and cubed
• Conversion functions →Poly and Poly→ to convert to and from polynomials
• Optional case-sensitive symbol matching
• Algebra configuration directory (like CASDIR on HP calculators)
• rewrites: Replace rewrite command with HP-compatible ↑Match and ↓Match
• rewrites: Add ExplicitWildcards option to match HP syntax (&A)
• rewrites: Add rules to expand powers
• rewrites: Add support for conditions when matching patterns
• rewrites: Add support for step-by-step rewrites
• rewrites: Add support for bottom-up rewrites
• flags: Purge now resets system flags to default value

Bug fixes

• editor: Fix unresponsive keys after using EXIT key while searching
• complex: Avoid emitting syntax errors while parsing
• rewrites: Avoid potential garbage collection corruption problem
• rewrites: Disable auto-simplification during rewrites
• rewrites: Factor out rewrite loop
• expressions: Encode expressions with type ID >= 128 correctly
• arithmetic: Add space around mod and rem in rendering
• graph: Do not add parentheses for X*(Y/Z)
• functions: Make percentage operations binary functions
• functions: Turn min and max into algebraic functions
• cycle: For expressions, cycle graphic/text rendering correctly
• menus: Replace EquationsMenu with ExpressionMenu in other menus
• ui: Insert space when inserting array inside function

Improvements

• menus: Updates to PolynomialMenu to enter polynomials and for conversions
• menus: Add product and sum to symbolic and algebra menus
• menus: Make ToolsMenu select SymbolicMenu for symbols
• expressions: Reorganize the code for rewrites
• rewrites: Add recorders for rewrites that are actually done
• tests: Some adjustments on color images
• rewrites: Convert algebraics into expression as needed
• complex: Parse 3i and i3 in addition to i
• tests: Add support for more characters
• simulator: Separator color and dm32 support
• graph: Add space when rendering simple function
• keyboard: Updated SVG files with latest menu labeling changes

Release 0.7.4 "Flesh" - Polishing and refinements

This release is mostly about polishing various aspects of the implementation to make it more convenient and more efficient. It also adds user-defined functions parsing and evaluation, pixel-manipulation commands, bit operations on binary numbers, memory operations like sto+ or incr, loading and saving BMP files, color support in the simulator, and more.

New features

• editor: Implement configurable word wrapping
• expressions: Add code for n-ary functions like sum
• expressions: Parse user-function calls like F(1;2;3;4)
• expressions: Ensure funcall objects are evaluated immediately
• functions: Add sum and product functions
• functions: Add combinations and permutations
• functions: Implement number rounding operations (rnd and trnc)
• graph: Add graphical rendering for cbrt (cube root) and xroot
• graph: Graphical rendering of combinations, permutations
• graph: Graphical rendering of sum and product
• graphics: Add pixon, pixoff and pix? commands
• graphics: Store and recall BMP files with sto and rcl
• graphics: ToGrob command converting object to graphic
• logical: Add SetBit, ClearBit and FlipBit commands
• memory: Implement the Clone (NewOb) function
• menus: Add log2 and exp2 to ExpLogMenu
• menus: Place ListMenu as a keyboard-accessible menu
• parsing: Parse n-ary functions
• program: Add vertical program rendering mode
• stack: Display error message emitted during stack rendering
• ui: Add colorization parameters for the user interface
• ui: Add some colorization
• variables: Add Sto+, Rcl+ and other variable arithmetic
• variables: Implement Increment and Decrement

Bug fixes

• decimal: Fix precision when computing gamma/lgamma
• decimal: Fix rounding bug when rounding increases exponent
• doc: Add missing dependencies on Fedora (submitted by @vkadlcik)
• files: Do not error when opening constants/equation/library files
• files: Open only one configuration file at a time
• graphics: Fix bug drawing a line of width 0
• graphics: Use foreground color for parenthese and ratio
• lists: Separate list sum/product from regular sum/product
• renderer: Make sure printf respects target buffer size
• simulator: process double-clicks correctly (submitted by @kjellc)
• tests: Change the height of ignored header

Improvements

• command: Factor out arity for all commands
• constants: Report parse error location for invalid constants
• demo: Add HP-48 style slow walk to Walk demo
• demo: Modernize the code a little
• demo: Modify performance benchmarks to use TEval
• demo: Replace imaginary unit constant
• doc: Remove reference to Intel Decimal Library
• files: Convert all file names to lowercase (Linux support)
• functions: Make it possible to interrupt a running sum/product
• graph: Improve rendering of exp, exp2, exp10
• graphics: Separate color conversion step
• help: Do not display command name while editing
• ids: Make room for a few additional 1-byte commands
• locals: Document the absence of compiled local variables
• makefile: Add configuration files to the release .tgz file
• parsing: Make the error message for sub-expressions more local
• readme: Remove reference to DM42 from top-level readme
• simulator: Avoid crash rendering %t in recorder
• simulator: Convert simulator code to support color
• simulator: Replicate open files limitations
• simulator: Separate db50x and db48x builds
• tests: Add colorized images to testing
• tests: Avoid occasional errors on some long-running tests
• ui: Define cursor position in SelfInsert with \t
• ui: Ignore EXIT, BSP and ENTER keys when clearing error

Release 0.7.3 "Perfume" - Mostly bug fixes

This release is mostly about bug fixes, improving the build on simulator, and accelerating the test suite while keeping it stable.

New features

• simulator: Add F8 key to save state in the simulator
• errors: Add a beep when an error is shown
• linux: Add -s option for screen scaling (when Qt gets scaling wrong)
• equations: Get library equation value for plotter, solver and integrator
• characters: Add constant, equation and lib markers to RPL menu
• characters: Add music-related characters and character menu
• commands: Add missing stack commands (nip, pick3, ndupn, unrot, unpick)

Bug fixes

• variables: Clone purged objects on stack after Purge
• units: unit * symbolic is preserved as is (e.g. 'A'_m)
• compare: Enforce the NumericalResults flag for comparisons
• constants: Fix parsing of constants, equations and library items
• sto: Repair file exists error storing to a source file
• simulator: Do not try to create directory if it exists
• Report file errors, e.g. permissions or I/O errors
• equations: Mark c and R as constants in equations
• simulator: Double clicks are now considered as virtual keyboard touches
• ui: Emit only one beep, not two, for a syntax error on the command line
• ui: Avoid rare null-dereference crash when menu label is not set
• complex: Report a syntax error if the second half is empty
• utf8: Do not accept constant/equation/library codepoint in names
• units: Multiplying by 1_m is OK even with algebraic
• tests: Avoid case where CLEAR does not clear errors
• audio: Improve audio reliability on the simulator
• linux: Rewrite the audio-generation code to avoid crashes
• linux: Avoid infinite recursion in the tests
• linux: Fix warnings about unused variables
• linux: Avoid warnings about null pointer in strcmp
• linux: Avoid build error due to bad ularge overload in settings
• linux: Fix type issue for the Insert function (reported as a warning)
• linux: Remove warning about mixing enums and integers
• linux: Avoid error on printf format
• linux: Avoid warnings about type qualifiers
• linux: Remove warnings about incompatible function casts
• linux: Address warnings about missing initializers
• linux: Fix warning about prinf formats
• linux: Address warning about signed vs unsigned
• linux: Remove warning about fall-through switch statement
• linux: Remove warnings about unused arguments
• tests: Repair several tests that were unstable due to scrolling images
• tests: Increase memory size to avoid occasional out of memory failures
• object: Make as_uint32 and as_uint64 consistent for negative input

Improvements

• ui: Emulate HP48/HP50G behavior for errors (do not require key to continue)
• simulator: Add I/O wrapper around file state save/restore
• dmcp: Remove double return in the code
• simulator: Accept numeric keys in DMCP menus
• doc: Add Kjell Christenson to list of authors
• tests: Run command-line tests silently
• tests: Clear settings the fast way for quick tests
• dmcp: Do not treat the buzzer as a recorder error (avoid message noise)
• simulator: Ensure error messages show up in a recorder dump
• tests: Increase memory size to avoid failing tests
• tests: Increase delay waiting for function plots to appear
• tests: Refactor test suite interaction with RPL thread to accelerate it
• tests: Add a delay before launching the test thread to load initial state
• tests: Add missing reference picture for char-menu

Release 0.7.2 "Light" - Libraries, Characters menu

This release introduces four relatively significant features:

1. An Equation Library
2. A more general Library
3. Character menus
4. A character modification catalog

There are also a number of bug fixes and improvements.

Features

• The Equation Library is similar in principle to what is found in the HP50G. It is intended to store equations covering a variety of topics. The Equation Library is accessible using the EQS key (🟦 '()'). It is presently only very sparsely populated, but a future release should add the equations listed in Chapter 5 of the HP50G Advanced User's Reference Manual. Elements of the Equation Library appear as named Equation Objects. The Equation Library is configured by file config/equations.csv.

• The Library is similar to the Equation Library, but for all kinds of objects such as programs or code snippets. The Library is accessible using the LIB key (🟦 VAR). It can be used to customize your calculator, and is intended to play the roles of the CST variable (quick access to common features) and Library Objects / XLIB (external extensions to RPL). Elements of the Library appear as named Library Objects. The Library is configured by file config/library.csv.

• The Characters Menu lets you enter Unicode characters easily, by presenting various classes of characters, such as RPL, Greek or Punct. The Characters Menus is accessible using the CHAR key (🟦 2). It can be used to enter international characters (e.g. Greek or Cyrillic), as well as special characters such as arrows or blocks. The Characters Menu is configured by file config/characters.csv.

• The Characters Catalog appears when the Catalog is active and the cursor is inside some text object. It gives you access to characters that are visually close to the character on the left of the cursor. For example, after typing A, the presented choices include À, a or α. The Characters Catalog is configured by file config/characters.csv.

• compare: Add comparisons for true and false values

• Add TEVAL command (timed evaluation)

Bug fixes

• Do not add unnecessary parentheses in ratios, e.g. (A+B)/(X-Y)
• Make sure we can save back the configuration files correctly
• Improve access path checks to accept config:constants.csv.
• Avoid syntax error in 1/(1+x) due to 1/ being seen as a fraction
• unitfile: Remove slight risk of bad menu display after garbage collection
• date/time: Make sure we save the stack and last args for Date, Time, ...
• parser: Skip spacing when parsing numbers (to parse back →Text result)
• time: Fix rendering of DMS time in lists, matrices, vectors
• catalog: Fix a subtle bug on DM32 leading to a crash using the catalog

Improvements

• constants: Get values of special π and e by name
• constants: Add prefix in editor to identify constants, equations and xlib
• constants: Represent constants with an index for memory and performance
• constants: Parse units containing text
• constants: Allow RCL to recall a constant value
• units: Direct insertion of units after numbers
• menu: Update Roll and RollDown menu entries
• show: Show all decimals for decimal values
• help: Display the correct on-line help topic for constants
• catalog: Use less memory for the sorted IDs
• integrate: Use numerical computations for faster convergence
• locals: Improve error message for bad locals
• graph: Improve graphical rendering of constants (bold) and equations
• graph: Do not add unnecessary parentheses in ratios
• tests: Add tests for characters menu/catalog
• tests: Fix the . vs 0. test
• ui: Do not enter DMS inside text
• tests: Display disabled tests in gray
• catalog: Keep a single spelling, e.g. no add duplicates
• tests: Add extra delay in the wait for update
• makefile: Add dependency of 'all' to the decimal constants
• save: Improve rendering control when saving files
• stack: Do not save stack in plot, integration or solver
• debug: Disable debugging when launching a program from function key
• simulator: Avoid piling up QT draw requests
• doc: Update performance numbers for 1M loops
• simulator: Add sound support
• simulator: Lazy screen refresh
• dmcp: Add UI refresh callback
• simulator: Move QT-dependent code out of dmcp.cpp
• Add reduced font
• runtime: Various changes to isolate QT build from the rest

Release 0.7.1 "Whip" - Bug fixes

Inserting variables, constants or units in a program was broken. Also a few less critical fixes.

Bug fixes

• decimal: Apply MinimumSignificantDigits to Sig modes
• tests: Fix missing ] at end of vector
• ui: Insert commands for unit conversions, constants and variables
• tests: Adjust help screen snapshot for authors
• menus: Do not clip text for hierarchical menus
• constants: Do not use units that don't parse correctly
• dmcp: Day of week convention adjustment
• help: Fix YouTube video preview

Release 0.7.0 "Temple" - Graphics Equation Rendering

This release introduces a few major improvements, including graphical rendering of equations and matrices, the Show command to display large objects full-screen, customizable constants, and date-related operations.

New features

• Graphical rendering of equations, fractions, matrices, vectors and lists. In graphical rendering mode, variables are showin in italics.
• Constants in the ConstantsMenu, split into categories, and loading from an optional config/constants.csv file, in a way similar to what existed for units.
• Inverse trigonometric functions (asin, acos and atan) now produce unit objects with the current angle mode as a unit. This can be configured by the SetAngleUnits / NoAngleUnits flags.
• Cycle (×10ⁿ key) now cycles between angle units.
• R→D and D→R commands to convert between degree and radian in a purely numerical way (no unit). This is for compatibility with HP.
• Add →Deg, →Rad, →Grad, →πr commands, which convert a number to the target unit using current angle mode, and convert an angle to the target angle unit.
• Conversion from DMS to HMS and from HMS to DMS
• Rendering of dates: 19681205_date renders as Fri 5/Dec/1968, with a format configuration using the same flags as for the header. Note that the date format is YYYYMMDD, not the same as on HP calculators. This allows YYYYMMDD.hhmmss for dates with time.
• Date and Time command to return the current date and time. Additionally, DateTime returns both date and time, and ChronoTime returns the time with 1/100s precision.
• →Date and →Time commands to set the system date and time
• Date+, DDays and date arithmetic using + or -, using day units for the results. As an extension relative to HP calculators, these will accept fractional days, or other time units. For example, adding 1000000_s to 19681205_date generates a date with time result, Tue 16/Dec/1968, 13:46:40
• JulianDayNumber and DateFromJulianDayNumber commands to convert between dates and Julian day numbers. These commands also accept fractional input.
• Show command showing a full-screen graphical rendering of the result on the stack. The resut is size-adjusted. For example, you can display all digits in 200!. If the result does not fit on the screen, you can scroll using the ◀︎ and ▶︎, as well as 8, 6, 4 and 2. The maximum pixel size for Show is set by MaxW (default is the width of the LCD), the maximum height is set by MaxH (default is 2048 pixels).
• AutoScaleStack and NoAutoScaleStack settings to automatically adjust the font size for the stack elements.
• Support for system flags -20 to -26 (infinite results, overflow and underflow).

Bug fixes

• simulator: Adjust DMCP month off-by-one error
• Repair insertion of while loops and similar commands on the command line
• Use stack format when drawing an object with DrawText (DISP)
• Arithmetic on unit objects no longer auto-simplifies, e.g. 1_s 1_s - returns 0_s and not 0.
• Perform computations for →Q using integer values, which avoids an issue where increasing the number of iterations with an unachievable precision could prodduce 1/1 as the fractional result.
• Repair auto-simplification for i*i=-1
• Display a negative mixed fraction as -1 1/3 and not 1 -1/3.
• Do not insert () after a multiplication in algebraic mode
• Accept units and tagged objects in PolarToReal and RealToPolar
• Accept angle units as input for →DMS
• Off-by-one clipping error in header, erasing the shift annunciator
• Fix help for FC? (incorrectly stating that it tested for flat set)
• Lookup units and constants in a case sensitive way
• Fix labels for ExpFit and LinFit in RegressionMenu.

Improvements

• tests: Adjust tests to match bugs fixed in v0.6.5
• dms: Accept entering minutes without third dot, e.g. 1.2.3 ENTER
• menus: Split the Time, Date and Alarm menus
• Split rendered objects at space boundaries. This notably ensures that large numbers are split at digit grouping boundaries, and makes it possible to display larger programs on the stack. The rendering of programs and matrices/vectors/lists has also been fine-tuned.
• The "white circle" glyph has a thicker border, makes it more readable in menus.
• doc: Update the list of unimplemented features
• menus: Draw a white circle for disabled flags, and allow the menu function to toggle the flag. This made it possible to reduce the number of menu entries for flag-heavy menus.
• Mixed fractions are now the default, as opposed to improper fractions
• doc: Improve the quickstart guide
• doc: Improve the documentation for sin, cos and tan
• tests: Make it possible to interrupt a running test
• help: Skip HTML tags, e.g.
• simulator: Add screenshot capability, and reduce window height
• menus: ToolsMenu selects time, date or angle menu based on units

Release 0.6.5 "Testimony": Small bug fixes

This release does not contain much because FOSDEM took a lot of energy.

New features

• menu: Connect ceil and floor functions
• Add real to polar conversions
• units: Add dms unit to angles menu

Bug fixes

• decimal: Compute ln(0.002) correctly
• integer: Do not parse degree sign if in a complex
• units: Fix parsing of angle units
• font: Add radian glyph

Release 0.6.4 "Healing": Testing and fixes

This release focuses on heavy testing of the new variable-precision decimal stack. Adding tests also means finding bugs.

Another significant change is support for fixed-precision hardware-accelerated floating point, using 32-bit and 64-bit IEEE754 binary floating-point representation. Since this uses a binary format, some decimal values do not map to decimal correctly. For example, displaying 1.2 with a large number of decimals will show residue, because 1.2 does not have an exact (zero-terminated) representation in binary.

New features:

• plotting: Make refresh rate configurable
• menu: Add / key to FractionsMenu
• hwfp: Add support for hardware-accelerated floating-point
• menus: Add hardware floating-point flag to MathModesMenu
• ui: Allow multiple uses of . to insert DMS separators
• HMS: Editing of HMS values in HMS format

Bug fixes:

• stats: Fix crash on variance with single-column statistics
• algebraic: Clear error before evaluating the function
• functions: Correctly emit a type error for non-algebraics
• ui: Make sure we save stack if closing the editor
• logical: Fix mask for rotate left with 64-bit size
• logical: Make sure we save args for single-argument logicals
• flags: Update flags on FlipFlag, consume them from BinaryToFlags
• stack: Show multi-line objects correctly
• lists: Returns Bad argument value for index with bad arguments
• lists: Return an empty list for tail of empty list
• arithmetic: →Frac should not error on integers
• power: Do not shut down during WAIT if on USB power

Improvements:

• menu: Shorten the labels →QIter and →QPrec to avoid scrolling
• stack: Avoid running same code twice on simulator
• ids: Add aliases for hardware floating point
• functions: Optimize abs and neg
• ui: Replace calls to rt.insert with calls to insert
• menu: Reorganize fractions menu
• dms: Do the DMS conversion using fractions
• list: Adjust multi-line rendering
• copyright: Update copyright to 2024
• text: Return null text when indexing past end of text

Testing:

• tests: Increase the delay for help to draw
• tests: Add tests for hardware-accelerated floating-point
• tests: Add shifts and rotate tests
• tests: Check flag functions
• tests: Test DMS and HMS operations
• tests: Add test for integrate using decimal values
• tests: Test multi-line stack display
• tests: Add tests for GETI
• tests: Min and max commands
• tests: Repair last regression test
• tests: Check behaviour of 0^0
• tests: Avoid string overflow in case of very long message

Release 0.6.3 "Come and See": Repair test suite

The focus of this release was to reactivate the test suite and fix the problems that were found activating it.

New features:

• HMS and DMS operations
• unit: Rendering of dms and hms units
• Allow · as a multiplication sign in equations
• ui: Display 'E' cursor inside parentheses
• graphics: Accept based integers as position for DrawText
• complex: Add setting to switch between 2+3i and 2+i3.

Bug fixes:

• decimal: Fix precision loss for addition with carry
• Base: limit range of bases to 2-36
• files: Do not add a trailing zero when reading a text file
• decimal: Adjust MinimumSignificantDigits behaviour
• units: Do not auto-simplify 1.0 during conversion
• decimal: Normalize parsed numbers
• solver: Fix sign error in epsilon exponent for solve/integrate
• parser: Accept x! as input
• simulator: Avoid faulty break-through in switch statement
• complex: Make tag higher-priority than complex
• editor: Adjust cursor and select correctly during replace
• decimal: Fix display of 0.2 in NoTrailingDecimal mode
• complex: Save this in a GC pointer when it can move
• arithmetic: Do not fail because of surrounding error
• decimal: Clamp int32 conversions from decimal
• commands: Parse exp10 correctly in expressions
• decimal: Avoid infinite loop computing expm1
• ids: Do not allow parsing of structures
• dmcp: Make sure the tests don't block on wait_for_key
• decimal: Use correct angle unit for negative gamma values

Improvements:

• settings: Add classes that save/restore a given setting
• Add XSHIFT to shift to XSHIFT state directly
• Add NOSHIFT constant to simplify test writing
• ui: Add a variant of close_editor without trailing zero
• decimal: Cache gamma_ck values (accelerate gamma and lgamma)
• Replace magic constant -1 with EXIT_PGM
• doc: Record performance data for 1000 iterations of SumTest
• decimal: Add tracing for gamma / lgamma function

New tests:

• Add tests for arithmetic truncation on short bitsizes
• Add tests for on-line help
• Add test for plotting flags
• Add test for Unicode to text conversions
• Add test for rectangular complex display options
• Add tests for plot scaling functions
• Add tests for the sorting functions
• Add test for parsing text with quotes inside
• Add test for file-based STO and RCL
• Add test for 2^256 computation (buf #460)
• Fix indentation of [PASS] or [FAIL] for UTF8 characters
• Add tests for units and conversions
• Add a keyboard test checking the single-colon insert in text
• Add test for i*i=-1 auto-simplification
• Add basic test for numerical integration
• Add test for fraction formats
• Add solver test
• Add missing tests
• Add test for immediate STO (#390)
• Add tests for the Cycle command
• Add test for catalog feature
• Add test for "smart" keyboard shortcuts introduced in 0.4.6
• Add regression test for #371
• Add tests for editor operations
• Test stack operations
• Add test for GXor, GOr and GAnd
• Add test for ResetModes
• Add plotting test for every decimal function
• Add image checking for graphical tests
• Add tests for graphic and text drawing commands
• Make it possible to individually run tests.
• Add plotting tests
• Add test parsing the various spellings for commands

Release 0.6.2 "Kephas": Restoring the test suite

The focus of this release was to complete the transition to the variable-precision decimal code. The full regression test suite was restored, with only two tests still failing (complex asin and asinh). The two missing functions, Gamma and LogGamma, were implemented. This also exposed many bugs that were fixed.

New features:

• NumberedVariables setting to allow 0 STO to ease RPN transcoding (#690)
• ClearStack (CLEAR) command
• Variable-precision gamma and lgamma functions (#710)

Bug fixes:

• Do not leave bad expression on stack after error (#663)
• Reject unit conversion between undefined units (#664)
• Accept names of menus on the command line (#669)
• tests: CLEAR clears stack and errors (#672)
• The : characters now starts a tag on empty command line (#673)
• Do not evaluate tagged objects too early (#674)
• test: Entry and editing of equations (#677)
• test: type returns negative values in "detailed" mode (#678)
• Run loop end pointer not GC-adjusted for last allocated object (#679)
• Do not erase alpha indicator when clearing busy cursor (#680)
• Do not emit trailing space when rounding 1.999 to 2. (#687)
• Allow expression rewrites to deal with pow (#694)
• Reject « character in symbols and commands (#695)
• Rendering of spacing for decimal numbers (#699)
• Improve precision of atan function
• Rendering of + and - operators in compatibility modes (#700)
• Rounding of decimal numbers no longer generates bad characters (#702)
• No longer error out rendering symbolic complex (#703)
• Parse complex numbers correctly inside equations (#704)
• Ensure sqrt(-1) has a zero real part (#705)
• Do not drop last digit of decimal subtraction (#706)
• Evaluate expressions during expression pattern matching (#708)
• LastMenu executes immediately while editing (#711)
• Add back missing angle glyphs in font (#712)
• Return correct angle quadrant for atan2 (#715)
• Get no longer rejects arrays as index values (#718)
• Get returns correct error for bad argument types (#718)

Improvements:

• Update .gitignore entry
• Automated testing of setting flags (#657)
• Automated testing of non-flag settings (#670)
• Test fixed-base based numbers using HP-compatible lowercase notation (#675)
• Test fraction rendering using fancy digits (#676)
• Add test for "compatible" variant of type command (#678)
• test: Recover from error during data entry (#681)
• Increase default MaxNumberBits to 4096 (#686)
• tests: Add test for cube root of -8 (#685)
• tests: Data entry for Σ, ∏ and ∆ (#689)
• Restrict STO to names, natural numbers and specific IDs (#688)
• doc: Document flas file access for STO and RCL (#691)
• list: Optimize iterators to avoid copies (#692)
• tests: spacing-independent testing of structure rendering (#693)
• tests: adjust test suite for variable-precision decimals (#696)
• tests: Automatically exit if -T option is given (#697)
• tests: Check we don't accept . as meaning 0. for RPL compatibility
• Add modulus alias back for abs (#707)
• Improve convergence speed and accuracy for logarithms
• Add decimal::make to minimize risk of sign errors
• Display stack level at top of stack level, not bottom (#709)
• Improve complex sqrt accuracy on real axis (#714)
• tests: Test decimal functions at full 34 digits precision (#716)
• Complex sqrt and cbrt with full precision (#717)
• tests: Take into account additional expression simplifications

Release 0.6.1 "Happy New Year": Quick bug fixes

A few quick bug fixes that make DB48X a bit more usable.

New features

• Setting to display 2+i3 instead of 2+3i (#660)
• HMS and DMS operations (#654)
• Special 1_dms and 1_hms units rendering in DMS / HMS (#650)

Bug fixes

• Improve behavior of +/- key while editing (#658)
• Do not accept base 37 (#656)
• Insert for statement in program instead of executing it (#655)
• Hide trailing decimal separator for decimals with integer values (#653)
• Fix display of 19.8 with 0 FIX (#652)
• Implement true decimal to integer conversion (#648)

Improvements

• doc: Record performance data for 0.6.0
• doc: Udpate status file

Release 0.6.0 "Christmas": Introducing variable precision

This release was a bit longer in coming than earlier ones, because we are about to reach the limits of what can fit on a DM42. This release uses 711228 bytes out of the 716800 (99.2%).

Without the Intel Decimal Library code, we use only 282980 bytes. This means that the Intel Decimal Library code uses 60.2% of the total code space. Being able to move further requires a rather radical rethinking of the project, where we replace the Intel Decimal Library with size-optimized decimal code.

As a result, release 0.6.0 introduces a new table-free and variable-precision implementation of decimal computations. In this release, most operations are implemented, but some features are still missing (e.g. Gamma function). This release will be simultaneous with 0.5.2, which is functionally equivalent but still uses the Intel Decimal library. The new implementation is much more compact, allowing us to return to normal optimizations for the DM42 and regain some of the lost performance. On the other hand, having to switch to a table free implementation means that it's significantly slower than the Intel Decimal Library. The upside of course is that you can compute with decimal numbers that have up to 9999 digits, and a decimal exponent that can be up to 2^60 (1 152 921 504 606 846 976).

New features

Variable precision decimal floating point implementation for arithmetic, trigonometrics, logs, exponential and integer factorial. Other functions may still return "unimplemented error".

Bug fixes

None. If anything, this release introduces bugs in computations and performance regressions. However, it frees a lot of space for further DM42 development.

Improvements

The Precision setting now sets the number of digits with a granularity of one, between 3 and 9999. Ideal use of memory is with multiples of 12 digits, e.g. 12, 24 or 36 digits, where decimal packing does not cause lost bits.

Performance on the DM42 is somewhat improved, since it is now possible to return to a higher level of optimization.

Regressions

In addition to lower performance and unimplemented functions, this version no longer builds a compatible QSPI. This means that returning to the DM42 requires flashing both the QSPI and the PGM file.

Release 0.5.2 "Christmas Eve": Reaching hard limits on the DM42

This release was a bit longer in coming than earlier ones, because we are about to reach the limits of what can fit on a DM42. This release uses 711228 bytes out of the 716800 (99.2%).

Without the Intel Decimal Library code, we use only 282980 bytes. This means that the Intel Decimal Library code uses 60.2% of the total code space. Being able to move further requires a rather radical rethinking of the project, where we replace the Intel Decimal Library with size-optimized decimal code.

As a result, release 0.5.2 will be the last one using the Intel Decimal Library, and is release in parallel with 0.6.0, which switches to a table-free and variable-precisions implementation of decimal code that uses much less code space. The two releases should otherwise be functionally identical

New features

• Shift and rotate instructions (#622)
• Add CompatibleTypes and DetsailedTypes setting to control Type results
• Recognize HP-compatible negative values for flags, e.g. -64 SF (#625)
• Add settings to control multiline result and stack display (#634)

Bug fixes

• Truncate to WordSize the small results of binary operations (#624)
• Fix day-of-week shortcut in simulator
• Avoid double-evaluation of immediate commands when there is no help
• Generate an error when selecting base 1 (#628)
• Avoid Number too big error on based nunbers
• Correctly garbage-collect menu entries (#630)
• Select default settings that allow solver to find solutions (#627)
• Fix display of decimal numbers (broken by multi-line display)
• Fix rendering of menu entries for Fix, Std, etc
• Detect non-finite results in arithmetic, e.g. (-8)^0.3m (#635, #639)
• Fix range-checking for Dig to allow -1 value
• Accept large values for Fix, Sci and Eng (for variable precision)
• Restore missing last entry in built-in units menu (#638)
• Accept Hz and non-primary units as input for ConvertToUnitPrefix (#640)
• Fix LEB128 encoding for signed value 64 and similar (#642)
• Do not parse IfThenElse as a command
• Do not consider E as a digit in decimal numbers (#643)
• Do not parse min as a function in units, but as minute (#644)

Improvements

• Add OnesComplement flag for binary operation (not used yet)
• Add ComplexResults (-103) flag (not used yet)
• Accept negative values for B→R (according to WordSize)
• Add documentation for STO and RCL accessing flash storage
• Mention True and False in documentation
• Rename MaxBigNumBits to MaxNumberBits
• Return HP-compatible values from Type function
• Minor optimization of flags implementation
• Catalog auto-completion now suggests all possible spellings (#626)
• Add aliases for CubeRoot and Hypothenuse
• Align based number promotion rules to HP calculators (#629)
• Expand the range of garbage collector integrity check on simulator
• Show command according to preferences in error messages (#633)
• Avoid crash in debug_printf if used before font initialization
• Update performance data in documentation
• Add ability to disable any reference to Intel Decimal Floating-point library
• Simplify C++ notations for safe pointers (+x and operartor bool())
• Fix link to old db48x project in README.md

Release 0.5.1 "Talents": More RPL commands

This release focuses on rounding up various useful RPL commands and bringing RPL a bit closer to feature-complete.

New features

• Portable bit pattern generation commands, gray and rgb (#617)
• Add support for packed bitmaps (#555)
• Implement RPL case statement, extended with case when (#374)
• Beep command (#50)
• List→ command (#573)
• Size command (#588)
• Str→ command (#590)
• Obj→ command (#596)
• Add flag to control if 0^0 returns 1 or undefined behaviour (#598)
• Unicode-based Num and Chr commands, Text→Code and Code→Text (#597)
• IP and FP commands (#601)
• Percentage operations %, %CH and %T (#602)
• Min and Max operations (#603)
• Floor and Ceil operations (#605)
• Get with a name argument (#609)
• Put command (#610)
• Head and Tail commands (#614)
• Map, Reduce and Filter commands (#613)

Bug fixes

• Ensure rounded rectangles stay within their boundaries (#618)
• Prevent auto-power-off for long-running programs (#587)
• Fix old-style RPL shortcuts for FS?C and the like
• Add FF shortcut for FlipFlag
• Fix rendering of <, >, etc in old-style RPL compatibility mode (#595)
• Update various menus
• Evaluate program arguments in IFT and IFTE (#592)
• Evaluate algebraic expressions in if, while and case (#593)
• Load variables from state file in correct order (#591)
• Avoid truncation of state file when ASCII conversions occur (#589)
• Clear debugging state more completely after kill (#600)
• Wait no longer makes it harder to stop a program (#619)
• mod no longer gives wrong result for negative fractions and bignums (#606)
• No longer strip tags in non-numeric arithmetic operations (#607)

Improvements

• Small updates to demo file
• A long Wait command allows the calculator to switch off (#620)
• Centering of variable names in VariablesMenu (#610)
• Makefile check-ids target to check if commands are in help or menus (#615)

Release 0.5.0: Statistics and flags

This release provides statistics functions and flags.

New features

• Statistics (#495) and linear regression (#569)
• File-based statistics (#571)
• Sort, QuickSort, ReverseSort, ReverseQuickSort and RevList (#572)
• Flags, i.e. CF, SF, FS?, etc (#43)
• Plot scaling commands such as SCALE, CENTR, XRNG, ... (#582)
• Add CurveFilling and DrawPlotAxes setting flags (#580)
• ScatterPlot (#577) and BarPlot (#579)

Bugs

• Save settings enumerations as portable text (#565)
• Avoid infinite loop when reading at end of help file
• Repair behaviour of -1 DIG, broken by settings improvements
• Fix definition of rpm in units and units file
• Crash in list::map when called function errors out (#570)
• Fix editor horizontal movement when inserting commands (#576)
• Repair plotting demo (#583)
• Fix vertical position of axes in DrawAxes (#584)
• Very long drawing loop if ppar axes are backwards (#585)

Improvements

• Sets editor selection correctly for command-line errors
• Ability to parse command and setting names in quotes, e.g. 'Radians'
• Insert command names inside quotes (#575)
• Update documentation of implemented features (#569)
• Make PlotParameters a keyword (#578)

Release v0.4.12: Emergency bug fixes, filesyste, access

A few quick bug fixes related to issues found in 0.4.11.

New features

• STO and RCL to file (#375)
• Parsing of text containing quotes (#562)

Improvements

• Rework file load/save dialog boxes
• Preliminary plumbing for statistics functions

Bugs

• Error loading state files that contain directories (#559)
• Font setting for result was taken from editor font (#560)
• Crash running the Shapes demo (#563)

Release 0.4.11: Debugging, Units, Settings

This release implements debugging, infinite RPL recursion, mixed fractions, customizable units cycling, and restores missing entries in the units menu.

New features

• Allow customization of Cycle for units (#534)
• Allow infinite recursion in RPL code (#537)
• RPL program and expression debugging (#552) including after EXIT
• Mixed fractions such as 1 1/3 (#554)
• BeepOn and SilentBeepOn features (#280)
• ScreenCapture and keyboard shortcut (#434)

Bugs

• Accept 2.3 FIX and #0 Background (#557)
• Do not parse 67.200525 as a decimal32 (#551)
• Bump low battery voltage to 2.550V (#553)

Improvements

• Catalog shows all commands containing typed text (#556)
• Reorganize the units menu (#550) and restore missing units
• Remember menu page for LastMenu (#545)
• SPC key inserts ; when inside parenthese (#499)
• Settings are now entirely defined by ids.tbl (#294)
• Improve user interface code consistency
• Improve GC handling of "just-past-end-of-object" pointers
• Remove the execute() RPL callback, rely on evaluate()
• Optimize allocation of 1-byte vs 2-byte opcodes
• Render abs as abs and not norm (accept norm while parsing)

Release v0.4.10: Performance and units file

This release focuses on display performance optimization and support for unit data files.

New features

• Cycle command for units (#517)
• Possibility to load units from config/units.csv file (#496, #544)
• Internal: debug_printf facility (#541)
• ShowBuiltinUnits and HideBuiltinUnits settings (#542)
• Provide config/units.csv example file (#543)
• Build units menu from units file (#544)

Bugs

• Possible memory corruption in expressions
• Calculator lock-up trying with unit conversions in numeric mode (#529)
• Numerator and divisor no longer truncated to 32-bit (#539)
• Correctly save LastArg for interactive operations (#540)

Improvements

• Optimize the font cache, makes stack drawing faster in SCI mode (#526)
• Add TypeName to object menu (#527)
• Regroup units in units menu by scale (#528)
• Status of implementation and performance data in documentation (#530)
• Performance: Reduce frequency of busy cursor drawing (#531)
• Performance: Reimplement range-based type checkig (#532)
• Performance: Focused -O3 optimizations on DM42 (#533)
• Makefile: Install target installs demo and config (#547)
• Garbage collector for menu labels (#548)

Release 0.4.9 - Support for units

This release focuses on support for units, but also adds a large number of other fixes and improvements.

New features

• Power-off message indicating low-battery situation (#521)
• Add ConvertToUnixPrefix command and SI prefix menu keys (#513)
• Recognize all units that exist in the HP48, and a few more (#491)
• UFACT (FactorUnit) command (#512)
• Unit simplification, e.g. turn 1_m^2*s/s/m into 1_m (#506)
• Converting unity units to numbers (#502)
• →Unit command (#501)
• UnitValue (UVAL) command (#493)
• Implement "kibibytes" (KiB) and power-of-two SI prefixes (#492)
• Unit arithmetic (#481)
• Add B->R and R->B to BasesMenu (#488)
• Implement term reordering capability in rewrite (#484)
• BaseUnits (UBase) command (#483)
• Unit parsing for complex units, e.g. 1_cm^2 (#482)
• Unit arithmetic (#481) including automatic conversions (#480)
• Convert command (#480)
• Implement the Cycle command for unit objects
• Add Å character for angstroem (#477)
• Add Merge state to State system menu (#475)
• Use Unicode font to display the name of a program when executing it (#469)
• Allow incremental search to find digits and Unicode (#468)
• Add tool glyph to user interface font

Bug fixes

• Do not parse symbols beyond input buffer (#524)
• Parse unit menu entries as expressions, not symbols (#523)
• Fix reduced-precision arithmetic (#521)
• Do not parse empty denominator as zero, e.g. 2/s (#520)
• Do not parse a fraction inside a power, e.g. X^2/3 (#519)
• Convert fractions to decimal in numeric mode (#516)
• Do not emit mantissa_error for valid numbers (#515)
• Apply negation correctly on unit objects (#500)
• Do not emit separator after trailing 0 in integer decimals (#489)
• Do not emit extra spacing before decimal separator (#485)
• Fix stack depth in one error case of evaluate_function()
• Fix display of next/previous icons for large menus (#478)
• Clear settings when loading a state (#474)
• Fix separators in whole part of decimal numbers when setting is not 3 (#464)
• Parse (sin x)²+(cos x)² correctly, as well as HP67 Mach example (#427)

Improvements

• Rename equation as expression (#518) and labelText as label_text
• Do not update LastArg except for command line (#511)
• ToolsMenu: Connect units to the UnitsConversionMenu (#514)
• Display unit using / and ·, e.g. 1_m·s^2/A (#507)
• Show units menu for inverse units as mm⁻¹ (#503)
• Display battery level more accurately, i.e. consider 2.6V "low" (#476)
• No longer acccept empty equations or parentheses, e.g. 1+() (#487)
• Make StandardDisplay mode obey MinimumSignificantDigits (#462)
• Add algebraic evaluation function for easier evaluation in C++ code
• Reimplement unit type as a derivative of complex (#471)
• documentation: Use 🟨 and 🟦 for more commands (#467)
• Swap Search and Copy commands in EditorMenu (#466)
• STO stores variables at beginning of directory (#462)
• documentation: Add quickstart guide, used for video recording
• documentation: Add links to YouTube videos
• documentation: Add release notes
• documentation: Some typos and other improvements
• documentation: Rework section on keyboard mappings

Implementation status

This section documents the implementation status for all HP50 RPL commands as listed in the HP50G Advanced Reference Manual. This is a strict superset of the HP48 implementation.

• Implemented
• Not implemented
• Additional

Implemented commands

The following is a list of the HP50 RPL commands which are implemented in DB48X.

• ! (Factorial)
• + (Add)
• < (Less than)
• == (Different meaning: object equality)
• = (Equal)
• > (Greater than)
• ABS
• ACOSH
• ACOS
• ADD
• ALOG
• AND
• ARG
• ARRY→
• →ARRY
• ASINH
• ASIN
• ASR
• ASRC
• ATANH
• ATAN
• AXES
• BARPLOT
• BEEP
• BESTFIT
• BIN
• BYTES
• B→R
• CASE
• CEIL
• CF
• %CH
• CHR
• CLEAR
• CLLCD
• CLΣ
• COLΣ
• COMB
• CON
• CONJ
• CONLIB
• CONST
• CONSTANTS
• CONT
• CONVERT
• COSH
• COS
• COV
• CRDIR
• C→R
• DATE
• →DATE
• DATE+
• DDAYS
• DBUG
• DEC
• DECR
• DEDICACE
• DEG
• DEPTH
• DET
• DIR
• DISP
• DISPXY
• DIV2
• DOERR
• DO
• DRAW
• DRAX
• DROP2
• DROPN
• DROP
• DTAG
• DUP2
• DUPN
• DUP
• D→R
• e
• ELSE
• END
• ENG
• ERR0
• ERRM
• ERRN
• EVAL
• EXPAND
• EXPAN
• EXPFIT
• EXPM
• EXP
• FACT
• FC?C
• FC?
• FIX
• FOR
• FP
• FS?C
• FS?
• FUNCTION
• GAMMA
• GET
• GETI
• GOR
• GROB
• GXOR
• HALT
• HEAD
• HELP (Different meaning)
• HEX
• HOME
• HMS–
• HMS+
• HMS→
• →HMS
• IFERR
• IFTE
• IFT
• IF
• IM
• INV
• IP
• KILL
• LASTARG
• LINE
• LINFIT
• LNP1
• LN
• LOG
• LOGFIT
• LR
• MAX
• MAXΣ
• MEAN
• MEM
• MIN
• MINΣ
• MOD
• NEG
• NEXT
• NOT
• NΣ
• NUM
• OBJ→
• OCT
• OFF
• OR
• OVER
• PARAMETRIC
• PATH
• PGDIR
• PICK
• PICT
• POLAR
• PMAX
• PMIN
• PURGE
• PUT
• PUTI
• PVAR
• PWRFIT
• RAD
• RCL
• RCLΣ
• RCWS
• RE
• RECT (Different meaning: draws a rectangle)
• REPEAT
• REVLIST
• REWRITE (Different meaning: performs a rewrite)
• RL
• RLB
• RLC
• ROLLD
• ROLL
• ROOT
• ROT
• RR
• RRB
• RRC
• R→B
• R→C
• R→D
• SAME
• SCALE
• SCALEH
• SCALEW
• SCI
• SF
• SIGN
• SINH
• SIN
• SL
• SLB
• SLC
• SORT
• SQ
• SR
• SRB
• SST
• SST↓
• START
• STD
• STEP
• STORE (Different meaning: long form of STO)
• STO
• STOΣ
• STR→
• STWS
• SWAP
• %T
• TAIL
• TANH
• TAN
• THEN
• TICKS
• TIME
• →TIME
• TOT
• TYPE
• UBASE
• UFACT
• UNTIL
• UPDIR
• UVAL
• VAR
• VERSION
• WAIT
• WHILE
• XCOL
• XOR
• XRNG
• XROOT
• YRNG
• YCOL
• %
• ^ (Power)
• i
• «» (Program delimiters)
• × (Multiply)
• ÷ (Divide)
• Σ+
• ΣXY
• ΣX
• ΣX²
• ΣY
• ΣY²
• Σ–
• π (Pi)
• – (Subtract)
• →LIST
• →NUM
• →Q
• →STR
• →TAG
• →UNIT
• → (Create Local)
• √ (Square root)
• ∫ (Integrate)
• ≠ (Not equal)
• ≤ (Less than or equal)
• ≥ (Greater than or Equal)
• ＿ (Unit attachment)

Unimplemented commands

The following is a list of unimplemented HP50 RPL commands, which is a superset of the HP48 commands.

• ABCUV
• ACK
• ACKALL
• ACOS2S
• ADDTMOD
• ADDTOREAL
• ALGB
• AMORT
• ANIMATE
• ANS
• APPLY
• ARC
• ARCHIVE
• ARIT
• ASIN2C
• ASIN2T
• ASN
• ASSUME
• ATAN2S
• ATICK
• ATTACH
• AUGMENT
• AUTO
• AXL
• AXM
• AXQ
• BAR
• BASIS
• BAUD
• BINS
• BLANK
• BOX
• BUFLEN
• C$
• C2P
• CASCFG
• CASCMD
• CENTR
• CHINREM
• CHOLESKY
• CHOOSE
• CIRC
• CKSM
• CLKADJ
• CLOSEIO
• CLUSR
• CLVAR
• CMPLX
• CNRM
• →COL
• COL→
• COL–
• COL+
• COLCT
• COLLECT
• COND
• CONIC
• CORR
• CR
• CROSS
• CSWP
• CURL
• CYCLOTOMIC
• CYLIN
• C→PX
• DARCY
• DEF
• DEFINE
• DEGREE
• DELALARM
• DELAY
• DELKEYS
• DEPND
• DERIV
• DERVX
• DESOLVE
• DETACH
• DIAG→
• →DIAG
• DIAGMAP
• DIFF
• DIFFEQ
• DISTRIB
• DIV
• DIV2MOD
• DIVIS
• DIVMOD
• DIVPC
• dn
• DOLIST
• DOMAIN
• DOSUBS
• DOT
• DRAW3DMATRIX
• DROITE
• DUPDUP
• EDIT
• EDITB
• EGCD
• EGV
• EGVL
• ENDSUB
• EPSX0
• EQNLIB
• EQW
• EQ→
• ERASE
• EULER
• EXLR
• EXP&LN
• EXP2HYP
• EXP2POW
• EXPANDMOD
• EXPLN
• EYEPT
• F0λ
• FACTOR
• FACTORMOD
• FACTORS
• FANNING
• FAST3D
• FCOEF
• FDISTRIB
• FFT
• FILER
• FINDALARM
• FINISH
• FLASHEVAL
• FLOOR
• FONT6
• FONT7
• FONT8
• FONT→
• →FONT
• FOURIER
• FREE
• FREEZE
• FROOTS
• FXND
• GAUSS
• GBASIS
• GCD
• GCDMOD
• GRAD
• GRAMSCHMIDT
• GRAPH
• GREDUCE
• GRIDMAP
• →GROB
• GROBADD
• *H
• HADAMARD
• HALFTAN
• HEADER→
• →HEADER
• HERMITE
• HESS
• HILBERT
• HISTOGRAM
• HISTPLOT
• HORNER
• IABCUV
• IBASIS
• IBERNOULLI
• IBP
• ICHINREM
• IDN
• IDIV2
• IEGCD
• IFFT
• ILAP
• IMAGE
• INCR
• INDEP
• INFORM
• INPUT
• INT
• INTEGER
• INTVX
• INVMOD
• IQUOT
• IREMAINDER
• ISOL
• ISOM
• ISPRIME?
• I→R
• JORDAN
• KER
• KERRM
• KEY
• KEYEVAL
• →KEYTIME
• KEYTIME→
• KGET
• LABEL
• LAGRANGE
• LANGUAGE→
• →LANGUAGE
• LAP
• LAPL
• LAST
• LCD→
• →LCD
• LCM
• LCXM
• LDEC
• LEGENDRE
• LGCD
• LIBEVAL
• LIBS
• lim
• LIMIT
• LIN
• ΣLINE
• LININ
• LINSOLVE
• LIST→
• ∆LIST
• ΠLIST
• ΣLIST
• LNAME
• LNCOLLECT
• LOCAL
• LQ
• LR
• LSQ
• LU
• LVAR
• MAD
• MAIN
• MANT
• MAP
• ↓MATCH
• ↑MATCH
• MATHS
• MATR
• MAXR
• MCALC
• MENU
• MENUXY
• MERGE
• MINEHUNT
• MINIFONT→
• →MINIFONT
• MINIT
• MINR
• MITM
• MKISOM
• MODSTO
• MODULAR
• MOLWT
• MROOT
• MSGBOX
• MSLV
• MSOLVR
• MULTMOD
• MUSER
• →NDISP
• NDIST
• NDUPN
• NEWOB
• NEXTPRIME
• NIP
• NOVAL
• NSUB
• NUMX
• NUMY
• OLDPRT
• OPENIO
• ORDER
• P2C
• PA2B2
• PARITY
• PARSURFACE
• PARTFRAC
• PCAR
• PCOEF
• PCONTOUR
• PCOV
• PDIM
• PERINFO
• PERM
• PERTBL
• PEVAL
• PICK3
• PICTURE
• PINIT
• PIX?
• PIXOFF
• PIXON
• PKT
• PLOT
• PLOTADD
• PMINI
• POLYNOMIAL
• POP
• POS
• POTENTIAL
• POWEXPAND
• POWMOD
• PR1
• PREDV
• PREDX
• PREDY
• PREVAL
• PREVPRIME
• PRLCD
• PROMPT
• PROMPTSTO
• PROOT
• PROPFRAC
• PRST
• PRSTC
• PRVAR
• PSDEV
• PSI
• Psi
• PTAYL
• PTPROP
• PUSH
• PVARS
• PVIEW
• PX→C
• →Qπ
• qr
• QR
• QUAD
• QUOT
• QUOTE
• QXA
• RAND
• RANK
• RANM
• RATIO
• RCEQ
• RCI
• RCIJ
• RCLALARM
• RCLF
• RCLKEYS
• RCLMENU
• RCLVX
• RDM
• RDZ
• RECN
• RECV
• REF
• REMAINDER
• RENAME
• REORDER
• REPL
• RES
• RESTORE
• RESULTANT
• RISCH
• RKF
• RKFERR
• RKFSTEP
• RND
• RNRM
• ROMUPLOAD
• ROW–
• ROW+
• ROW→
• →ROW
• RPL>
• rref
• RREF
• RREFMOD
• RRK
• RRKSTEP
• RSBERR
• RSD
• RSWP
• RULES
• R→I
• SBRK
• SCATRPLOT
• SCATTER
• SCHUR
• SCLΣ
• SCONJ
• SCROLL
• SDEV
• SEND
• SEQ
• SERIES
• SERVER
• SEVAL
• SHOW
• SIDENS
• SIGMA
• SIGMAVX
• SIGNTAB
• SIMP2
• SIMPLIFY
• SINCOS
• SINV
• SIZE
• SLOPEFIELD
• SNEG
• SNRM
• SOLVE
• SOLVEQN
• SOLVER
• SOLVEVX
• SPHERE
• SRAD
• SRECV
• SREPL
• STEQ
• STIME
• STOALARM
• STOF
• STOKEYS
• STOVX
• STO+
• STO–
• STO*
• STO/
• STREAM
• STRM
• STURM
• STURMAB
• SUB
• SUBST
• SUBTMOD
• SVD
• SVL
• SYSEVAL
• SYLVESTER
• SYST2MAT
• TABVAL
• TABVAR
• TAN2CS2
• TAN2SC
• TAN2SC2
• TAYLOR0
• TAYLR
• TCHEBYCHEFF
• TCOLLECT
• TDELTA
• TESTS
• TEVAL
• TEXPAND
• TEXT
• TINC
• TLIN
• TLINE
• TMENU
• TRACE
• TRAN
• TRANSIO
• TRIG
• TRIGCOS
• TRIGO
• TRIGSIN
• TRIGTAN
• TRN
• TRNC
• TRUNC
• TRUTH
• TSIMP
• TSTR
• TVARS
• TVM
• TVMBEG
• TVMEND
• TVMROOT
• UFL1→MINIF
• UNASSIGN
• UNASSUME
• UNBIND
• UNPICK
• UNROT
• UTPC
• UTPF
• UTPN
• UTPT
• V→
• →V2
• →V3
• VANDERMONDE
• VARS
• VER
• VISIT
• VISITB
• VPOTENTIAL
• VTYPE
• *W
• WIREFRAME
• WSLOG
• XGET
• XMIT
• XNUM
• XPON
• XPUT
• XQ
• XRECV
• XSEND
• XSERV
• XVOL
• XXRNG
• YSLICE
• YVOL
• YYRNG
• ZEROS
• ZFACTOR
• ZVOL
• | (Where)
• ?
• ∞
• Σ
• ∂
•  (Store)
• ; (Semicolon)

Additional commands

The following commands are unique to DB48X and are not found in any Hewlett-Packard RPL implementation.

• ATAN2: Arc-tangent from two arguments
• AngleUnitsMenu
• AnglesMenu
• ApplyInverseUnit
• ApplyUnit
• AreaUnitsMenu
• AutoSimplify: Automatically simplify expressions
• BASE: Select an arbitrary base for based numbers
• Background: Select background pattern for graphic operations
• BasedDotOrComma: Use dot or comma as based number digit separator
• BasedSpaces: Use thin spaces as based number digit separator
• BasedSpacing: Grouping of digits for based numbers
• BasedTicks: Use tick marsk ' as based number digit separator
• BasedUnderscore: Use underscore _ as based number digit separator
• BasesMenu
• CBRT: Cube root
• CYCLE: Cycle between object representations
• Capitalized: Show commands capitalized
• Catalog: Present catalog of all functions with auto-completion
• CharsMenu
• CircularMenu
• ClassicExponent: Use E as exponent marker, e.g. 1.3E128
• ClearThingsMenu
• CompareMenu
• ComplexMenu
• ComputerUnitsMenu
• ConstantsMenu
• ConvertToUnitPrefix
• ConvertToUnit
• CursorBlinkRate: Select cursor blink rate in milliseconds
• DebugMenu
• DecimalComma: Select comma as decimal separator
• DecimalDot: Select dot as decimal separator
• DifferentialSolverMenu
• DifferentiationMenu
• DisplayModesMenu
• EQUIV: Logical equivalence
• ERFC: Complementary error function
• ERF: Error function
• EXCLUDES: Logical exclusion
• EditMenu
• EditorBegin
• EditorClear
• EditorCopy
• EditorCut
• EditorEnd
• EditorFlip
• EditorFontSize: Select font size for text editor
• EditorMultilineFontSize: Select font size for multi-line text editor
• EditorPaste
• EditorReplace
• EditorSearch
• EditorSelect
• EditorWordLeft
• EditorWordRight
• ElectricityUnitsMenu
• EnergyUnitsMenu
• EquationsMenu
• ExpLogMenu
• FancyExponent: Use power-of-ten rendering, e.g. 1.3×₁₀¹²⁸
• FilesMenu
• FinanceSolverMenu
• FlagsMenu
• FlatMenus: Flatten menus (no use of shift)
• ForceUnitsMenu
• Foreground: Select foreground pattern for graphic operations
• FractionSpacing: Grouping of digits for fractional part of numbers
• FractionsMenu
• GAND: Graphical And
• GarbageCollect
• GraphicsMenu
• GraphicsStackDisplay: Select graphic display of the stack
• HYPOT: Hypothenuse
• HideBuiltinUnits
• HyperbolicMenu
• IMPLIES: Logical implication
• IOMenu
• IntegrationMenu
• LastMenu: Select last menu
• LastX: Return last X argument (for easier translation of RPN programs)
• LengthUnitsMenu
• LibrariesMenu
• LightUnitsMenu
• LineWidth: Select line width for line drawing operations
• LinearSolverMenu
• ListMenu
• LongForm: Show commands in long form
• LoopsMenu
• LowerCase: Show commands in lowercase
• MainMenu
• MantissaSpacing: Grouping of digits for whole part of numbers
• MassUnitsMenu
• MathMenu
• MathModesMenu
• MatrixMenu
• MaxNumberBits: Maximum number of bits used by a number
• MaxRewrites: Maximum number of equation rewrites
• MemoryMenu
• MenuFirstPage
• MenuNextPage
• MenuPreviousPage
• MinimumSignificantDigits: adjustment of FIX mode switch to SCI
• ModesMenu
• MultiSolverMenu
• NAND: Not And
• NOR: Not Or
• NoAutoSimplify: Do not automatically simplify expressions
• NoTrailingDecimal: display 1.0 as 1
• NumberDotOrComma: Use dot or comma as digit group separator
• NumberSpaces: Use thin spaces as digit group separator
• NumberTicks: Use tick marks ' as digit group separator
• NumberUnderscore: Use underscore _ as digit group separator
• NumbersMenu
• NumericResults: Produce numeric (decimal) results
• NumericalSolverMenu
• ObjectMenu
• PIRADIANS: Angle mode with multiples of pi
• PartsMenu
• PlotMenu
• PolynomialSolverMenu
• PolynomialsMenu
• PowerUnitsMenu
• PowersMenu
• Precision: Select decimal computing precision
• PressureUnitsMenu
• PrintingMenu
• ProbabilitiesMenu
• ProgramMenu
• REM: remainder
• RadiationUnitsMenu
• RealMenu
• ResultFontSize: Select font size to display level 1 of stack
• RoundedMenus: Select round menu style
• SIG: Significant digits mode
• SaveState: Save system state to current state file
• SelfInsert
• SeparatorModesMenu
• ShowBuiltinUnits
• SignalProcessingMenu
• SingleRowMenus: Display menus on single row
• SolverMenu
• SpeedUnitsMenu
• SquareMenus: Select square (C47-like) menu style
• StackFontSize: Select font size to display levels above 1 of stack
• StackMenu
• StandardExponent: Display with standard exponent mode
• StatisticsMenu
• SymbolicMenu
• SymbolicResults: Produce symbolic results
• SymbolicSolverMenu
• SystemMemory
• SystemSetup: Enter DMCP system setup menu
• Tag→
• TemperatureUnitsMenu
• TestsMenu
• TextMenu
• TextStackDisplay: Select text-only display of the stack
• ThreeRowsMenus: Display menus on up to three rows
• TimeMenu
• TimeUnitsMenu
• ToFractionDigits: Required digits of precision for →Q
• ToFractionIterations: Max number of iterations for →Q
• ToolsMenu: Automatically select a menu based on context
• TrailingDecimal: display 1.0 with trailing decimal separator
• TypeName
• Undo: Restore stack to state before command
• UnitsConversionsMenu
• UnitsMenu
• UpperCase: Show commands in uppercase
• UserInterfaceModesMenu
• VariablesMenuExecute
• VariablesMenuRecall
• VariablesMenuStore
• VariablesMenu
• VectorMenu
• ViscosityUnitsMenu
• VolumeUnitsMenu

Performance measurements

This sections tracks some performance measurements across releases.

Constants library

The DB48X calculator features a library of constants covering mathematics, physics, chemistry and computer science. The built-in constants can be extended using the config/constants.csv configuration file.

Mathematics constants

π constant

The ratio between the circumference and the diameter of a circle.

e constant

Euler's constant is the base for the natural logarithm.

ⅈ constant

The imaginary unit, such that ⅈ²=-1.

The picture below shows imaginary unit ⅈ in the complex plane: Real numbers are conventionally drawn on the horizontal axis, and imaginary numbers on the vertical axis.

ⅉ constant

An alternative notation, often preferred by physicists, for the imaginary unit ⅈ, verifying ⅉ²=-1.

∞ constant

Infinity is something that is larger than any natural number. Its numerical value is an arbitrary large number that is not really infinite.

? constant

The undefined constant is used to represent undefined values, such as the result of undefined operations.

Chemistry constant

NA constant

Avogradro constant is the number of constituent particles per mole.

k constant

The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas.

Vm constant

Molar volume of an ideal gas at 1 atmosphere of pressure and 0°C.

R constant

The universal gas constant is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature increment per amount of substance, rather than energy per temperature increment per particle.

StdT constant

Standard temperature as defined by IUPAC in 1982.

Standard temperature and pressure (STP) or Standard conditions for temperature and pressure are various standard sets of conditions for experimental measurements used to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC, used by DB48X) and the National Institute of Standards and Technology (NIST). Other organizations have established a variety of other definitions.

StdP constant

Standard pressure as defined by IUPAC in 1982, corresponding to 1 atm

Standard temperature and pressure (STP) or Standard conditions for temperature and pressure are various standard sets of conditions for experimental measurements used to allow comparisons to be made between different sets of data. The most used standards are those of the International Union of Pure and Applied Chemistry (IUPAC, used by DB48X) and the National Institute of Standards and Technology (NIST). Other organizations have established a variety of other definitions.

σ constant

Stefan-Boltzmann constant, the factor of proportionality in the Stefan-Boltzmann law describing the intensity of the thermal radiation emitted by matter in terms of that matter's temperature.

For an ideal absorber/emitter or black body, the Stefan–Boltzmann law states that the total energy radiated per unit surface area per unit time (also known as the radiant exitance) is directly proportional to the fourth power of the black body's temperature, T:M°=σ·T⁴

Physics constants

ⅉ constant

Notation often used in physics for the imaginary verifying ⅉ²=-1.

c constant

Speed of light in vaccuum, a universal physical constant that is exactly equal to 299,792,458 metres per second (by definition of the metre).

According to the special theory of relativity, c is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space.

The theory of incomplete measurements presents space and time as having no existence on their own. We only derive them from measurements of distance and duration made using photons. In that viewpoint, c is the limit of what can be measured using photons. Anything travelling faster than light is indistinguishable from anti-matter. This is illustrated by the thought experiment known (or not) as the bat and the supersonic jet. This little tidbit is only mentioned here because this particular theory was devised by the primary author of DB48X.

ε0 constant

Vacuum permittivity, commonly denoted ε0 (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. It is a measure of how dense of an electric field is "permitted" to form in response to electric charges and relates the units for electric charge to mechanical quantities such as length and force.

μ0 constant

The vacuum magnetic permeability (variously vacuum permeability, permeability of free space, permeability of vacuum, magnetic constant) is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0 (pronounced "mu nought" or "mu zero"). It quantifies the strength of the magnetic field induced by an electric current.

g constant

Acceleration of Earth gravity, equivalent to the free-fall acceleration.

G constant

The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.

According to Newton's law of universal gravitation, the magnitude of the attractive force (F) between two bodies each with a spherically symmetric density distribution is directly proportional to the product of their masses, m₁ and m₂, and inversely proportional to the square of the distance, r, directed along the line connecting their centres of mass:

h constant

The Planck constant is a fundamental physical constant that appears in quantum mechanics. A photon's energy is equal to its frequency multiplied by the Planck constant (E=h·ν), and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum (λ=h/p).

ℏ constant

The reduced Planck constant, ℏ, also known as the Dirac Constant, is defined as ℏ=h/2π.

qe constant

The elementary electric charge is a fundamental physical constant, defined as the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −qe.

In the SI system of units, the value of the elementary charge is exactly defined as qe=1.602176634⁳⁻¹⁹ coulombs. Since the 2019 redefinition of SI base units, the seven SI base units are defined by seven fundamental physical constants, of which the elementary charge is one. As a consequence of this change, the value of that constant in DB48X differs from the value in the HP50G, which named it q, with value 1.60217733⁳⁻¹⁹ coulombs.

me constant

Electron mass. In particle physics, the electron mass is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about 9.109⁳⁻³¹ kilograms

qme constant

Ratio between the electron charge and its mass.

mp constant

Mass of the proton.

mpme constant

Ratio between the mass of the proton and the mass of the electron.

α constant

Fine-structure constant. In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α (the Greek letter alpha), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.

It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field.

ø constant

Magnetic flux quantum. The (superconducting) magnetic flux quantum is a combination of fundamental physical constants: the Planck constant h and the electron charge e. Its value is, therefore, the same for any superconductor.

F constant

Faraday constant. In physical chemistry, the Faraday constant is a physical constant defined as the quotient of the total electric charge (q) by the amount (n) of elementary charge carriers in any given sample of matter

R∞ constant

Rydberg constant. In spectroscopy, the Rydberg constant is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants according to his model of the atom.

a0 constant

Bohr radius. The Bohr radius is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state.

μB constant

Bohr magneton. In atomic physics, the Bohr magneton is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by its orbital or spin angular momentum. In SI units, the Bohr magneton is defined as μB=qe*ℏ/(2·me).

μN constant

The nuclear magneton is a physical constant of magnetic moment, defined in SI units by μN=qe·ℏ/(2·mp).

λ0 constant

Photon wavelength. Photon energy can be expressed using any unit of energy such as the electronvolt (eV) or the Joule (J). For short wavelength sources, researchers often discuss photon energies in units of eV (or keV for hard X-rays) out of convenience. The SI definition for 1 eV derives from the definitional value of the electron charge. Photon energy E in eV can be computed from wavelength l in nm as: E=λ0/l.

f0 constant

Photon frequency. This is the frequency associated to the [photon wavelength λ0][#λ0-constant].

λc constant

Compton wavelength. The Compton wavelength is a quantum mechanical property of a particle, defined as the wavelength of a photon whose energy is the same as the rest energy of that particle (based on the mass–energy equivalence).

The standard Compton wavelength λ of a particle of mass m is given by λ=h/(m·c)

rad constant

One radian.

twoπ constant

Two π radian (one full circle).

angl constant

Half turn in degrees.

c3 constant

Wien's constant. In physics, Wien's displacement law states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. The shift of that peak is a direct consequence of the Planck radiation law, which describes the spectral brightness or intensity of black-body radiation as a function of wavelength at any given temperature. However, it had been discovered by German physicist Wilhelm Wien several years before Max Planck developed that more general equation, and describes the entire shift of the spectrum of black-body radiation toward shorter wavelengths as temperature increases.

Formally, the wavelength version of Wien's displacement law states that the spectral radiance of black-body radiation per unit wavelength, peaks at the wavelength λpeak=c3/T where T is absolute temperature.

kq constant

Ratio of the [Boltzman constant][#k-constant] by the elementary charge: kq=k/qe.

ε0q constant

Ratio of the vaccum permittivity by the elementary charge: ε0q=ε0/qe.

qε0 constant

Product of the vaccum permittivity by the elementary charge: qε0=ε0·qe.

εsi constant

Dielectric constant of silicon. The dielectric constant (or relative permittivity), is a material property that measures how well an applied electric field can penetrate a dielectric medium compared to a vacuum. A higher value corresponds to a lower penetration.

εox constant

SiO2 dielectric constant. The dielectric constant (or relative permittivity), is a material property that measures how well an applied electric field can penetrate a dielectric medium compared to a vacuum. A higher value corresponds to a lower penetration.

I0 constant

Reference sound intensity. Sound intensity level or acoustic intensity level is the level of the intensity of a sound relative to a reference value. It is a logarithmic quantity, most often expressed in decibels dB. I0 is the sound intensity used as a reference, corresponding to 0dB.

Dates Constants

BastilleDay constant

French national day

MartinLutherKingDeath constant

Martin Luther King Jr., an African-American clergyman and civil rights movement leader, was fatally shot at the Lorraine Motel in Memphis, Tennessee, on April 4, 1968, at 6:01 p.m.

IndependenceDay constant

Independence Day, known colloquially as the Fourth of July, is a federal holiday in the United States which commemorates the ratification of the Declaration of Independence by the Second Continental Congress on July 4, 1776, establishing the United States of America.

Computing constants

No constant

The value of "No" is false

Yes constant

The value of "Yes" is true

UnixEpoch constant

Date from which all dates are counted in Unix computer systems.

SinclairZX81RAM constant

Amount of memory in the Sinclair ZX81 personal computer. This is also the amount of memory used in the video memory for the mouse cursor at its smallest size on modern computers.

PageSize constant

Base page size in the virtual memory system of most modern computers. Note that for performance reason, many modern computers now support multiple page sizes.

HelloWorld constant

A constant often used in computer programs to denote joy, happiness and the emergence into the world of some new computer language.

Equations library

The DB48X calculator features a library of equations covering mathematics, physics, chemistry and computer science. The built-in equations can be extended using the config/equations.csv configuration file.

Columns and Beams

The variables in the columns and beams section are:

• o: Eccentricity (offset) of load
• σcr: Critical stress
• σmax: Maximum stress
• θ: Slope at x
• A: Cross-sectional area
• a: Distance to point load
• 'ε': Eccentricity
• c: Distance to edge fiber (Eccentric Columns), or Distance to applied moment (beams)
• E: Modulus of elasticity
• I: Moment of inertia
• K: Effective length factor of column
• L: Length of column or beam
• M: Applied moment
• Mx: Internal bending moment at x
• P: Load (Eccentric Columns), or Point load (beams)
• Pcr: Critical load
• r: Radius of gyration
• V: Shear force at x
• w: Distributed load
• x: Distance along beam
• y: Deflection at x

For simply supported beams and cantilever beams (“Simple Deflection” through “Cantilever Shear”), the calculations differ depending upon the location of x relative to the loads.

• Applied loads are positive downward.
• The applied moment is positive counterclockwise.
• Deflection is positive upward.
• Slope is positive counterclockwise
• Internal bending moment is positive counterclockwise on the left-hand part.
• Shear force is positive downward on the left-hand part.

Elastic Buckling

These equations apply to a slender column (K·L/r>100) with length factor K.

Eccentric Columns

These equations apply to a slender column (K·L/r>100) with length factor K.

Simple Deflection

Simple Slope

Simple Moment

Simple Shear

Cantilever Deflection

Cantilever Slope

Cantilever Moment

Cantilever Shear

Electricity

Fluids

Forces and Energy

Gases

Heat transfer

Magnetism

Motion

Optics

Oscillations

Plane geometry

Solid geometry

Solid state devices

Stress analysis

Waves

Menus

Menus display at the bottom of the screen, and can be activated using the keys on the top row of the calculator. Menus can refer to other menus. The calculator keeps a history of the menus you visited previously, and you can return to an earlier menu with the BackMenu function.

Here are the main menus in DB48X, in alphabetical order.

MainMenu

The Main menu gives access to all the functions in your calculator, sorted by cathegory. It includes the following submenus:

• Math: Mathematical operations
• Symb: Symbolic operations
• Units: Unit conversions
• System: System configuration
• Prog: Programming
• Vars: User variables

MathMenu

The Math menu gives access to mathematical functions like SIN in your calculator. It includes the following submenus:

• Arith: Arithmetic functions
• Base: Based numbers
• Trans: Transcendental functions
• Stats: Statistics
• Lists: List operations
• Matrix: Matrices and vectors
• Solve: Numerical solver

VariablesMenu (VARS)

The variables menu displays the variables in the current directory. It is a three row menu, where for each variable:

• The primary function evaluates the variable
• The first shifted function recalls the variable
• The second shifted function stores in the variable

VariablesMenuExecute

Hitting the primary function in the Vars menu evaluates the corresponding variable.

VariablesMenuRecall

Hitting the first shifted function in the Vars menu will recall the corresponding variable on the stack.

VariablesMenuStore

Hitting the second shifted function in the Vars menu will store the top of stack in the corresponding variable.

ToolsMenu

The ToolsMenu maps to the A key (Σ+ on the original DM42 keyboard). It invokes a context-dependent menu adapted to the top level of the stack.

LastMenu

The LastMenu function (🟨 A), returns back in the history of past visited menus. The history contains up to 8 entries.

Operations with Angles

ToDegrees (→Deg)

Convert a number or angle to an angle in degrees. If given a number, that number is interpreted using the current angle mode.

ToRadians (→Rad)

Convert a number or angle to an angle in radians. If given a number, that number is interpreted using the current angle mode.

ToGrads (→Grad)

Convert a number or angle to an angle in grads. If given a number, that number is interpreted using the current angle mode.

ToPiRadians (→πr)

Convert a number or angle to an angle in multiple of π radians. If given a number, that number is interpreted using the current angle mode.

ANGTODEG

Convert an angle to degrees

ANGTORAD

Convert an angle to radians

ANGTOGRAD

Convert an angle to grads (gons)

ANGTODMS

Convert an angle to DMS (DD.MMSS)

TORECT

Convert vector or complex to cartesian coordinates

TOPOLAR

Convert vector or complex to polar coordinates

TOSPHER

Convert vector or complex to spherical coordinates

Arithmetic

+ (add)

Add two values.

Y X ▶ Y+X

• For integer, fractional, decimal or complex numbers, this performs the expected numerical addition. For example, 1 2 + is 3.
• For equations and symbols, build a sum, eliminating zero additions if autosimplify is active.
• For lists, concatenate lists, or add objets to a list. For example, { A } { B } + is { A B }, and { A B C } "D" + is { A B C "D" }.
• For text, concatenate text, or concatenate the text representation of an object to an existing text. For example "X" "Y" + gives "XY", and "X=" 1 + gives "X=1".

- (sub)

Subtract two values

Y X ▶ Y-X

• For integer, fractional, decimal or complex numbers, this performs the expected numerical subtraction. For example, 1 2 - is -1.
• For equations and symbols, build a difference, eliminating subtraction of 0 if autosimplify is active.

× (*, mul)

Multiply two values.

Y X ▶ Y×X

• For integer, fractional, decimal or complex numbers, this performs the expected numerical multiplication. For example, 3 2 * is 6.
• For vectors, multiply individual elements (this is a deviation from HP48). For example, [ 1 2 3 ] [ 4 5 6 ] + is [ 4 10 18 ].
• For matrices, perform a matrix multiplication.
• For a matrix and a vector, apply the matrix to the vector.
• For equations and symbols, build a product, eliminating mulitplication by 1 or 0 when autosimplify is active.
• For a list and a positive integer, repeat the list For example, { A } 3 * is { A A A }.
• For a text and a positive integer, repeat the text. For example "X" 3 * gives "XXX".

÷ (/, div)

Divide two values two values

Y X ▶ Y÷X

• For integer, build a fraction. For example 1 7 / gives 1/7.
• For fractional, decimal or complex numbers, this performs the expected numerical division. For example, 1. 2. / is 0.5.
• For vectors, divide individual elements. For example, [ 1 2 3 ] [ 3 2 1 ] / is [ 1/3 1 3 ].
• For equations and symbols, build a ratio, eliminating division by one and division of 0 when autosimplify is active.

↑ (^, pow)

Raise to the power

Y X ▶ Y↑X

• For integer, fractional, decimal or complex numbers, this raises the value in level 2 to the value in level 1. For example, 2 3 ↑ is 8.
• For vectors, raise individual elements in the first vector to the power of the corresponding element in the second vector.
• For equations and synbols, build an expression, eliminating special cases when autosimplify is active.

xroot

Raise to the inverse power. X Y xroot is equivalent to X Y inv pow.

Y X ▶ Y↑(1/X)

Integer arithmetic and polynomials

This section documents newRPL commands that are not implemented yet in DB48X.

SETPREC

Set the current system precision

GETPREC

Get the current system precision

Floor

Largest integer less than the input

Ceil

Smallest integer larger than the input

IntegerPart (IP, IntPart)

Integer part of a number

FractionalPart (FP, FracPart)

Fractional part of a number

MODSTO

Set the current system modulo for all MOD operations

MODRCL

Get the current system modulo

POWMOD

Power operator MOD the current system modulo

MOD

Remainder of the integer division

SQ

Square of the input

NEXTPRIME

Smallest prime number larger than the input

FACTORIAL

Factorial of a number

ISPRIME

Return true/false (1/0) if a number is prime or not

MANT

Mantissa of a real number (M*10^exp)

XPON

Exponent of a number represented as (M*10^exp)

Sign

Sign of a number, -1, 0 or 1.

For complex numbers, returns a unit number on the unit circle with the same argument as the original number.

Percent (%)

Percentage of a number

Y X ▶ Y×(X÷100)

PercentChange (%CH)

Percentage of change on a number

Y X ▶ (X÷Y-1)×100

PercentTotal (%T)

Get percentage of a total

Y X ▶ (X÷Y)×100

GCD

Greatest common divisor

LCM

Least common multiple

IDIV2

Integer division, get quotient and remainder. On DB48X, this is an alias for div2.

Y X ▶ IP(Y/X) Y rem X

IQUOT

Quotient of the integer division

ADDTMOD

Addition operator MOD the current system modulo

SUBTMOD

Subtraction operator MOD the current system modulo

MULTMOD

Multiplication operator MOD the current system modulo

PEVAL

Evaluation of polynomial given as vector of coefficients

PCOEF

Coefficients of monic polynomial with the given roots

IEGCD

Extended euclidean algorithm

IABCUV

Find integers u,v to solve au+bv=c

PTCHEBYCHEFF

Nth Tchebycheff polynomial

PLEGENDRE

Nth Legendre polynomial

PHERMITE

Nth Hermite polynomial as used by physics

PTCHEBYCHEFF2

Nth Tchebycheff polynomial of the second kind

PHERMITE2

Nth Hermite polynomial as used in probabilities

DIV2 (QuoRem, IDIV2, QuotientRemainder)

Euclidean division, returning quotient and remainder.

On HP calculators, this only applies for polynomials.

On DB48X, this applies to integers, big integers, decimals, fractions and polynomials. It puts both the quotient and the remainder on the stack. For many data types, this operation is significantly more efficient than computing the quotient and the remainder separately.

Y X ▶ IP(Y/X) Y rem X

PDIV2

Polynomial euclidean division as coefficient vector

PDER

Derivative of polynomial as coefficient vector

PINT

Integration of polynomials as coefficient vector

PMUL

Multiplication of polynomials as coefficient vectors

PADD

Addition of polynomials as coefficient vector

PSUB

Subtraction of polynomials as coefficient vector

Min

Smallest of 2 objects

Max

Largest of 2 objects

RND

Round a number to the given number of figures

TRNC

Truncate a number to the given number of figures

DIGITS

Extract digits from a real number

PROOT

All roots of a polynomial

PREVPRIME

Largest prime smaller than the input

FACTORS

Factorize a polynomial or number

Base functions

Evaluate (EVAL)

Evaluate the object at stack level 1.

Mapped to the _ R/S _ key

X ▶ Result of X evaluation

Negate (NEG)

Negate the value in level 1.

Mapped to the _ +/- _ key

X ▶ 0-X

Invert (INV)

Invert the value in level 1

Mapped to the _ 1/X _ key

X ▶ 1/X

Bitwise operations

Bitwise operations represent bit-manipulation operations such as rotations and shifts. They operate on based numbers, integers or big integers. When operating on based numbers, the operation happens on the number of bits defined by the WordSize setting. For integer values, the maximum number of bits is defined by the MaxNumberBits setting.

ShiftLeft (SL)

Shift the value left by one bit.

Value ▶ Value*2

ShiftLeftByte (SLB)

Shift the value left by one byte (8 bits).

Value ▶ Value*256

ShiftLeftCount (SLC)

Shift the value left by a given number of bits.

Value Shift ▶ Value*2^Shift

ShiftRight (SR)

Shift the value right by one bit.

Value ▶ Value/2

ShiftRightByte (SRB)

Shift the value right by one byte (8 bits).

Value ▶ Value/256

ShiftRightCount (SRC)

Shift the value right by a given number of bits.

Value Shift ▶ Value/2^Shift

ArithmeticShiftRight (ASR)

Shift the value right by one bit, preserving the sign bit.

Value ▶ Signed(Value)/2

ArithmeticShiftRightByte (ASRB)

Shift the value right by one byte (8 bits), preserving the sign bit.

Value ▶ Signed(Value)/256

ArithmeticShiftRightCount (ASRC)

Shift the value right by a given number of bits, preserving the sign bit.

Value Shift ▶ Signed(Value)/2^Shift

RotateLeft (RL)

Rotate the value left by one bit.

Value ▶ RLC(Value, 1)

RotateLeftByte (RLB)

Rotate the value left by one byte (8 bits).

Value ▶ RL(Value, 8)

RotateLeftCount (RLC)

Rotate the value left by a given number of bits.

Value Shift ▶ RLC(Value, Shift)

RotateRight (RR)

Rotate the value right by one bit.

Value ▶ RRC(Value, 1)

RotateRightByte (RRB)

Rotate the value right by one byte (8 bits).

Value ▶ RRC(Value, 8)

RotateRightCount (RRC)

Rotate the value right by a given number of bits.

Value Shift ▶ RRC(Value, Shift)

Logical operations

Logical operations operate on truth values. They can either operate on numbers, where a non-zero value represent True and a zero value represents False. On based numbers, they operate bitwise on the number of bits defined by the WordSize setting.

Or

Logical inclusive "or" operation: the result is true if either input is true.

Y X ▶ Y or X

And

Logical "and" operation: the result is true if both inputs are true.

Y X ▶ Y and X

Xor

Logical exclusive "or" operation: the result is true if exactly one input is true.

Y X ▶ Y xor X

Not

Logical "not" operation: the result is true if the input is false.

X ▶ not X

NAnd

Logical "not and" operation: the result is true unless both inputs are true.

Y X ▶ Y nand X

NOr

Logical "not or" operation: the result is true unless either input is true.

Y X ▶ Y nor X

Implies

Logical implication operation: the result is true if the first input is false or the second input is true.

Y X ▶ Y implies X

Equiv

Logical equivalence operation: the result is true if both inputs are true or both inputs are false.

Y X ▶ Y equiv X

Excludes

Logical exclusion operation: the result is true if the first input is true or the second input is false.

Y X ▶ Y excludes X

Bitmaps

TOSYSBITMAP

Comments

STRIPCOMMENTS

Remove all comments from a compiled program

Operations with Complex Numbers

RE

Real part of a complex number

IM

Imaginary part of a complex number

ARG

Argument of a complex number

CONJ

Conjugate of a complex number

CPLX2REAL

Split Complex into two Reals

REAL2CPLX

Make Complex from real and imaginary parts

Lists, Matrix and String commands

PUT

Replace an item in a composite

PUTI

Replace an item and increase index

GET

Extract an item from a composite

GETI

Extract an item and increase index

HEAD

Extract the first item in a composite

TAIL

Removes the first item in a composite

OBJDECOMP

Explode an object into its components

REPL

Replace elements in a composite

POS

Find the position of an element in a composite

NPOS

Find object in a composite, starting from index N

POSREV

Find the position of an element, starting from the end

NPOSREV

Find the position from the end, starting at index N

SUB

Extract a group of elements from a composite

SIZE

Number of elements in a composite

RHEAD

Returns the last element from the composite

RTAIL

Removes the last element from the composite

Constants

Constants are defined by the config/constants.csv, and accessed using the ConstantsMenu or the CONST command.

Library equations are defined by the config/equations.csv, and accessed using the EquationsMenu or the LibEq command.

Library items are defined by the config/library.csv, and accessed using the Library command or the XLib command.

Constant (CONST)

Returns the value of a constant from the constants library. The name can be given as a symbol or as text.

'c' ▶ 299792458_m/s

LibraryEquation (LIBEQ)

Returns the value of a library equation from the equation library. The name can be given as a symbol or as text.

"RelativityMassEnergy" ▶ "'E=m*c^2'"

LibraryItem (XLIB)

Returns the value of a library item from the library. The name can be given as a symbol or as text.

'Dedicace'" ▶ "À tous ceux qui se souviennent de Maubert électronique"

Debugging

DB48X offers a variety of capabilities to help debugging RPL programs. These are made available through the DebugMenu, which is the menu that ToolsMenu selects when a program is on the stack.

DebugMenu

The debug menu contains operations necessary to debug RPL programs:

• Debug
• Step
• Over
• Steps
• Continue
• Halt
• Kill
• Step↑

Debug (DBUG)

The Debug command takes a program or expression as an argument, and starts debugging execution of it. When a program is halted for debugging, the header area shows a ♦ symbol, and the next instruction to be executed is shown above the stack. When a program is single-stepping, the header area shows a › symbol.

While a program is being debugged, you can use the command line normally and even execute programs from it. However, only a single debugging session can exist. If the program being executed halts, e.g. through the HALT command or by being interrupted using the EXIT key, then this is seen as part of the same debugging session.

SingleStep (SST)

The SingleStep command steps through a single instruction in the RPL program.

StepOver

The StepOver command steps over the next instruction. If the next instruction is a variable name containing a program, execution halts after executing the program. If the next instruction being shown is a sequence of instructions, for example the test or the sequence of instructions in tests or loops, then the entire sequence is evaluated at once.

StepOut

The StepOut command steps out of the current code block.

MultipleSteps

The MultipleSteps instruction evaluates an arbitrary number of steps in the program being debugged. The number of steps to execute is passed as an argument in the first level of the stack. For example, 40 MultipleSteps will execute the next 40 RPL instructions.

Continue (CONT)

The Continue command resumes execution of the current RPL program at the current instruction.

Halt

The Halt instruction interrupts the execution of a program, making it possible to insert breakpoints at specific locations in a program.

Kill

The Kill instruction stops the execution of the program currently being debugged.

Variables

Variables are named storage for RPL values.

Store (STO)

Store an object into a specified location. For example 2 'ABC' STO stores the value 2 in a global variable named ABC.

Value Name ▶

The Value is copied in a storage location identified by Name. The storage location depends on the type of Name, which can be quoted in an expression:

• Symbol or integer: The value is stored in a global variable with that name in the current directory, which is created if necessary. Whether integers can be used as variable names depends on the NumberedVariables setting.

• Local name: The value is stored in the corresponding local variable.

• Setting name: The value is used for the corresponding setting, as if the setting command had been executed. For example, 16 'Base' STO has the same effect as 16 Base.

• Text: Value is stored in a named file on the flash storage.

Recall (RCL)

Recall an object from a specified location. For example 'ABC' RCL recalls the value from a global variable named ABC.

Name ▶ Value

The Value is fetched from a storage location identified by Name. The storage location depends on the type of Name, which can be quoted in an expression:

• Symbol or integer: The value is fetched from a global variable with that name in the current directory or any enclosing directory. Whether integers can be used as variable names depends on the NumberedVariables setting.

• Local name: The value is fetched from the corresponding local variable.

• Setting name: The value is fetched from the corresponding setting. For example, 'Base' RCL returns the current value as set by Base.

• Text: Value is fetched from a named file on the flash storage

Flash storage

SwissMicros calculators have built-in flash storage, that can act as a USB disk when the calculator is connected to a computer. DB48X can read and write to this flash storage using the regular STO and RCL commands, simply by giving a text containing the file name as the Name argument of these commands.

The format of the file depends on how the name ends:

• .txt: the value is stored as text.

• .48s: the value is stored as source code in text format. This differs from .txt files for text objects, which will be quoted.

• .48b: the value is stored in version-specific binary format. This format is only guaranteed to be readable by the same firmware version that wrote it, but it is more compact, faster and energy efficient than the source format.

• .csv: The value is stored in comma-separated values format. This is mostly interesting for arrays and lists, which can be echanged with spreadsheets and other PC applications that can input or output CSV files.

StoreAdd (STO+)

Add a value to the content of a variable

StoreSub (STO-)

Subtract a value from the contents of a variable

StoreMul (STO×)

Multiply the contents of a variable by a value

StoreDiv (STO÷)

Divide the contents of a variable by a value

RecallAdd (RCL+)

Add the content of a variable to a value on the stack

RecallSub (RCL-)

Subtract the contents of a variable from a value on a stack

RecallMul (RCL×)

Multiply a value on the stack by the contents of a variable

RecallDiv (RCL÷)

Divide a value on the stack by the contents of a variable

Increment (INCR)

Add one to the content of a variable

Decrement (DECR)

Subtract one from content of a variable

Purge

Delete a global variable from the current directory

Remark: Purge only removes a variable from the current directory, not the enclosing directories. Since Recall will fetch variable values from enclosing directories, it is possible that 'X' Purge 'X' Recall will fetch a value for X from an enclosing directory. Use PurgeAll if you want to purge a variable including in enclosing directories.

PurgeAll

Delete a global variable from the current directory and enclosing directories.

Remark: If a variable with the same name exists in multiple enclosing directories, PurgeAll may purge multiple variables. Use Purge if you want to only purge a variable in the current directory.

CreateDirectory (CRDIR)

Create new directory

PurgeDirectory (PGDIR)

Purge entire directory tree

UpDirectory (UPDIR)

Change current directory to its parent

HomeDirectory (HOME)

Change current directory to HOME

DirectoryPath (PATH)

Get a path to the current directory

Variables (VARS)

List all visible variables in a directory

▶ { Variables... }

TypedVariables (TVARS)

List variables of a specific type

type ▶ { Variables... } { types... } ▶ { Variables... }

See the Type command for a list of types.

ORDER

Sort variables in a directory

QUOTEID

Add single quotes to a variable name

UNQUOTEID

Remove single quotes from a variable name

HIDEVAR

Hide a variable (make invisible)

UNHIDEVAR

Make a hidden variable visible

CLVAR

Purge all variables and empty subdirectories in current directory

LOCKVAR

Make variable read-only

UNLOCKVAR

Make variable read/write

RENAME

Change the name of a variable

SPROP

Store a property to a variable

RPROP

Recall a property of a variable

PACKDIR

Pack a directory in an editable object

Errors and error handlers

EXITRPL

Panic exit - abort the RPL engine.

EVAL1NEXT

Perform EVAL1 on the next object in a secondary and skips it

RESUME

End error handler and resume execution of main program

DOERR

Issue an error condition

ERRN

Recall the previous error code

ERRM

Recall the previous error message

ERR0

Clear previous error code

HALT

Halt the execution of RPL code

CONT

Continue execution of a halted program

SST

Single-step through a halted program, skip over subroutines

SSTIN

Single-step through a halted program, goes into subroutines

KILL

Terminate a halted program

SETBKPOINT

Set a breakpoint on a halted program

CLRBKPOINT

Remove a breakpoint

DBUG

Halt the given program at the first instruction for debugging

BLAMEERR

Issue an error condition, blame other program for it

EXIT

Early exit from the current program or loop

Flow control

If

The if statement provides conditional structurs that let a program make decisions. It comes in two forms:

• if condition then true-clause end: This evaluates condition and, if true, evaluates true-clause.

• if condition then true-clause else false-clause end: This evaluates condition and, if true, evaluates true-clause, otherwise evaluates false-clause.

A condition is true if:

• It is a number with a non-zero value
• It is the word True

A condition is false if:

• It is a number with a zero value
• It is the word False

Case

The case statement can be used to select one case among many. Inside a case, there is a list of conditions, each followed by then or when. Code following then or when is executed when the condition is met.

• A condition preceding then is a boolean condition, similar to the condition in an if statement.

• A condition preceding when is a value that must match the current value on the stack exactly.

For example, X case dup 0 < then "N" end dup 0 > then "P" end "Z" end will return the value "N", "P" or "Z" depending on whether X is negative, positive or null.

The when syntax is useful to test exact values, for example X case 0 when "zero" end 1 when "one" end 2 when "two" end end will compute the English spelling for value 0, 1 and 2.

THENCASE

Conditional CASE ... THEN ... END THEN ... END END statement

ENDTHEN

Conditional CASE ... THEN ... END THEN ... END END statement

ENDCASE

Conditional CASE ... THEN ... END THEN ... END END statement

FOR

Loop FOR ... NEXT/STEP statement

START

Loop START ... NEXT/STEP statement

NEXT

Loop FOR/START ... NEXT statement

STEP

Loop FOR/START ... STEP statement

DO

Loop DO ... UNTIL ... END statement

UNTIL

Loop DO ... UNTIL ... END statement

ENDDO

Loop DO ... UNTIL ... END statement

WHILE

Loop WHILE ... REPEAT ... END statement

REPEAT

Loop WHILE ... REPEAT ... END statement

ENDWHILE

Loop WHILE ... REPEAT ... END statement

IFERR

Conditional IFERR ... THEN ... ELSE ... END statement

THENERR

Conditional IFERR ... THEN ... ELSE ... END statement

ELSEERR

Conditional IFERR ... THEN ... ELSE ... END statement

ENDERR

Conditional IFERR ... THEN ... ELSE ... END statement

FORUP

Loop FORUP ... NEXT/STEP statement

FORDN

Loop FORUP ... NEXT/STEP statement

Flags

Flags are truth value that can be controled and tested by the user. User flags are identified by a natural number. There are MaxFlags user flags (default is 128). System flags are identified by a settings name or a negative integer.

SETLOCALE

Change the separator symbols

SETNFMT

Change the display format for numbers

SetFlag (SF)

Set a user or system flag.

33 SF sets user flag 0. 'MixedFractions' SetFlag enables the MixedFractions setting.

ClearFlag (CF)

Clear a user or system flag

FlipFlag

Invert a user or system flag

TestFlagSet (FS?)

Test if a flag is set

TestFlagClear (FC?)

Test if a flag is clear

TestFlagClearThenClear (FC?C)

Test if a flag is clear, then clear it

TestFlagSetThenClear (FS?C)

Test if a flag is set, then clear it

TestFlagClearThenSet (FC?S)

Test if a flag is clear, then set it

TestFlagSetThenSet (FS?S)

Test if a flag is set, then set it

FlagsToBinary (RCLF)

Recall all system flags as a binary number.

BinaryToFlags (STOF)

Store and replace all system flags from a binary number

Fonts

FNTSTO

Install a user font for system use

FNTRCL

Recall a system font

FNTPG

Purge a user-installed system font

FNTSTK

Recall name of current font for stack area

FNT1STK

Recall name of current font for stack level 1

FNTMENU

Recall name of current font for menu area

FNTCMDL

Recall name of current font for command line area

FNTSTAT

Recall name of current font for status area

FNTPLOT

Recall name of current font for plot objects

FNTFORM

Recall name of current font for forms

STOFNTSTK

Change current font for stack area

STOFNT1STK

Change current font for stack level 1

STOFNTMENU

Change current font for menu area

STOFNTCMDL

Change current font for command line area

STOFNTSTAT

Change current font for status area

STOFNTPLOT

Change current font for plot objects

STOFNTFORM

Change current font for forms

FNTHELP

Recall name of current font for help

FNTHLPT

Recall name of current font for help title

STOFNTHELP

Change current font for help text

STOFNTHLPT

Change current font for help title

Graphic commands

DB48X features a number of graphic commands. While displaying graphics, the stack and headers will no longer be updated.

Coordinates

DB48X recognizes the following types of coordinates

• Pixel coordinates are specified using based numbers such as #0, and correspond to exact pixels on the screen, and . Pixels are counted starting from the top-left corner of the screen, with the horizontal coordinate going from 10#0 to 10#399, and the vertical coordinate going from 10#0 to 10#239.

• User unit coordinates are scaled according to the content of the PPAR or PlotParameters reserved variables.

• Text coordinates are given on a square grid with a size corresponding to the height of a text line in the selected font. They can be fractional.

Coordinates can be given using one the following object types:

• A complex number, where the real part represents the horizontal coordinate and the imaginary part represents the vertical coordinate.

• A 2-element list or vector containing the horizontal and vertical coordinates.

• A 1-element list of vector containing one of the above.

For some operations, the list or vector can contain additional parameters beyond the coordinates. The selection of unit or pixel coordinates is done on a per coordinate basis. For exmaple, { 0 0 } will be the origin in user coordinates, in the center of the screen if no PPAR or PlotParameters variable is present.

Note that unlike on the HP48, a complex value in DB48X can contain a based number.

ClearLCD (CLLCD)

Clear the LCD display, and block updates of the header or menu areas.

DrawText (DISP)

Draw the text or object in level 2 at the position indicated by level 1. A text is drawn without the surrounding quotation marks.

If the position in level 1 is an integer, fraction or real number, it is interpreted as a line number starting at 1 for the top of the screen. For example, "Hello" 1 disp will draw Hello at the top of the screen. If the position is a based number, it is a row number in pixels. For example, "Hello" #120d disp will show the test in the middle of the screen.

If the position in level 1 is a complex number or a list, it is interpreted as specifying both the horizontal or vertical coordinates, in either pixel or unit coordinates. For example "Hello" { 0 0 } disp will draw Hello starting in the center of the screen.

Text is drawn using the stack font by default, using the foreground and background patterns.

If level 1 contains a list with more than 2 elements, additional elements provide:

• A font number for the text

• An erase flag (default true) which indicates whether the background for the text should be drawn or not.

• An invert flag (default false) which, if set, will swap the foreground and background patterns.

For example, "Hello" { #0 #0 3 true true } DrawText will draw Hello in the top-left corner (#0 #0) with the largest (editor) font (font identifier 3), erasing the background (the first true), in reverse colors (the second true).

DrawStyledText (DISPXY)

Draw the text or object in level 3 at the position indicated by level 2, using the font specified in level 1. This behaves like DrawText, except for the additional parameter specifying the font size.

This command is compatible with the HP50G usage, where the position is specified by a list containing two decimal integer values. A font size of 1 displays with a small font, a font size of 2 displays with a regular font.

In addition to this HP50G-compatible usage, DispXY will also accept:

• A smaller font size, 0, for the help size, and other font sizes above 2, which are compatible with the values given to StackFont.

• The position can accept the same values as DrawText, including a single integer value indicating a line number, a fractional line position, or coordinates scaled according to PlotParameters.

Show

Display the first level of the stack using the entire screen, with a possible scroll using the 4, 8, 6 and 2 keys if the object is larger than fits on screen. This makes it possible to comfortably examine very large objects, like 300!, a large program or a complicated equation. Arrow keys can also be used for horizonal or vertical scrolling.

The maximum size of the graphic object is defined by the MaximumShowWidth and MaximumShowHeight settings.

DrawLine (line)

Draw a line between two points specified by level 1 and level 2 of the stack.

The width of the line is specified by LineWidth. The line is drawn using the foreground pattern.

PlotParameters (PPAR)

The PlotParameters reserved variable defines the plot parameters, as a list, with the following elements:

• Lower Left coordinates as a complex (default -10-6i)

• Upper Right coordinates as a complex (default 10+6i)

• Independent variable name (default x)

• Resolution specifying the interval between values of the independent variable (default 0). A binary numnber specifies a resolution in pixels.

• Axes which can be a complex giving the origin of the axes (default 0+0i), or a list containing the origin, the tick mark specification, and the names of the axes.

• Type of plot (default function)

• Dependent variable name (default y)

Local Variables

LSTO

Store to a new local variable

LRCL

Recall content of local variable

HIDELOCALS

Hide local variables from subroutines

UNHIDELOCALS

Unhide local variables from subroutines

INTERNAL_NEWNLOCALS

Arbitrary data containers

MKBINDATA

Create binary data container object

BINPUTB

Store bytes into binary data object

BINGETB

Extract binary data as list of bytes

BINPUTW

Store 32-bit words into binary data object

BINGETW

Extract data from a binary data object as a list of 32-bit words

BINPUTOBJ

Store an entire object into a binary data container

BINGETOBJ

Extract an entire object from a binary data container

BINMOVB

Copy binary data block into a binary data object

BINMOVW

Copy 32-bit words between binary data objects

User Libraries

CRLIB

Create a library from current directory

ATTACH

Install a library

DETACH

Uninstall a library

LIBMENU

Show a menu within a library

LIBMENUOTHR

Show library menu in the other menu

LIBMENULST

Show library menu in the last used menu

LIBSTO

Store private library data

LIBRCL

Recall private library data

LIBDEFRCL

Recall private data with default value

LIBCLEAR

Purge all private data for a specific library

Operations with data

Data in RPL is generally represented using lists, such as { {1 2 } 3 "A"}. Numerical data can be represented using arrays, such as [1 2 3 4]. In the DB48X implementation of RPL, arrays and list can have any number of dimensions, and are not necessarily rectangular, although some operations (e.g. matrix operations using arrays as input) can impose stricter constraints.

→List (ToList)

Build a list from elements on the stack. Level 1 of the stack contains the number of elements in the list. The elements are on the stack, the first element being deepest in the stack. This is the opposite of List→.

A B ... Count ▶ { A B ... }

List→ (FromList)

Expand a list on the stack and return the number of elements. After executing the command, level 1 contains the number of elements, and a corresponding number of stack levels contain individual elements of the list, the first element being at the deepest level in the stack. This is the opposite of →List. The Obj→ command performs the same operation when applied to a list.

{ A B ... } ▶ A B ... Count

List→ (FromList)

Expand a list on the stack and return the number of elements. After executing the command, level 1 contains the number of elements, and a corresponding number of stack levels contain individual elements of the list, the first element being at the deepest level in the stack. This is the opposite of →List. The Obj→ command performs the same operation when applied to a list.

{ A B ... } ▶ A B ... Count

Head

Return the first element of a list, or an Invalid dimension error if the list is empty.

{ A B ... } ▶ A

Tail

Return all but the first element of a list, or an Invalid dimension error if the list is empty.

{ A B ... } ▶ { B ... }

Map

Apply an operation on all elements in a list or array. The operation on the first level of the stack should take one argument and return a single value.

{ A B ... } F ▶ { F(A) F(B) ... }

Reduce

Apply a cumulative pairwise operation on all elements in a list or array. The operation on the first level of the stack should take two arguments and combine them into a single value. The result is the repeated application of that operation to all elements.

{ A B ... } F ▶ F(F(A, B), ...)

Filter

Filter elements in a list of array based on a predicate. The predicate given on level 1 of the stack takes a value as argument, and returns a truth values. The resulting list is built with all elements where the predicate is true.

{ A B ... } P ▶ { A ... } if P(A) is true and P(B) is false.

Get

Get an element from composite data, such as list, an array or a text. Elements are numbered starting at 1. The index can itself be a list, which is interpreted as successive indices in the data.

For example, { A B C } 2 GET returns B, "ABC" 3 GET returns "C", [ [ 1 2 ] [ 4 5 ] [ 5 6 ] ] { 2 2 } GET returns 5.

When the data is a name, data is feched directly from the given named variable.

Data Index ▶ Element

Put

Put an element into composite data, such as list, an array or a text. This performs the opposite operation compared to Get.

Elements are numbered starting at 1. The index can itself be a list, which is interpreted as successive indices in the data.

For example, { A B C } 2 'X' PUT returns { A X C }, "ABC" 2 "Hello" PUT returns "AHelloC", [ [ 1 2 ] [ 4 5 ] [ 5 6 ] ] { 2 2 } 7 PUT returns [ [ 1 2 ] [4 7 ] [5 6] ].

When the data is a name, data is feched directly from the given named variable.

Data Index ▶ Element

Sort

Sort elements in a list or array, sorting by increasing values when comparing numers, text or symbols.

This may be a little slower than QuickSort, but is useful to sort lists or arrays of numerical values or text values.

QuickSort

Sort elements in a list or array using the memory representation of objects. This guarantees a consistent sorting order, but one that does not necessarily preserve numerical or textual properties, unlike Sort. Comparisons are, however, significantly faster than Sort.

ReverseSort

Sort a list or array by value, in reverse order compared to Sort.

ReverseQuickSort

Sort a list or array using the memory representation of objects, in reverse order compared to QuickSort.

ReverseList (REVLIST)

Reverse the order of elements in a list

ADDROT

Add elements to a list, keep only the last N elements

SEQ

Assemble a list from results of sequential procedure

Operations with Matrices and vectors

ToArray (→Arry)

Stack to Array Command: Returns a vector of n real or complex elements or a matrix of n × m real or complex elements.

The elements of the result array should be entered in row order.

A1 ... An n ▶ [ A1 ... An ]

A11 ... Arc { r c } ▶ [[ A11 A1c] [ A21 ... Arc ]]

FromArray (Arry→)

Array to Stack Command: Takes an array and returns its elements as separate real or complex numbers. Also returns a list of the dimensions of the array. If the argument is an n-element vector, the first element is returned to level n + 1 (not level nm + 1), and the nth element to level 2.

[ A1 ... An ] ▶ A1 ... An n

[[ A11 A1c] [ A21 ... Arc ]] ▶ A11 ... Arc { r c }

TOCOL

Split an array into column vectors

ADDCOL

Instert a column into an array

REMCOL

Remove a column from an array

FROMCOL

Assemble a matrix from its columns

TODIAG

Extract diagonal elements from a matrix

FROMDIAG

Create a matrix with the given diagonal elements

TOROW

Split an array into its row vectors

ADDROW

Insert a row into an array

REMROW

Remove a row from an array

FROMROW

Assemble an array from its rows

TOV2

Assemble a vector from two values

TOV3

Assemble a vector from three values

FROMV

Split a vector into its elements

AXL

Convert a matrix to list and vice versa

BASIS

Find vectors forming a basis of the subspace represented by the matrix

CHOLESKY

Perform Cholesky decomposition on a matrix

CNRM

Column norm (one norm) of a matrix

CON (ConstantArray)

Returns a constant array, defined as an array whose elements all have the same value.

The constant value is an object taken from argument 2/level 1. The resulting array is either a new array, or an existing array with its elements replaced by the constant, depending on the object in argument 1/level 2.

• Creating a new array: If level 2 contains a list of one or two integers, CON returns a new array. If the list contains a single integer n, CON returns a constant vector with n elements. If the list contains two integers n and m, CON returns a constant matrix with n rows and m columns.

• Replacing the elements of an existing array: If level 2 contains an array, CON returns an array of the same dimensions, with each element equal to the constant.

• If level 2 contains a name, the name must identify a variable that contains a valid input for con, such as an array. In this case, the content of the variable is replaced with the value generated by CON

n k ▶ [ k ... k ]

{ n } k ▶ [ k ... k ]

{ n m } k ▶ [ [ k ... k ] [ k ... k ] ... [ k ... k ] ]

[ vec ] k ▶ [ k ... k]

[ [ mat ] ] k ▶ [ [ k ... k ]]

'name' k ▶

COND

Column norm condition number of a matrix

CROSS

Cross produce of vectors

CSWP

Swap two columns in a matrix

Determinant (DET)

Compute the determinant of a matrix

DIAGMAP

DOT

Internal product (dot product) of vectors

EGV

EGVL

Compute the eigenvalues of a matrix

GRAMSCHMIDT

HADAMARD

Multiply corresponding elements in a matrix

HILBERT

Assemble a Hilbert symbolic array

IBASIS

Find a basis of the intersection of two vector spaces

IDN (IdentityMatrix)

Identity Matrix Command: Returns an identity matrix, that is, a square matrix with its diagonal elements equal to 1 and its off-diagonal elements equal to 0.

The result is either a new square matrix, or an existing square matrix with its elements replaced by the elements of the identity matrix, according to the argument.

• Creating a new matrix: If the argument is an integer n, a new real identity matrix is returned, with its number of rows and number of columns equal to n.

• Replacing the elements of an existing matrix: If the argument is a square matrix, an identity matrix of the same dimensions is returned.

• Generating the identity matrix for a vector: If the argument is a vector with n elements, an identity matrix with n rows and n columns is created.

• If the argument is a name, the name must identify a variable containing on of the valid inputs. In this case, it is replaced with the result.

n ▶ IDN(n)

{ n } ▶ IDN(n)

{ n n } ▶ IDN(n)

[ n-vec ] ▶ IDN(n)

[[ nxn-mat ]] ▶ IDN(n)

'name' ▶

IMAGE

Find a basis of the image of a linear application

ISOM

JORDAN

KER

Find a basis for the kernel of a linear application

LQ

LSQ

LU

LU factorization of a matrix

MAD

MKISOM

PMINI

Minimal polynomial of a matrix

QR

QR Decomposition of a matrix

RANK

Rank of a matrix

RANM (RandomMatrix)

Returns an array containing random integer values between -9 and 9.

RCI

Multiply a row by a constant

RCIJ

Multiply a row by a constant and add to other row

RDM

Change dimensions of an array

REF

Reduce matrix to echelon form (upper triangular form)

RNRM

Row norm (infinity norm) of a matrix

RREF

Fully reduce to row-reduced echelon form

RREFMOD

RSD

Residual R=B-AX' on a system AX=B

RSWP

Swap two rows in a matrix

SCHUR

SNRM

SRAD

SVD

SVL

SYLVESTER

TRACE

Sum of the items in the diagonal of a matrix

TRAN

Transpose a matrix

TRN

Complex conjugate transpose of a matrix

VANDERMONDE

LDUP

Decompose A into LDUP such that PA=LD^-1*U

MMAP

Apply expression or program to the elements of a matrix

Catalog

The Catalog command is triggered by the + command while in Alpha mode, or using 🟨 + otherwise (CAT). It is an auto-completing catalog of all the available commands or characters.

When entering a program, all commands matching the text currently matched will be shown. For example, if you typed A, all commands containing an A are displayed in alphabetical order. If you type ACO, ACOS, ACOSHandDataColumn(a possible spelling forColΣ`) will all be shown.

Inside text, all characters related to the last entered character will be shown. For example, if you typed A, options to add accents to A or to select the Greek α or the related ª character. If no matching character is found, the CharactersMenu characters menu is presented, allowing you to select specific characters from predefined categories.

CharactersMenu

The CharactersMenu, which can be accessed using 🟦 2 (CHAR), presents a convenient way to insert characters.

While entering text, the Catalog also presents matching characters, or the characters menu if none is found.

The characters menus and the catalog behaviour can be configured by modifying the config/characters.csv file. Each row in that file contains two texts:

• The first is the name of the menu. If the name is empty, the menu is not shown, but is used to find characters related to a given character.

• The second is the list of characters to be shown.

ConstantsMenu

The ConstantsMenu gives access to numerous constants, shown in various categories. This includes basic mathematical constants such as π or e, as well as constants related to chemistry, physics, computer science or history.

The constants menu is defined by the config/constants.csv file. You are encouraged to tailor this file to suit your own needs.

Numerical functions

∫ (Integrate)

Perform a numerical integration of a function for a specified variable on a numerical interval. For example 2 3 'X*(X-3)' 'X' Integrate returns -7/6.

The function takes four arguments:

• The lower bound of the integration range
• The higher bound of the integration range
• The program or expression to evaluate
• The integration variable

Root

Root-finder command. Returns a real number that is a value of the specified variable for which the specified program or algebraic object most nearly evaluates to zero or a local extremum. For example, 'X^2=3' 'X' 0 returns X:1.732050807568877293527446341953458.

The function takes three arguments:

• The program or expression to evaluate
• The variable to solve for
• An initial guess, or a list containing an upper and lower guess.

Objects

Cycle

Cycle through various representations of the object on the first level of the stack.

• Polar <-> Rectangular for complex numbers
• Decimal <-> Fraction
• Integer <-> Based (cycles through the 2, 8, 10 and 16 base)
• Array <-> List <-> Program
• Text <-> Symbol

For unit objects, Cycle will cycle through all SI prefixes such that the decimal representations fits within the StandardExponent range (i.e. that would not display in scientific mode), increasing the numerical value, and then switch the value to a fraction and cycle through all fraction representations that fit within the same numerical range.

For example, if the StandardExponent is set to 6, the value 0.1_m will cycle as follows:

• 0.1_m being a decimal, we move to next scale up as decimal
• 1._dm
• 10._cm
• 100._mm
• 100000._μm, which is the limit of what can be displayed with 6 digits, so we switch to a fractional representation.
• 100000_μm being a fraction, we go through the prefixes going down.
• 100_mm
• 10_cm
• 1_dm
• 1/10_m
• 1/100_dam
• 1/1000_hm
• 1/10000_km, at which point the conversion would be out of range, so we switch back to decimal.
• 0.0001_km
• 0.001_hm
• 0.01_dam
• 0.1_m at which point the cycle repeats.

Explode (OBJ→)

Explode an object into its sub-components. The various sub-components are placed on the stack, and if necessary, information about the size is places on the first level of the stack.

• Complex numbers are split into real and imaginary part (for rectangular form) or modulus and argument (for polar form). The latter is an extension compared to classical RPL, which always represent complex numbers in rectangular form.

• Unit objects are split into the value and unit expression. This is a deviation from standard RPL, which places a unit object on the first level of the stack.

• Lists, programs and expressions are split into their individual components, and the number of components is placed on the first level of the stack. For programs, this is an extension of standard RPL. For expressions, this is a deviation: HP calculators instead place only the top level object and the arity.

• Arrays and vectors are split into their individual components, and the number of elements is placed as a list on the first level of the stack. The dimension list has one element for vectors, and two for matrices. If a given matrix is not rectangular, then the command reports an Invalid dimension error.

• Text is evaluated as if it had been executed on the command line, in a way similar to the STR→ command.

Scalable plots and graphics

BEGINPLOT

Initialize a new current plot object

EDITPLOT

Set the current plot object to the given graphic

ENDPLOT

Finish current plot object and leave it on the stack

STROKECOL

Change the current stroke color

STROKETYPE

Change current stroke type

FILLCOL

Change the current fill color

FILLTYPE

Change the current fill type

FILL

Fill the last polygon

STROKE

Draw the outline of the last polygon

FILLSTROKE

Draw the outline and fill the last polygon

MOVETO

Move current coordinates

LINETO

Draw a line

CIRCLE

Draw a circle

RECTANG

Draw a rectangle

CTLNODE

Add a control node to the current polygon

CURVE

Draw a curve using all previous control points

BGROUP

EGROUP

DOGROUP

BASEPT

TRANSLATE

ROTATE

SCALE

CLEARTRANSF

SETFONT

TEXTHEIGHT

TEXTOUT

INITRENDER

Set which library will be used as default renderer

DORENDER

Render a graphics object using the current renderer

PANVIEW

Shift the center of viewport to render graphics

ROTVIEW

SCLVIEW

Set scale to render graphics

VIEWPORT

VIEWALL

SD Card

SDRESET

Reset the file system module

SDSETPART

Set active partition

SDSTO

Store a an object into a file

SDRCL

Recall an object from a file

SDCHDIR

Change current directory

SDUPDIR

Change to parent directory

SDCRDIR

Create a new directory

SDPGDIR

Delete an entire directory

SDPURGE

Delete a file

SDOPENRD

Open a file for read-only operation

SDOPENWR

Open a file for writing

SDOPENAPP

Open a file in append mode

SDOPENMOD

Open a file in modify mode

SDCLOSE

Close an open file

SDREADTEXT

Read text from an open file (UTF-8 encoding)

SDWRITETEXT

Write text to a file (UTF-8 encoding)

SDREADLINE

Read one line of text from a file

SDSEEKSTA

Move position to given offset from start of file

SDSEEKEND

Move position to given offset from end of file

SDSEEKCUR

Move position to given offset from the current point.

SDTELL

Get the current position

SDFILESIZE

Get the file size in bytes

SDEOF

Return true if last operation reached end of file

SDOPENDIR

Open a directory to scan entries

SDNEXTFILE

Get the next entry in a directory that is a file

SDNEXTDIR

Get the next entry in a directory that is a subdirectory

SDNEXTENTRY

Get the next entry in a directory

SDMOVE

Move or rename a file

SDCOPY

Copy a file

SDPATH

Get the path to current directory

SDFREE

Get the free space in the current volume

SDARCHIVE

Create a full calculator backup on a file

SDRESTORE

Restore from a backup stored in a file

SDGETPART

Get the current partition number

Settings

The calculator has a number of user-configurable settings:

• Display
• Angles
• Command display
• Decimal separator
• Precision
• Base
• User interface
• Compatibility

The current preferences can be retrieved and saved using the Modes command.

Modes

Returns a program that will restore the current settings. This program can be saved into a variable to quickly restore a carefully crafted set of preferences. Note that the calculator automatically restores the mode when it loads a state.

Display settings

The display mode controls how DB48X displays numbers. Regardless of the display mode, numbers are always stored with full precision.

DB48X has five display mode (one more than the HP48)s:

• Standard mode
• Fixed mode
• Scientific mode
• Engineering mode)
• Significant digits mode)

StandardDisplay (STD)

Display numbers using full precision. All significant digts to the right of the decimal separator are shown, up to 34 digits.

FixedDisplay (FIX)

Display numbers rounded to a specific number of decimal places.

ScientificDisplay (SCI)

Display numbers in scientific notation, i.e. with a mantissa and an exponent. The mantissa has one digit to the left of the decimal separator and shows the specified number of decimal places.

EngineeringDisplay (SCI)

Display nunmbers as a mantissa with a sepcified number of digits, followed by an exponent that is a multiple of 3.

SignificantDisplay (SIG)

Display up to the given number of digits without trailing zero. This mode is useful because DB48X can compute with large precision, and it may be useful to not see all digits. StndardDisplay is equivalent to 34 SignificantDisplay, while 12 SignificantDisplay should approximate the HP48 standard mode using 12 significant digits.

StandardExponent

Select the maximum exponent before switching to scientific notation. The default value is 9, meaning that display uses scientific notation for exponents outside of -9..9.

MinimumSignificantDigits

Select the minimum number of significant digits before switching to scientific notation in FIX and SIG mode. The default value is 3, meaning that at least 3 significant digits will be shown.

A value of 0 is similar to how HP calculators before the HP Prime perform. For example, with 2 FIX, the value 0.055 will display as 0.06, and 0.0055 will display as 0.01.

A higher value will switch to scienfic mode to show at least the given number of digits. For instance, with 2 FIX, if the value is 1, then 0.055 will still display as 0.06 but 0.0055 will display as 5.50E-3. If the value is 2, then 0.055 will display as 5.5E-2. A setting of 1 correspond to what the HP Prime does.

A value of -1 indicates that you do not want FIX mode to ever go to scientific notation for negative exponents. In that case, 0.00055 will display as 0.00. This corresponds to how older HP calculators render numbers.

TrailingDecimal

Display a trailing decimal separator to distinguish decimal from integer types. With this setting, 1.0 will display as 1.. This can be disabled with NoTrailingDecimal.

NoTrailingDecimal

Hide the trailing decimal separator for decimal values with no fractional part. In that mode, 1.0 and 1 will both display identically, although the internal representation is different, the former being a floating-point value while the latter is an integer value.

FancyExponent

Display the exponent in scientific mode using a fancy rendering that is visually similar to the normal mathematical notation.

ClassicExponent

Display the exponent in scientific mode in a way reminiscent of classical HP48 calculators, for example 1.23E-4.

MixedFractions

Display fractions as mixed fractions when necessary, e.g. 3/2 will show up as 1 1/2.

ImproperFractions

Display fractions as improper fractions, e.g. 3/2 will show up as 3/2 and not 1 1/2.

SmallFractions

Show fractions using smaller characters, for example ¹²/₄₃

BigFractions

Show fractions using regular characters, for example 12/43

Angle settings

The angle mode determines how the calculator interprets angle arguments and how it returns angle results.

DB48X has four angle modes:

• Degrees: A full circle is 360 degress
• Radians: A full circle is 2π radians
• Grads: A full circle is 400 radians
• PiRadians: Radians shown as multiple of π

Degrees (DEG)

Select degrees as the angular unit. A full circle is 360 degrees.

Radians (RAD)

Select radians as the angular unit. A full circle is 2π radians, and the angle is shown as a numerical value.

Grads (GRAD)

Select grads as the angular unit. A full circle is 400 grads.

PiRadians (PIRAD)

Select multiples of π as the angular unit. A full circle is 2π radians, shown as a multiple of π.

SetAngleUnits

When this setting is active, inverse trigonometric functoins asin, acos and atan return a unit value with a unit corresponding to the current AngleMode. This makes it possible to have values on the stack that preserve the angle mode they were computed with. The opposite setting is NoAngleUnits.

Note that the sin, cos and tan will copmute their value according to the unit irrespective of this setting. In other words, 30_° SIN will always give 0.5, even when computed in Rad or Grad mode,

NoAngleUnits

This is the opposite setting to SetAngleUnits. Inverse trigonometric functions behave like on the original HP-48 calculator, and return a numerical value that depends on the current angle mode.

Command display

DB48X can display commands either using a short legacy spelling, usually identical to what is used on the HP-48 series of calculators, or use an alternative longer spelling. For example, the command to store a value in a variable is called STO in the HP-48, and can also be spelled Store in DB48X.

Commands are case insensitive, and all spellings are accepted as input irrespective of the display mode.

DB48X has four command spelling modes:

• Lowercase: Display sto
• Uppercase: Display STO
• Capitalized: Display Sto
• LongForm: Display Store

There are four parallel settings for displaying a variable name such as varName:

• LowercaseNames: Display as varname
• UppercaseNames: Display as VARNAME
• CapitalizedNames: Display as VarName
• LongFormNames: Display as varName

LowerCase

Display comands using the short form in lower case, for example sto.

UpperCase

Display comands using the short form in upper case, for example STO.

Capitalized

Display comands using the short form capitalized, for example Sto.

LongForm

Display comands using the long form, for example Store.

LowerCaseNames

Display names using the short form in lower case, for example varName will show as varname.

UpperCase

Display names using the short form in upper case, for example varName will show as VARNAME.

Capitalized

Display names using the short form capitalized, for example varName will show as VarName.

LongForm

Display names using the long form, for example varName will show as varName.

Decimal separator settings

The decimal separator can be either a dot (1.23) or a comma (1,23).

DecimalDot

Select the dot as a decimal separator, e.g. 1.23

DecimalComma

Select the comma as a decimal separator, e.g. 1,23

Precision settings

Precision

Set the default computation precision, given as a number of decimal digits. For example, 7 Precision will ensure at least 7 decimal digits for compuation, and 1.0 3 / will compute 0.3333333 in that case.

DB48X supports an arbitrary precision for decimal numbers, limited only by memory and the size of built-in constants needed for the computation of transcendental functions.

SolverImprecision

Set the number of digits that can be ignored when solving. The default value is 6, meaning that if the current precision is 24, we only solve to an accuracy of 18 digits (i.e. 24-6).

Base settings

Integer values can be reprecended in a number of different bases:

• Binary is base 2
• Ocgtal is base 8
• Decimal is base 10
• Hexadecimal is base 16

Binary (BIN)

Selects base 2

Octal (OCT)

Selects base 8

Decimal (DEC)

Selects base 10

Hexadecimal (HEX)

Selects base 16

Base

Select an arbitrary base for computations

WordSize (STWS)

Store the current word size in bits. The word size is used for operations on based numbers. The value must be greater than 1, and the number of bits is limited only by memory and performance.

RecallWordSize (RCWS)

Return the current word size in bits.

STWS

STWS is a compatibility spelling for the WordSize command.

RCWS

RCWS is a compatibility spelling for the RecallWordSize command.

MaxRewrites

Defines the maximum number of rewrites in an equation.

Equations rewrites can go into infinite loops, e.g. 'X+Y' 'A+B' 'B+A' rewrite can never end, since it keeps rewriting terms. This setting indicates how many attempts at rewriting will be done before erroring out.

MaxNumberBits

Define the maxmimum number of bits for numbers.

Large integer operations can take a very long time, notably when displaying them on the stack. With the default value of 1024 bits, you can compute 100! but computing 200! will result in an error, Number is too big. You can however compute it seting a higher value for MaxNumberBits, for example 2048 MaxNumberBits.

This setting applies to integer components in a number. In other words, it applies separately for the numerator and denominator in a fraction, or for the real and imaginary part in a complex number. A complex number made of two fractions can therefore take up to four times the number of bits specified by this setting.

ToFractionIterations (→QIterations, →FracIterations)

Define the maximum number of iterations converting a decimal value to a fraction. For example, 1 →FracIterations 3.1415926 →Frac will give 22/7, whereas 3 →FracIterations 3.1415926 →Frac will give 355/113.

ToFractionDigits (→QDigits, →FracDigits)

Define the maximum number of digits of precision converting a decimal value to a fraction. For example, 2 →FracDigits 3.1415926 →Frac will give 355/113.

User interface

Various user-interface aspects can be customized, including the appearance of Soft-key menus. Menus can show on one or three rows, with 18 (shifted) or 6 (flat) functions per page, and there are two possible visual themes for the labels, rounded or square.

ThreeRowsMenus

Display menus on up to three rows, with shift and double-shift functions showns above the primary menu function.

SingleRowMenus

Display menus on a single row, with labels changing using shift.

FlatMenus

Display menus on a single row, flattened across multiple pages.

RoundedMenu

Display menus using rounded black or white tabs.

SquareMenus

Display menus using square white tabs.

CursorBlinkRate

Set the cursor blink rate in millisecond, between 50ms (20 blinks per second) and 5000ms (blinking every 5 seconds).

ShowBuiltinUnits

Show built-in units in the UnitsMenu even when a units file was loaded.

HideBuiltinUnits

Hide built-in units in the UnitsMenu when a units file was loaded. The built-in units will still show up if the units file fails to load.

MultiLineResult

Show the result (level 1 of the stack) using multiple lines. This is the opposite of SingleLineResult. Other levels of the stack are controled by MultiLineStack

SingleLineResult

Show the result (level 1 of the stack) on a single line. This is the opposite of MultiLineResult. Other levels of the stack are controled by SingleLineStack

MultiLineStack

Show the levels of the stack after the first one using multiple lines. This is the opposite of SingleLineStack. Other levels of the stack are controled by MultiLineResult

SingleLineStack

Show the levels of the stack after the first one on a single line This is the opposite of MultiLineStack. Other levels of the stack are controled by SingleLineResult

GraphicResultDisplay

Display the first level of the stack (result) using a graphical representations for objects such as expressions or matrices. Note that enabling this setting may increase CPU utilization and reduce battery life compared to text-only rendering.

This is the opposite of TextResultDisplay

TextResultDisplay

Display the first level of the stack (result) using a text-only representations.

This is the opposite of TextResultDisplay

GraphicStackDisplay

Display the stack levels above the first one using a graphical representations for objects such as expressions or matrices. Note that enabling this setting may increase CPU utilization and reduce battery life compared to text-only rendering.

This is the opposite of TextStackDisplay

TextStacktDisplay

Display the stack levels above the first one using a text-only representations.

This is the opposite of GraphicStackDisplay

AutoScaleStack

When using graphic result display, automatically scale down the font size in order to make stack elements fit. Enabling this setting may increase CPU utilization and reduce battery life compared to fixed-size rendering.

This is the opposite of NoStackAutoScale.

NoStackAutoScale

When using graphic result display, do not automatically scale down the font size in order to make stack elements fit.

This is the opposite of AutoScaleStack.

MaximumShowWidth (MaxW)

Maximum number of horizontal pixels used to display an object with Show.

MaximumShowHeight (MaxH)

Maximum number of vertical pixels used to display an object with Show.

EditorWrapColumn

Column at which the editor will start wrapping long lines of code. Wrapping occurs at the end of an object, not in the middle of it.

TabWidth

Width of a tab in the editor, in pixels.

ExitKeepsMenu

By default, the EXIT key clears the current menu if not editing. When ExitKeepsMenu is set, the EXIT key does not clear the menu.

ExitClearsMenu

Restore the default behaviour where EXIT clears the current menu when not editing.

ShowEmptyMenu

Show empty menu entries. For example, when selecting the VariablesMenu and there is no variable defined, an empty menu shows up.

HideEmptyMenu.

Restore the default behaviour where empty menus entries are not shown, leaving more space for the stack display.

Statistics settings

LinearFitSums

When this setting is active, statistics functions that return sums, such as ΣXY or ΣX², operate without any adjustment to the data, i.e. as if the fitting model in ΣParameters was LinearFit.

CurrentFitSums

When this setting is active, statistics functions that return sums, such as ΣXY or ΣX², will adjust their input according to the current fitting model in special variable ΣParameters, in the same way as required for LinearRegression.

RandomGeneratorBits

Define the number of random bits generated by ACORN random number generator, between 32 and 4096 bits. The default value is 128 bits. A lower value uses less memory and accelerates computations, but some digits in the resulting numbers may not be adequately random. Conversely, a higher value increases true randomness in the resulting numbers and should be used if you need random numbers with higher Precision than the default 24 digits.

For example, with a value of 64, the generated random numbers will very often contain zeros after the 12th digit. The reason is that 64 bits of randomness corresponds to only 20 digits, which is less than the default 24-digits precision of DB48X.

RandomGeneratorOrder

Define the order of the ACORN random number generator, i.e. the value called k in the ACORN documentation. This is the number of seed numbers preserved between generations. A higher value requires more memory and takes more time to compute but generates higher-quality random numbers. On DB48X, the ACORN order can be set between 10 and 256. The default value is 32.

Compatibility settings

Various settings control the compatibility of DB48X with various classes of HP calculators.

DetailedTypes

The Type command returns detailed DB48X type values, which can distinguish between all DB48X object types, e.g. distinguish between polar and rectangular objects, or the three internal representations for decimal numbers. Returned values are all negative, which distinguishes them from RPL standard values, and makes it possible to write code that accepts both the compatible and detailed values.

This is the opposite of CompatibleTypes.

CompatibleTypes

The Type command returns values as close to possible to the values documented on page 3-262 of the HP50G advanced reference manual. This is the opposite of NativeTypes.

NumberedVariables

This flag enables numbered variables similar to what existed on earlier RPN calculators. For example, when the setting is active, 2.5 0 STO stores the value 2.5 in numbered register 0.

NoNumberedVariables

This flag disables numbered variables, behaving closer to the way RPL calculators work. For example, when the setting is active, 2.5 0 STO generates an Invalid name error.

IgnoreSymbolCase

Ignore the case in symbols, i.e. variables X and x are the same. Note that this is different from the way RPL in HP calculators works.

DistinguishSymbolCase

Distinguish the case in symbols, i.e. variables X and x are distinct. This is the way RPL in HP calculators works.

ListAsProgram

When this setting is set, DB48X behaves like the HP48S and later HP devices and evaluates lists as if they were programs. For example, { 1 2 + } EVAL returns 3. The default is ListsAsData.

ListsAsData

When this setting is set, DB48X behaves like the HP28 and evaluates lists as data. For example, { 1 2 + } EVAL returns { 1 2 + }.

KillOnError

An error kills the program without giving you the possibility to debug the problem. If you want to debug, you need to start the program with Debug and then use the Continue command.

DebugOnError

An error during a program enters the debugger, letting you correct the problem before resuming execution. This is the default setting.

States

The calculator can save and restore state in files with extension .48S. This feature is available through the Setup menu (Shift-0).

The following information is stored in state files:

• Global variables
• Stack contents
• Settings

Numeric solvers

NUMINT

Numerical integration (adaptive Simpson)

ROOT

Root seeking within an interval

MSOLVE

Multiple non-linear equation solver/optimization search

BISECT

Root seeking (bisection method)

Stack manipulation

ClearStack (CLEAR)

Remove all objects from the stack

Depth

Get the current stack depth

Drop

Remove an object from the stack

X ▶

Drop2

Remove two objects form the stack

DropN

Remove N objects from the stack, N being given in level 1.

Duplicate (DUP)

Duplicate an object on the stack

Duplicate2 (DUP2)

Duplicate two objects on the stack

DuplicateTwice (DUPDUP)

Duplicate the same object twice on the stack

DuplicateN (DUPN)

Duplicate a group of N objects, N being given in stack level 1

LastArguments (LASTARG)

Put the last arguments back on the stack

LastX

Put the last first argument on the stack.

This command does not exist on HP RPL calculators, and is here to make it easier to adapt RPN programs that use LastX a bit more often.

Undo

Restore the stack to its last state before executing an interactive command. Note that this command can be used from a program, but it will restore the state prior to program execution.

NDUPN

Replicate one object N times and return N

Nip

Remove object at level 2 on the stack

Over

Duplicate object at level 2 on the stack

Pick

Duplicate object at position N on the stack

Pick3

Duplicate object at level 3 on the stack

Roll

Move object at level N to level 1

RollD

Move object from level 1 to level N

Rot

Move object from level 3 to level 1

Swap

Exchange objects in levels 1 and 2

Mapped to X⇆Y key

Y X ▶ X Y

Unpick

Move object from level 1 to level N.

UnRot

Move object from level 1 to level 3

IFT

Evaluate objects on the stack conditionally

IFTE

Evaluate objects on the stack conditionally

STKPUSH

Push a snapshot of the current stack on the undo stack

STKPOP

Pop a stack snapshot from the undo stack

STKDROP

Drop a snapshot from the undo stack

STKPICK

Copy snapshot in level N to the current stack

STKDEPTH

Get the depth of the undo stack

STKNEW

Push a snapshot of the current stack on the undo stack and clears the current stack

Statistics

RDZ

Initialize random number generator with a seed. If the given seed is zero, then a truly random value based on the internal system clock is used, and the value changes every millisecond.

For any given non-zero value, the sequence of numbers generated by RAND or Random will always be identical.

RAND

Generate a random real number between 0 and 1, 1 being excluded.

DB48X uses an additive congruential random number generator (ACORN), which is configured by two settings, RandomGeneratorOrder and RandomGeneratorBits.

Random

Generate a random number between two bounds.

If the two bounds are integers, then the result is an integer, and the upper bound is included. For example, 2 4 Random can generate 2, 3 or 4.

Otherwise, the upper bound is excluded. For example, 2. 4. Random can generate any number between 2.0 and 4.0, but the upper bound 4.0 cannot be generated.

The resulting number is

ΣData (ΣDAT)

The ΣData variable contains the statistics data, in the form of a matrix.

Note: The ΣData name is considered a command internally, and as such, is subject to CommandDisplayMode and not NamesDisplayMode.

ΣParameters (ΣPAR)

The ΣParameters variable contains the statistics parameters, as a list with five elements:

{ xcol ycol intercept slope fit }

The xcol value is an integer starting at 1, indicating the independent column. The ycol value similarly indicates the dependent column.

The intercept and slope are the parameters for the linear regression. The fit value is the type of fit being used: (LinFit, ExpFit, PwrFit, LogFit);

Note: The ΣParameters name is considered a command internally, and as such, is subject to CommandDisplayMode and not NamesDisplayMode.

Σ+

Add data to the statistics data array ΣData.

• If data is a real or complex number, statistics data is single-column

• If data is a vector, statistics data has the same number of columns as the size of the vector.

Σ-

Remove the last data entered in the statistics array, and pushes it on the stack.

RecallΣ (RCLΣ)

Recall statistics data and puts it on the stack

StoreΣ (STOΣ)

Stores an array from the stack as statistics data in the ΣData variable.

ClearΣ (CLΣ)

Clear statistics data.

Average (MEAN, AVG)

Compute the average (mean) of the values in the statistics data. If there is a single column of data, the result is a real number. Otherwise, it is a vector for each column of data.

Median

Compute the median of the values in the statistics data array ΣData.

MinΣ

Compute the smallest of the values in the statistics data array ΣData.

MaxΣ

Compute the largest of the values in the statistics data array ΣData.

ΣSize (NΣ)

Return the number of data rows in the statistics data array ΣData.

SumOfX (ΣX)

Return the sum of values in the XCol column of the statistics data array ΣData. The values are adjusted according to the current fitting model defined in ΣParameters if the CurrentFitSums setting is active.

SumOfY (ΣY)

Return the sum of values in the YCol column of the statistics data array ΣData. The values are adjusted according to the current fitting model defined in ΣParameters if the CurrentFitSums setting is active.

SumOfXY (ΣXY)

Return the sum of the product of values in the XCol and YCol columns of the statistics data array ΣData. The values are adjusted according to the current fitting model defined in ΣParameters if the CurrentFitSums setting is active.

SumOfXSquares (ΣX²)

Return the sum of the squares of the values in the XCol column of the statistics data array ΣData. The values are adjusted according to the current fitting model defined in ΣParameters if the CurrentFitSums setting is active.

SumOfYSquares (ΣY²)

Return the sum of the squares of the values in the YCol column of the statistics data array ΣData. The values are adjusted according to the current fitting model defined in ΣParameters if the CurrentFitSums setting is active.

Total (TOT)

Returns the sum of all columns in the statistics data array ΣData.

Variance (VAR)

Calculates the sample variance of the coordinate values in each of the columns in the current statistics matrix (ΣData).

Correlation (CORR)

Returns the correlation coefficient of the independent and dependent data columns in the current statistics matrix (reserved variable ΣData).

The columns are specified by the first two elements in the reserved variable ΣParameters, set by XCol and YCol, respectively. If ΣParameters does not exist, Correlation creates it and sets the elements to their default values (1 and 2).

Covariance (COV)

Returns the sample covariance of the independent and dependent data columns in the current statistics matrix (reserved variable ΣData).

The columns are specified by the first two elements in the reserved variable ΣParameters, set by XCol and YCol, respectively. If ΣParameters does not exist, Correlation creates it and sets the elements to their default values (1 and 2).

StandardDeviation (SDEV)

Calculates the sample standard deviation of each of the columns of coordinate values in the current statistics matrix (reserved variable ΣData).

StandardDeviation returns a vector of numbers, or a single number there is only one column of data.

The standard deviation is the square root of the Variance.

LinearRegression (LR)

Uses the currently selected statistical model to calculate the linear regression coefficients (intercept and slope) for the selected dependent and independent variables in the current statistics matrix (reserved variable ΣData).

The columns of independent and dependent data are specified by the first two elements in the reserved variable ΣParameters, set by XCol and YCol, respectively. The default independent and dependent columns are 1 and 2.

The selected statistical model is the fifth element in ΣParameters. LR stores the intercept and slope (untagged) as the third and fourth elements, respectively, in ΣParameters.

The coefficients of the exponential (ExpFit), logarithmic (LogFit), and power (PwrFit) models are calculated using transformations that allow the data to be fitted by standard linear regression.

The equations for these transformations are:

• LinFit: y = slope * x + intercept
• LogFit: y = slope * ln(x) + intercept
• ExpFit: y = intercept * exp(slope * x)
• PwrFit: y = intercept * x ^ slope

where b is the intercept and m is the slope. The logarithmic model requires positive x-values (XCOL), the exponential model requires positive y-values (YCOL), and the power model requires positive x- and y-values.

Intercept

Return the intercept value last computed by LinearRegression

This is a DB48X extension, not present on HP calculators

Slope

Return the slope value last computed by LinearRegression

This is a DB48X extension, not present on HP calculators

BestFit

Select the best linear regression mode based on current data, i.e. the regression mode where the correlation value is the highest.

LinearFit (LINFIT)

Select linear fit, i.e. try to model data with a linear equation y = a*x+b.

ExponentialFit (EXPFIT)

Select exponential fit, i.e. try to model data with an equation y = b*exp(a*x)

LogarithmicFit (LOGFIT)

Select logarithmic fit, i.e. try to model data with an equation y = a*ln(x)+b.

PowerFit (PWRFIT)

Select power fit, i.e. try to model data with an equation y = x^a * b.

FrequencyBins (BINS)

Sorts the elements of the independent column (XCol) of the current statistics matrix (the reserved variable ΣDat) into (nbins + 2) bins, where the left edge of bin 1 starts at value xmin and each bin has width xwidth.

FrequencyBins returns a matrix containing the frequency of occurrences in each bin, and a 2-element array containing the frequency of occurrences falling below or above the defined range of x-values. The array can be stored into the reserved variable ΣData and used to plot a bar histogram of the bin data, for example, by executing BarPlot.

xmin xwidth nbins ▶ [[ n1 .. n2 ]] [ nlow nhigh ]

PopulationVariance (PVAR)

Calculates the population variance of the coordinate values in each of the m columns in the current statistics matrix (ΣData).

The population variance (equal to the square of the population standard deviation) is returned as a vector of m real numbers, or as a single real number if there is a single column of data.

PopulationStandardDeviation (PSDEV)

Calculates the population standard deviation of each of the m columns of coordinate values in the current statistics matrix (reserved variable ΣData).

The command returns a vector of m real numbers, or a single real number if there is a single column of data.

PopulationCovariance (PCOV)

Computes the population covariance of the independent and dependent data columns in the current statistics matrix (reserved variable ΣData).

The columns are specified by the first two elements in reserved variable ΣParameters, set by XCol and YCol respectively. If ΣParameters does not exist, PCOV creates it and sets the elements to their default values, 1 and 2.

IndependentColumn (XCOL)

Set the independent variable column in the reserved variable ΣParameters.

XCol ▶ (Update ΣParameters)

DependentColumn (YCOL)

Set the dependent variable column in the reserved variable ΣParameters.

YCol ▶ (Update ΣParameters)

DataColumns (COLΣ)

Set both the independent and dependent data columns in the reserved variable ΣParameters.

XCol YCol ▶ (Update ΣParameters)

Operations with Symbolic Expressions

↑Match

Match pattern up and rewrite expression, starting with the innermost subexpressions first. This approach works well for simplifications. A subexpression simplified during one execution will be a simpler argument of its parent expression, so the parent expression can be simplified further.

Expr { From To } ▶ Expr Count Expr { From To Cond } ▶ Expr Count

The first argument Expr is the expression to transform.

The second argument is a list containing the pattern to match From, the replacement pattern To, and an optional condition Cond on the pattern.

↓Match

Match pattern down and rewrite expression, starting with the outermost expression first. This approach works well for expansion. An expression expanded during one execution of ↓Match will contain additional subexpressions, and those subexpressions can be expanded further.

Expr { From To } ▶ Expr Count Expr { From To Cond } ▶ Expr Count

The first argument Expr is the expression to transform.

The second argument is a list containing the pattern to match From, the replacement pattern To, and an optional condition Cond on the pattern.

Expression rewrite

Operations such as ↑Match and ↓Match apply arbitrary transformations on algebraic expressions. The way this operates is similar to how HP calculators perform, but with important differences, controlled by flags.

First, patterns can contain wildcards, which are substituted with the corresponding sub-expression in the matched Expr.

• On HP calculators, the wildcard names must begin with &, and only an optional external conditions can control what matches or not.

• On DB48X, by default, any name in the pattern acts as a wildcard, and we use & to refer to a specific variable i.e. &A only matches the variable named A.

Rationale: The default DB48X approach makes it easier to write transformation rules for the common cases, the & character being a bit harder to access on the calculator's keyboard. The assumption is that we rarely write patterns to match a specific variable, i.e. replace an expression only if it refers to X but not to Y. The HP behaviour can be restored using the ExplicitWildcards flag.

A further extension in DB48X is to give a semantic meaning to the first letter of variable names:

• a, b and c denote numerical constants, like real or integer values.
• i, j are positive integer values which may be zero and may be the result of a computation, i.e. 3-3 will match.
• k, l, m are non-zero positive integer values, which may be the result of a compuation, i.e. 3-2 will match.
• n, o, p are symbols or names like 'ABC'.
• u, v, w are unique terms, i.e. terms that cannot be presented more than once in an expression.
• Names where the initial is lowercase must be sorted, so that x+y will match A+B but not B+A.

Another important difference is that on HP calculators, the number of rewrites of subexpressions is limited to a single pass, irrespective of flag -100 (step-by-step CAS mode), whereas DB48X will repeat application by default (this can be changed by setting StepByStepAlgebraResults, or alternatively, by clearing flag -100).

This leads to the last important difference. On HP calculators, ↑Match and ↓Match return either 0 or 1 in the first level of the stack to indicate if a replacement occurred. On DB48X, the number of replaced subexpressions is returned, and it can be greater than 1.

Examples:

• 'A+B+0' {'X+0' 'X' } ↓Match returns 'A+B' 1
• 'A+B+C' { 'X+Y' 'Y-X' } ↓Match returns 'C-(B-A)' 2
• '(A+B)^3' { 'X^N' 'X*X^(N-1)' } ↓Match returns (A+B)*(A+B)^2.

AutoSimplify

Enable automatic reduction of numeric subexpressions according to usual arithmetic rules. After evaluating AutoSimplify 'X+0' will evaluate as 'X' and 'X*1-B*0' witll evaluate as 'X'.

The opposite setting is NoAutoSimplify

NoAutoSimplify

Disable automatic reduction of numeric subexpressions according to usual arithmetic rules. After evaluating NoAutoSimplify, equations such as'X+0' or X*1-B*0 will no longer be simplified during evaluation.

The opposite setting is AutoSimplify

FinalAlgebraResults

Evaluate algebraic rules on symbolic expressions repeatedly until no futher change results from applying them.

StepByStepAlgebraResults

Evaluate algebraic rules on symbolic expressions one step at a time.

→Num (→Decimal, ToDecimal)

Convert fractions and symbolic constants to decimal form. For example, 1/4 →Num results in 0.25.

→Frac (→Q, ToFraction)

Convert decimal values to fractions. For example 1.25 →Frac gives 5/4. The precision of the conversion in digits is defined by →FracDigits, and the maximum number of iterations for the conversion is defined by →FracDigits

ListExpressionNames (LName)

List all variables used in an expression or polynomial, leaving the original object on the stack, and returning the result as an array. Names are sorted in decreasing order of size, and for the same size, in alphabetical order.

'A*Foo*G(X;Y;cos Z) ▶ 'A*Foo*G(X;Y;cos Z) [ Foo A G X Y Z ] '(U_V)=(I_A)*(R_Ω)' ▶ '(U_V)=(I_A)*(R_Ω)' [ I R U ]

As a DB48X extension, this command also applies to programs, list and arrays. Another extension is the ExpressionVariables command, which extracts the units associated with the variables if there are any. The LName command only returns the names, without the associated unit.

ExpressionVariables (XVars)

List all variables used in an expression or polynomial, returning the result as a list. Names are sorted in decreasing order of size, and for the same size, in alphabetical order. If there are units in the expression, the units are returned in the resulting list.

'A*Foo*G(X;Y;cos Z) ▶ { Foo A G X Y Z } '(U_V)=(I_A)*(R_Ω)' ▶ { (I_A) (R_Ω) (U_V) }

This is a variation of the HP command LNAME, which is a bit more convenient to use in programs.

RULEAPPLY1

Match and apply a rule to an expression only once

TRIGSIN

Simplify replacing cos(x)^2+sin(x)^2=1

ALLROOTS

Expand powers with rational exponents to consider all roots

CLISTCLOSEBRACKET

RANGE

Create a case-list of integers in the given range.

ASSUME

Apply certain assumptions about a variable to an expression.

Time, Alarms and System Commands

Date format

The date format is YYYYMMDD, with an optional fractional part defining the time, as in YYYYMMDD.HHMMSS.

Note: the date format is intentionally different from the format on the HP-48.

Time format

The time format is HH.MMSS with optional hundredths of a second as in HH.MMSSCC.

SetDate

Set current system date.

The date format is YYYYMMDD, with an optional fractional part defining the time, as in YYYYMMDD.HHMMSS. If the fractional part is zero, then the time is not changed.

Note: the date format is intentionally different from the format on the HP-48.

Date+

Add days to a date. The date format is YYYYMMDD, with an optional fractional part defining the time, as in YYYYMMDD.HHMMSS, and an optional unit, as in YYYMMDD_date.

SetTime

Set current time from a stack value HH.MMSSCC.

An HMS value can also be given, as returned by the Time command.

ToHMS

Convert decimal time to HH.MMSS format.

FomHMS

Convert time in HH.MMSS format to decimal time.

HMS+

Add time in HH.MMSS format.

HMS-

Subtract time in HH.MMSS format

Ticks

Return system clock in milliseconds

TEVAL

Perform EVAL and measure elapsed time

Date

Return the current system date as a unit object in the form YYYYMMDD_date. This displays on the stack according to date format settings, in a way similar to what is shown in the header, e.g. 23/Feb/2024 or 2024-02-23.

DateTime

Return the current system date as a unit object in the form YYYYMMDD_date. This displays on the stack according to date format settings, in a way similar to what is shown in the header, e.g. 23/Feb/2024 or 2024-02-23.

DDays

Number of days between dates.

Time

Return the current system time as a unit object in the form HH.MMSS_hms. This displays on the stack as HH:MM:SS.

TSTR

JulianDayNumber

Return the Julian day number for the given date and time

ACK

Acknowledge oldest alarm (dismiss)

ACKALL

Acknowledge (dismiss) all alarms

RCLALARM

Recall specified alarm

STOALARM

Create a new alarm

DELALARM

Delete an existing alarm

FINDALARM

Get first alarm due after the given time

Version

Return DB48X version information as text.

▶ "Version information"

FreeMemory

Return the number of bytes immediately available in memory, without performing a cleanup of temporary values (garbage collection).

See also: GarbageCollect, FreeMemory

AvailableMemory (MEM)

Return the number of bytes available in memory.

Remark: The number returned is only a rough indicator of usable memory. In particular, recovery features consume or release varying amounts of memory with each operation.

Before it can assess the amount of memory available, AvailableMemory removes objects in temporary memory that are no longer being used. Like on the HP48, you can therfore use MEM DROP to force garbage collection. However, there is also a dedicated command for that, GarbageCollect.

See also: FreeMemory, GarbageCollect

GarbageCollect

Perform a clean-up of temporary objects and return number of bytes reclaimed.

In order to speed up normal operations, temporaries are only discarded when necessary to make room. This clean-up process, also called garbage collection, occurs automatically when memory is full. Since garbage collection can slow down calculator operation at undesired times, you can force it to occur at a desired time by executing GarbageCollect.

See also: FreeMemory, Purge

Bytes

Return the size of the object and a hash of its value. On classic RPL systems, teh hash is a 5-nibbles CRC32. On DB48X, the hash is a based integer of the current wordsize corresponding to the binary representation of the object.

For example, the integer 7 hash will be in the form #7xx, where 7 is the value of the integer, and xx represents the integer type, as returned by the Type command.

X ▶ Hash Size

Type

Return the type of the object as a numerical value. The value is not guaranteed to be portable across versions of DB48X (and pretty much is guarantteed to not be portable at the current stage of development).

If the CompatibleTypes setting is active, the returned value roughly matches the value returned by the HP50G. It always returns 29 for arrays, not 3 (real array) nor 4 (complex array). It returns 1 for both polar and rectangular complex numbers, irrespective of their precision. 128-bit decimal values return 21 (extended real), 32-bit and 64-bit return 0 (real number). The separation between 18 (built-in function) and 19 (built-in command) may not be accurate.

If the DetailedTypes setting is active, the return value is negative, and matches the internal representation precisely. For example, distinct values will be returned for fractions and expressions.

Note The TypeName command returns the type as text, and this is less likely to change from one release to the next. DB48X-only code should favor the use of TypeName, both for portability and readability.

TypeName

Return the type of the object as text. For example, 12 type returns "integer".

PEEK

Low-level read memory address

POKE

Low level write to memory address

NEWOB

Make a new copy of the given object

USBFWUPDATE

PowerOff (OFF)

Turn calculator off programmatically

SystemSetup

Display the built-in system setup

SaveState

Save the machine's state to disk, using the current state if one was previously loaded. This is intended to quickly save the state for example before a system upgrade.

ScreenCapture

Capture the current state of the screen in a dated file stored on the flash storage under the SCREENS/ directory. This is activated by holding 🟨 and O simultaneously. Pressing the keys one after another activates the DisplayMenu.

Tagged objects

Tagged objects are a way to indicate what a value represents, using a tag between colons and preceding the object. For example, :X:3 is a tagged integer, where the tag is X and the object is 3.

When displayed on the stack, tags are shown without the leading colon for readability. For example, the object above shows as X:3 on the stack.

→Tag (ToTag)

Apply a tag to an object. The tag is in level 1 as text or name. The object to be tagged is in level 2. For example, "Hello" 1 →Tag results in :Hello:1. Like on the HP calculators, it is possible to next tags.

Tag→ (FromTag)

Expand a tagged object in level 1 into its object and tag. The object will be in level 2, the tag will be in level 1 as a text object.

For example, :Hello:1 Tag→ results in "Hello" in level 1 and 1 in level 2.

DeleteTag (DTAG)

Remove a tag from an object. For example, :Hello:1 DeleteTag results in 1. If there is no tag, the object is returned as is.

Operations on text

TOUTF

Create a Utf8 string from a list of code points

FROMUTF

List all code points in a Utf8 string

ToText (→STR, →TEXT)

Convert an object to its text representation.

Compile (STR→, TEXT→)

Compile and evaluate the text, as if it was typed on the command line.

"1 2 + 4" TEXT→ will push 3 and 4 on the stack.

Char→Code (NUM, CODEPOINT, CharToUnicode)

Return the Unicode codepoint of the first character in the text, or -1 if the text is empty. "Hello" NUM returns 72.

Text→Code (TextToUnicode)

Return a list of the Unicode codepoints for all codepoints in the given text. "Hello" Text→Code returns { 72 101 108 108 111 }.

Code→Text (CHR, Code→Char)

Build a text out of a Unicode codepoint. The argument can be either a single numerical value or a list of numerical values. A negative numerical value produces an empty text. { 87 111 114 -22 108 100 } returns "World", the value -22 producing no character. 42 CHR returns "*", and 34 CHR returns """", which is a 1-character text containing an ASCII quote ".

SREV

Reverse the characters on a string

NTOKENS

Number of tokens in a string

NTHTOKEN

Token at position N in a string

NTHTOKENPOS

Position of token N in a string

TRIM

Remove characters at end of string

RTRIM

Remove characters at start of string

SSTRLEN

Length of string in characters

STRLENCP

Length of string in Unicode code points

TONFC

Normalize a string to Unicode NFC

SREPL

Find and replace text in a string

TODISPSTR

Decompile formatted for display

TOEDITSTR

Decompile formatted for edit

Analytic functions

In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions.

DB48X analytic functions generally have a symbolic differentiation form. Many of them also have a symbolic primitive for symbolic integration.

Transcendental functions

sin

Analytic function returning the sine of the argument.

For real arguments, the current angle mode determines the number’s units, unless angular units are specified. If the argument for sin is a unit object, then the specified angular unit overrides the angle mode to determine the result.

For complex arguments, the computation is always done considering that the real part is in radians.

z ▶ sin z

x_angleunit ▶ sin x_angleunit

symbexpr ▶ sin symbexpr

cos

Analytic function returning the cosine of the argument

For real arguments, the current angle mode determines the number’s units, unless angular units are specified. If the argument for cos is a unit object, then the specified angular unit overrides the angle mode to determine the result.

z ▶ cos z

x_angleunit ▶ cos x_angleunit

symbexpr ▶ cos symbexpr

tan

Analytic function returning the tangent of the argument

For real arguments, the current angle mode determines the number’s units, unless angular units are specified. If the argument for tan is a unit object, then the specified angular unit overrides the angle mode to determine the result.

For a real argument that is an odd-integer multiple of 90 degrees, an infinite result is generated.

z ▶ tan z

x_angleunit ▶ tan x_angleunit

symbexpr ▶ tan symbexpr

ASIN

Compute the arcsine

ACOS

Compute the arccosine

ATAN

Compute the arctangent

ATAN2

Compute arctangent(y/x)

LN

Compute natural logarithm

EXP

Compute exponential function

SINH

Compute the hyperbolic sine

COSH

Compute the hyperbolic cosine

TANH

Compute the hyperbolic tangent

ASINH

Compute the hyperbolic arcsine

ACOSH

Compute the hyperbolic arccosine

ATANH

Compute the hyperbolic arctangent

LOG

Compute logarithm in base 10

ALOG

Compute anti-logarithm in base 10

SQRT

Compute the square root

EXPM

Compute exp(x)-1

LNP1

Compute ln(x+1)

PINUM

Numeric constant π with twice the current system precision

User Interface

COPYCLIP

Copy an object to the clipboard

CUTCLIP

Move an object to the clipboard

PASTECLIP

Insert the clipboard contents on the stack

Wait

Wait for a key press or a time lapse.

When the argument is greater than 0, interrupt the program for the given number of seconds, which can be fractional.

When the argument is 0 or negative, wait indefinitely until a key is pressed. The key code for the key that was pressed will be pushed in the stack. If the argument is negative, the current menu will be displayed on the screen during the wait.

KEYEVAL

Simulate a keypress from within a program

KEY

Get instantaneous state of the keyboard

DOFORM

Take a variable identifier with a form list

EDINSERT

Insert given text into the editor

EDREMOVE

Remove characters in the editor at the cursor position

EDLEFT

Move cursor to the left in the editor

EDRIGHT

Move cursor to the right in the editor

EDUP

Move cursor up in the editor

EDDOWN

Move cursor down in the editor

EDSTART

Move cursor to the start of text in the editor

EDEND

Move cursor to the end of text in the editor

EDLSTART

Move cursor to the start of current line in the editor

EDLEND

Move cursor to the end of current line in the editor

EDTOKEN

Extract one full word at the cursor location in the editor

EDACTOKEN

Extract one word at the left of cursor location (suitable for autocomplete)

EDMODE

Change the cursor mode in the editor

SETTHEME

Set system color theme

GETTHEME

Operations with Units

UDEFINE

Create a user-defined unit

UPURGE

Delete a user-defined unit

UnitValue (UVAL)

Return the numeric part of a unit object.

3_km ▶ 3

BaseUnits (UBASE)

Expand all unit factors to their base units.

3_km ▶ 3000_m

Convert

Convert value from one unit to another. This convert the values in the second level of the stack to the unit of the object in the first level of the stack. Only the unit in the first level of the stack is being considered, the actual value is ignored. For example:

3_km 2_m ▶ 3000_m

FactorUnit (UFACT)

Factor the unit in level 1 from the unit expression of the level 2 unit object.

1_W 1_N ▶ 1_N*m/s

→Unit (ToUnit)

Creates a unit object from a real number and the unit part of a unit object. →Unit adds units to a number, combining the number and the unit part of a unit object. The numerical part of the unit object is ignored.

→Unit is the reverse of Unit→ or of Obj→ applied to a unit object.

3000 2_km ▶ 3000_km

ULIST

List all user-defined units

USB Communications

USBSTATUS

Get status of the USB driver

USBRECV

Receive an object through USB link

USBSEND

Send an object through the USB link

USBOFF

Disable USB port

USBON

Enable USB port

USBAUTORCV

Receive an object and execute it

USBARCHIVE

Create a backup on a remote machine

USBRESTORE

Restore a backup from a remote machine