Release 0.9.4 "Face, meet palms" - Pixmaps, bug fixes

This release fixes embarassing numerical bugs introduced in 0.9.3 and introduces a new pixmap type intended to capture screen pixel maps including in color. Builds for hardware calculators are also smaller due to switching to a nano configuration for the compiler.

New features

• graphics: Add pixmap type

Bug fixes

• Adjust unit conversion in StdRnd
• Fix parsing of ΣY² in equations
• Render non-fancy large exponents correctly (e.g. 1E123456789012345)
• The precision of numerical constants now adjusts after changing PREC
• Avoid unnecessary purging of constants cache due to internal precision changes
• Return tests values to rounded valus as validated with Wolfram Alpha
• directory: Fix STOVX and Store to non-current directories

Improvements

• Fix sqrt precision, notably for perfect squares (ouch)
• Improve support for recent ARM compilers
• Eliminate new clang warnings
• Eliminate warnings about function pointers in latest XCode
• Add documentation for DisplayModesMenu
• Precision adjustments are now more consistent across decimal functions

Release 0.9.3 "Transfigured" - Documentation, bug fixes

This release keeps improving the documentation based on the original HP50G Advanced Reference Manual, and fixing issues that are found along the way. It also improves statistics support and adds low-level array manipulation.

New features

• Add PredX, PredY and ΣLine commands for linear regression predictions.
  • The PredX command predicts the independent value from the dependent one.
  • The PredY command predicts the dependent value from the independent one.
  • The ΣLine command returns the regression formula.
• Add Median command to compute the median of statistics series
• Add low-level array manipulation commands, COL+, COL-, ROW+, ROW-, CSWP and RSWP, to add, remove and swap rows or columns.

Bug fixes

• Strip trailing zeros from decimals converted from integers, in order to avoid producing incorrectly normalized values. For example, 70000 converted to decimal now produces a 5-bytes decimal value and no longer a 6-bytes decimal value. This fixes the result of the SigDig command on this input value, as well as fixes cases where comparisions would be incorrect.
• Accept quoted names in == and same. HP calculators evaluate A and B in 'A' 'B' == but not in 'A' 'B' same.
• Add symbolic support for logical operations, i.e. correctly create an expression for 'X' 3 and instead of a type error.
• Compute linear regression for each mode when running BestFit. The previous implementation would erroneously compute the correlation with various modes (linear, log, exp and power), but without optimally recomputing the parameters with that mode.
• Consume arguments in XCol, YCol and ColΣ
• Write slope and intercept in the correct order when updating ΣPar. The order was wrong, causing various commands to either update them in the wrong order, or to swap them.
• Do not emit an error if the stack is empty when running Σ-
• Fix and optimize parsing of ==
• Fix a bug in decimal comparisions used by sqrt and cbrt, fixes the computation of the last digits of sqrt(163) at 24-digit precision.
• Compute log with 3 additional digits to avoid getting the last digit wrong in 'ln(640320^3+744)/sqrt(163)'
• Compute exp, exp10, log and log10 with additional internal digits to make sure that the last digit is good (verifiied using calc).
• Fix sign error in buoyancy equation for Champagne bubbles
• Fix ppar parsing and premature validty checking, which caused 20 30 XRNG to fail because of a transient state where xmin<xmax was not verified.
• expression: Fix rare GC bug in expression::simplify

Improvements

• Compute all decimal functions with increased precision. The tests now check that the last digit of the functions result for the tested input is correctly rounded.
• Add type value for xlib objects in HP compatibility mode
• Add TruthLogicForIntegers flag for compatibility with HP calculators when evaluating something like 42 and 4. DB48x by default computes this bitwise, which returns 0, a logically False value. With the new compatibility flag, the arguments are interpreted as truth values, and the computation produces True for improved compatibility with HP calculators.
• Add RPL programming examples in the documentation, lifted from the HP50G Advanced Reference Manual, covering conditional statements such asIF, IFT, IFTE, documentation about tests and conditional structures, type tests, logical commands such as and, or, not.
• Add documentation and menu entry for Header command
• Add documentation about local variables and the scope of local variables
• Add tests for statistics operations
• Optimize retention of slope and intercept in BestFit
• Micro-optimization on stack operation for comparisons
• Add MSolvr alias for SolverMenu for compatibility with HP calculators
• Allow nested precision adjustments in decimal::precision_adjust class
• Tests now display failures in a way that makes it easier to compare.
• Add documentation for SeparatorModesMenu entries
• runtime: Add check that we push only valid objects
• runtime: Cleanup, remove leftovers from earlier debug
• runtime: Add check for pointer validity
• runtime: Add utility to dump GC pointers
• arithmeric: Add recorder entry to record what operations happen
• Update copyright year to 2025 in VERSION command

Release 0.9.2 "Temptations" - Multi-variate solver, documentation

This release introduces a true multiple-variables solver, additional matrix operations, and extends the RPL programming documentation.

New features

• The Root command now selects a true multi-variable solver (Jacobian solver), capable of solving systems of equations with multiple variables, even when variables cannot be isolated one at a time, for example solving { 'sin(x)=y' 'sin(y)=x+1' }. As a result, the DB48x Root command now covers the functionality provided by the HP50G's ROOT, MROOT and MSLV .
• Compatibility for MSLV is preserved thanks to a dedicated command, which like the HP50G leaves input equations and variables on the
  stack.
• Add RNRM and CNRM (row and column norms) commands for matrices.
• Add TRN and TRAN commands (matrix transpose, with or without conjugate)

Bug fixes

• Add several missing images used by the test suite to the git repository, e.g. for the TVM menu.
• Fix rare bug parsing lists causing a validation error
• Fix theoretical risk of memory corruption in det
• Solutions found by the solver no longer depend on the existence and value of global variables by the same name prior to solving
• Emit "Interrupted" error when interrupting the solver
• Fix bug comparing decimal zero with small decimal values

Improvements

• Add a section with RPL programming examples, seeded with examples from Chapter 1 of the HP50G Advanced Reference Manual.
• Add documentation about program objects, text, symbols and comments.
• Update documentation for complex numbers, e.g. ℝ→ℂ command.
• Add documentation for abs
• Add links to "Rules" in constant uncertainty section
• Add a few additional tests in the documentation
• Split instrumentation for the three solver algorithms.
• The solver now uses the display precision to limit the precision of the desired result, like the integrator and like HP calculators.

Video demo: https://www.youtube.com/watch?v=hj-LGN2nhzU

Release 0.9.1 "Follow" - Finances, bit-counting and constants

This release follows-up on 0.9.0 by improving the way constants are evaluated to better serve the equation library. It also adds finance-related functions, and specialized bit-counting functions.

New features

• Add standard and relative uncertainty for all constants. For a constant like G, which when edited looks like ⒸG, the standard uncertainty is ⓈG and the relative uncertainty is ⓇG. This shows as UsG and UrG on screen, to match common practice.

• The constants menu now contains helpers to enter constants, and for the commands Const, StdUnc and RelUnc, which generate a constant, a standard uncertainty or a relative uncertainty from a name.

• Implement precision-control functions that make it possible to adjust the result of computatoins adjusting to relative or standard uncertainty. →Us and →Ur convert betwen standard and relative uncertainty. StandardRound, RelativeRound and PrecisionRound round a value based on its standard or relative uncertainty, or according to the precision of some other value.

• Add bit-counting operations. FirstBitSet and LastBitSet find the position of the first and last bit set in an integer value. CountBits counts the number of bits set in an integer value.

• Add finance operations. The finance menu TVM now shows a solver for time value of money, with payments at beginning (TVMBeg) or at end (TVMEnd). The Amort command generates the amortization (principal, interest and balance). The AmortTable, a DB48x extension, generates a complete amortization table. A new setting, FinanceRounding, a DB48x extension, sets the rounding of finance results.

• Add the Sub command to extract a subset of texts, lists or grobs. As an illustration, the Anagram program was added to the demo state. As a side effect, the named variants for arithmetic operators have been renamed from sub, mul and div to subtract, multiply and divide.

Bug fixes

• Avoid possible crash when using the delete key while searching.

• Fix a few broken (obsolete) links in the help file.

• UVal now works on numbers, not just on unit objects, like on HP calculators.

• Remove NewRPL names for some commands like ToRectangular, and replace them with the DB48x spelling.

Improvements

• Constants are brought up to date to the latest best practice from the scientific community. This includes computing many derived constants from a smaller subset of exact constants, as well as providing standard and relative uncertainty for each constant.

• Constant values are cached to accelerate their evaluation. This avoids having to parse and evalute constant definitions.

• The ConstantMenus was reorganized with more constant categories covering dates, mathematics, chemistry, phsyics, particle masses, electromagnetism, atomic sizes, Compton scattering, magnetism, materials and computing.

• The MathMenu was reorganized, notably to make the exp and log functions easier to access. This merges the former PowerMenu and ExpLogMenu so that the MathMenu still has less than 18 entries.

• Numerical integration now uses the refinements documented in Kahan's 1980 HP Journal article about numerical integration on the HP34. This makes it possible for example to integrate 'sin(x)/x' over 0 to π interval.

• Numerical integration now limits its precision to the number of digits being displayed, like on HP calculators.

• Document the difference and rationale for parsing quoted names compared to HP calculators.

Release 0.9.0 "Wilson's Dream" - Full equation library

This version integrates an extended version of the HP50G equation library that Jean Wilson has been working on for many weeks. Equations are also fully documented, with examples illustrating how to use them, and a full documentation of the variables they contain.

It also fully enables the algebraic-assisted solver, i.e. a version of the solver that attempts to isolate variables to evaluate expressions directly, which is both faster and more accurate when possible.

WARNING Equations in the current state of the library are not fully validated yet. DB48x users are invited to test them and report issues they find.

WARNING Constants used in the library are relatively accurate and have been modernized compared to the HP50G version. However, an effort is underway to compute the physical constants that are not fundamental but derived from other constants. It is expected that the numerical values returned from the equations will changeslightly as constants are udpated.

Features

• Improved equation library and documentation The equation library now features more than 650 equations, more than 700 variables, 18 sections and 158 subsections. This is roughtly twice as big as the HP50G equation library, and covers more modern aspects of science such as nuclear physics.

Bug fixes

• solver: Do not propagate errors during isolate When using the algebraic-assisted solver, errors raised by the internal calls to isolate no longer manifest as solver errors.
• units: Do not leave error behind in unit::convert_to_real This could cause spurious Inconsistent units errors while solving.
• logical: Make logical operations behave symmetrically, i.e. ensure that #100+1 and 1+#100 both return #101.
• nfunctions: Evaluate symbolic arguments symbolically and fix bugs converting arguments to decimal. The evaluation of '∫(0;1;x+1;x)' after x=3 would result in a nonsensical expression '∫(0;1;4;3)'.
• integrate: Report errors in bound evaluation. An error in the evaluation of the first bound could be "erased" if the evaluation of the second bound was successful. For example, in '∫(0;1;sin(x)/x;x)', the Divide by zero error evaluating 'sin(x)/x' at x=0 is erased by the successful evaluation at x=1 that follows.

Improvements

• equations: Accept units in isolate This allows many equations in the equation library to successfully use the symbolic approach, improving accuracy significantly.
• add/sub: Accept zero as an operand around units. An operation like 1_km+0 is now accepted, and evaluates as 1_km.

Signed-off-by: Christophe de Dinechin [email protected]

Release 0.8.11 "Accomplishment" - Towards full equation library

This release contains a number of fixes and features intended for use in the equation library being contributed by Jean Wilson

Features

• Accept library items for functionc calls. For example, the expression 'ⓁSiDensity(273_K)' is now accepted. This function is usd in semi-conductor equations in the library.
• The Root command now attempts symbolic solving using the Isol command. This can lead to exact solutions for common equations.
• The SigDig command is a DB48x extension that returns the number of significant digits in a number, i.e. the number of non-zero digits.
• The xpon and mant now apply to unit objects
• Functions now accept assignments as input, e.g. x=9 sqrt gives 3.0
• The equation referenced to by the Equation variable can now be identified using a name.
• The NxEq command now works with quoted equations

Bug fixes

• The ln(1E-100) expression no longer gives a Argument outside domain error. The error was caused by rounding during argument reduction.
• Comparison between a value and a unit object now work correclty
• Arithmetic now correctly deals with dimensionless unit objects, for example in expression '1-1000_mm/m', and improves the evaluation of unit expressions when adding or subtracting unit objects.
• Names containing programs or functions are now evaluated as part of algebraic evaluation
• The solver now correctly processes equations wrapped in an expression.
• Convert now correclty evaluates its arguments when necessary
• Assignment objects no longer cause a crash on error. For example, x='ln(0)' no longer crashes.

Improvements

• Improve solver heuristic when slope is small. This allows the solver to find a solution for an equation like 'tan(x)=224' in degrees mode.
• Add more recorder entries in the solver describing what is being solved.
• Move recorder entries for tests to tests data logger.
• Tests use a larger text rendering limit
• Tests now purge the directory between examples. This prevents stray variables from influencing later tests.
• The handling of long UTF-8 sequences in tests was improved, which allows tests involving a lot of text (e.g. examples) to run faster.

Release 0.8.10 "Fire Dove" - Input and Prompt, Android preparation

The focus of this release is support for user input in programs, with the addition of the Input and Prompt commands. Internally, a lot of groundwork was performed towards Android builds.

New features

• Add Prompt command, which programs can use to let users manipulate the stack or do other operations before resuming execution.

• In order to facilitate the use of Prompt, added the Run command, which resumes execution of halted programs and otherwise evaluates the first item on the stack. The key at the left of the + key, which is labeled R/S on the DM-42 calculators, is now bound to the Run command instead of Evaluate. Therefore, after a Prompt, you can resume execution with a single key.

• Add Input command, which programs can use to let users enter data. The DB48x version makes it easier to enter and validate numerical data or other non-text objects, with input validators for numbers, integer values, arithmetic objects or expressions. It is also possible to use custom code to validate user input.

• Additional Compile variants were created to help with this user input validation, checking if the input is a number, an integer, a positive integer, a real number, a single object, a single algebraic object or an expression.

Bug fixes

• Fixed problem with the computation of the length of the integer value being parsed if it was parsed from a text value at the end of the temporaries.

• Emit an error from Step and variants if no program is being debugged. The effect was that the next program being run would halt after the first step.

• Avoid persisting beep in the simulator when two beeps were emitted rapidly in successioon.

• Reload the user-selected keymap file after loading the state file.

Improvements

• Change capitalization of DTag as a shortcut for DeleteTag.

• Various code improvements making it easier to compile for Android. A side effect is that the simulator can now safely be started from any current directory.

• Improve rescaling of the window in the simulator to keep the keyboard and screen larger and easier to read.

• Improve the detection of the default simulator size for Hi-DPI screens.

• Add documentation about matrix multiplication performance

• Make the default memory size more consistent with the simulated device.

Release 0.8.9 "Advent" - Mostly bug fixes

This is a relatively minor release, with mostly bug fixes, but also a new, explicit syntax for hardware-accelerated floating-point.

New features

• Hardware-accelerated IEEE-754 binary floating-point values are now identified with a suffix, D for double (64-bit), F for float (32-bit). For example, 1.23 is a variable-precision decimal value, 1.23D is a 64-bit binary floating-point value, and 1.23F is a 32-bit binary floating-point value. This ensures that the HardwareFloatingPoint setting does not change the way a program is compiled or presented, only its computations.
• plot: Draw a bar on the horizontal axis for errors. This makes it easier to identify where the function is not defined.
• probabilities: Extend COMB and PERM to real arguments. For real argument, the Gamma function extension of the factorial is
  used with the usual expressions to compute combinations and permutations. One user remarked that some half-integer combinations of arguments, for example, directly give some common Taylor series factors with a single expression.
• decimal: Add decimal to integer conversion (R→I)
• simulator: Add -N option to disable sound. This is notably useful on Linux where some hardware platforms takes tens of seconds to fail, slowing down error messages.
• simulator: Recognize settings on the command line. For example, you can enable the silent beep feature (flashing screen on error) by passing the SilentBeepOn=true parameter on the command-line.
• parser: Add PREC alias for Precision.

Bug fixes

• random: Fix bias in integer version of Random. Using 1 10 Random would generate values 1 and 2 at half the frequency of other
  values.
• help: Do not process links that are not visible. This could cause links that had scrolled past the top of the screen to be incorrectly selected when pressing the ENTER key, even if there was an RPL code example visible on the screen.
• simplifications: Do not simplify infinities. Earlier versions would incorrectly apply a rule like X-X=0 to the case where X was an infinity, giving incorrect results. This could manifest for example in Comb with decimal input returning 1 for large values (as a result of dividing ∞ by ∞) and Det returning 0 (as a result of subtracting ∞ from ∞).
• expression: Fix rendering of derivative, primitive and where in HP compatibility mode. This could cause programs to become unparseable, e.g. with ∂X(X+1) turning into DERIVATIVEX(X+1).
• expression: Do not render arity-2 commands as infix. For example, CONVERT(X;1_m/s) no longer renders as X CONVERT 1_m/s.
• simulator: Improve extension checks on case-independent filesystems. On such systems, files foo.48s and FOO.48S are identical. The simulator could incorrectly add a second extension if the case did not match.
• arcsin: Fix the incorrect computation of arcsin(1). More generally, improve the way exact angles are generated by functions that require them. This allows such functions to now return non-rounded results when using angle modes such as degrees. Previously, a computation involving the value of the π constant would cause some rounding even if an exact result was possible.
• Fix a rare bug in the user interface which could lead to memory corruption if a garbage collection happened at the wrong time.
• Accelerated arithmetic evaluation is now correctly disabled when the HardwareFloatingPoint setting changes.
• Fix silent errors when NumericalResults is on and computations involve non-normal results (e.g. infinities).
• Convert infinities correctly from hardware floating-point to decimal.

Improvements

• simulator: Return relative paths when selecting files when possible. For example, when selecting the name of a keyboard layout, a file is written on disk that used to contain the absolute path of the layout file being used. As a result, moving the simulator directory elsewhere would make the file unreadable.
• files: Automate tracking of open files. A mechanism was implemented in earlier releases to avoid opening two files at the same time, because that is a limitation of the DMCP implementation on SwissMicros calculators. That mechanism required manual maintenance by developers, and was the source of many bugs. A new mechanism replaces it that transparently manages scenarios where multiple files are open simultaneously. This should quash annoying bugs, such as one where the simulator would write state files with incorrect spelling for constants or library items.
• doc: Remove the docol.md section of the help. This file was inherited from newRPL documentation, and incorrectly documented existing DB48x functions, or mentioned functions that do not exist on DB48x.
• grob: Accept BMP files with zero colours. Some contributors have submitted files generated by Windows tools that describe the BMP file as a bitmap with 0 colours instead of 2. These files were not loading in the helpfile. They are now read and displayed correctly.
• Hardware-accelerated floating-point arithmetic now also benefits from the accelerated dynamic dispatch.

Release 0.8.8 "Voice" - Power usage reduction

This release focuses on reducing power usage and improving reactivity, notably while running on battery.

Features

• Cache rendered graphics and text on the stack to reduce the time spent redrawing the stack.

• Limit the size of objects being rendered on the stack. Objects that are too large will simply render as something like Large bignum (399 bytes) on the stack. This is configured by two new settings, TextRenderingSizeLimit and GraphRenderingSizeLimit.

• Limit the size spent rendering graphical objects. There are four settings controlling the maximum time spent rendering objects graphically. ResultGraphingSizeLimits controls the display for the first level on the stack, StackGraphingSizeLimit controls the display for the other levels on the stack, ShowTimeLimit controls the display for the Show command, and GraphingTimeLimit controls other graphical rendering.

• Blink the battery icon when in a low-battery situation.

• Add configurable MinimumBatteryVoltage to adjust the threshold for low-battery detection and automatic power-off.

• Power-related commands: The BatteryVoltage and PowerVoltage read the battery and power voltage respectively. The USBPowered commands detects if the calculator is running on USB power. The LowBattery command detects if the calculator is running low on battery.

• Detect and reject Unicode characters that look like mathematical characters, and are produced by auto-correction on Windows, notably the- and * signs that look like - and *. This is notably useful when copy-pasting in the simulator on Windows.

Bug fixes

• Fix NDupN again. While the previous release fixed what NDupN does, it did not fix the detection of the number of arguments, meaning that NDupN would incorrectly complain about missing arguments if the stack was not deep enough.

• Fix the precedence of unary - when in front of a parenthesized expression. For example, -(X)^2 now parses correctly.

• Disable keyboard repeat timer when no key is pressed. It was possible to trigger a condition where the keyboard repeat timer would trigger continuously if two keys had been pressed in rapid succession, keeping the CPU in a busy loop and depleting the battery unnecessarily rapidly until another key was pressed. This could also trigger incorrect long-press detections, e.g. the shift key triggering alpha mode instead of a simple shift.

• Disable all timers when switching the calculator off. In some situations, the display refresh timer could still remain active
  after the calculator had been switched off.

• RclΣ now returns the statistics data even when the ΣData variable contains the name of a variable or file.

• The Off command can now be used while editing and no longer causes immediate command-line evaluation.

• Return to the first page of the catalog menus when updating it, to avoid scenarios where the catalog appeared empty

• Return to the first page of the cartalog menu when changing directories, to avoid showing an empty variables menu in a non-empty directory.

• Do not leave garbage on the stack after failed array arithmetic.

• Avoid occasional test crashes due to concurrent pixmap updates in the simulator.

• Avoid occasional spurious error on Primitive test due to long execution time.

• Switch to kg as the base unit for UBASE instead of g, following the SI standard.

Improvements

• Reduce animations more drastically while on battery power. Notably, the cursor does not blink, and menu animations are entirely disabled.

• Rework the animation and screen refresh system to make it easier to maintain and more power-efficient while on battery.

• Refresh the display using hardware-accelerated background refresh routines provided by the DMCP platform. This can be disabled using the SoftwareDisplayRefresh flag.

• Redraw the battery immediately on power change, i.e. plugging or unplugging the USB cable.

• Updated built-in constants with latets CODATA values(contributed by Jean Wilson)

v0.8.7 "Signs" - Performance optimizations

This release focuses on performance improvements and bug fixes for issues reported by users and contributors.

Features

• Long array operations such as matrix multiplications can now be interrupted with the EXIT key.

• Eliminate local names from LNAME output. For example, if you perform a sum with a variable named i as an index, no longer report i as being a name used by the expression..

• Implement HEAD and TAIL for text objects.

• Allow constant definitions to contain expressions, which will be fully evaluated when using the →Num. This makes it possible now define constants using other constants, in the spirit of the more recent CODATA recommandations.

• Library management commands Attach, Detach and Libs are now implemented. These commands make it possible to reload a library entry after changing its definition on disk. While they take arguments that are similar to what HP calculators do, they are not interpreting them in the same way due to hardware differences between SwissMicros and HP calculators.

Bug fixes

• Fix hard crash when running some RPL programs using conditional loops, local variables and/or deep recursion. The crash was caused by a non-robust check of whether the call stack needed to grow or shrink, which was replaced with a much more robust check.

• Fixed the precedence of the unary - operator, so that -X^2 now parses correctly (it used to be interpretd as (-X)^2)

• Fix a crash where an error during an array operation could cause a null pointer to be pushed on the stack.

• The test suite now correctly reports error detected while checking the examples in the online help.

• The multi-solver no longer considers the index variable in a sum or product as a variable to solve for. This avoids spurious errors claiming that a solution cannot be found. The same also applies other functions that take a variable name as an argument, such as Root, Integrate or Isolate.

• Fix a crash when comparing unit objects that cannot be converted from one to the other, e.g. comparing 1_m and 1_h.

• Fix the order of commands in the build instructions for Windows.

• Fix the NDupN command to duplicate an object N times. In earlier releases, it was incorrectly duplicating N objects and leaving N on the stack.

• Accept addition and subtraction between a number and a unit object where the unit can be reduced to a number, so that '1+1_km/m' is now a valid expression. A few additional entries in the equation library now work thanks to that fix.

• Avoid a rare crash where the error command would be corrupted when cleaning temporaries.

Improvements

• Performance optimizations for decimal arithmetic, using 25x25 matrix multiplication as a test scenario to optimize. The performance of such multiplication was improved by about one order of magnitude, and is now comparable to DM42 performance. This was achieved in particular by making more aggressive cleanup of temporaries, by reducing the need for garbage collection, by adding a fast-tracked path for arithmetic operations when the types are the same as for the last operation, and by deferring the construction of arrays until the value of all elements are computed.

• Add a few new sanity checks for the runtime when running on the simulator, notably to detect cases where the internal pointers are not in the expected order, and to more precisely report issues if integrity checks fail during garbage collection

• Add locking to the garbage collected pointers list when running on the simulator, in order to improve test stability. Testing on the simulator is the one case where multiple threads may concurently access the pointers list.

• Accelerate the tests that insert large amounts of text from source code, notably the equation parsing tests and the help examples checks. In addition, use a smarter method to insert RPL separators such as [] or '', taking advantage of the fact that they are usually entered in pairs. These two improvements reduce the total runtime of the entire test suite by a factor of more than 4.

• While testing the online help examples, only report the exact section title and not all the section titles that contain the same
  text.

• Systematically strip tags and assignment objects for all arithmetic operations.

• Add a version of the debug_printf that automatically selects where to draw on the screen, and automatically clear what follows the printed text using a gray pattern.

• Render the DB48x TrueType font to bitmap using a more recent version of the FreeType library. This causes minor glyph differences compared to earlier releases. The test suite was adjusted accordingly.

• Remove some of the leftover references to newRPL commands that will not be implemented or make no sense for DB48x. This work is not finished yet. The mechanism to remember which command caused a particular error was also made somewhat more efficient.

• Consolidate the two distinct documentations of the Root command.