Calc - Java Calculator for cell-phones and MIDP devices

Current version: 4.00, change-log
Copyright: 2003-2006 Roar Lauritzsen, roarl at users sourceforge net
Demo: Click here to open a demo applet for reference while reading the documentation
Development and patches: Join the development effort at http://sourceforge.net/projects/midp-calc, where the source is available under the GPL license
Contribute: If you find this program useful, you can inspire to future work by donating e.g. $10 here:
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Introduction

Calc is a Java calculator for MIDP or J2ME devices, such as a Java-enabled mobile phone or PDA. It was developed on a Sony Ericsson T610, which was my first Java-enabled phone but which has such a pitiful built-in calculator that I was compelled to develop this application.

Calc works much like a good old HP calculator with RPN logic, but the stack has 16 elements and you can see many of the elements on the stack simultaneously. I have chosen to use RPN logic (Reverse Polish Notation), because operating it requires less keys, you need only ENTER instead of "(", ")" and "=". Additionally, being able to store and see intermediate results on the stack is very advantageous.

Using the Real Java floating point library, Calc has 63 bits internal precision, which amounts to approximately 19 decimal digits accuracy, considerably more than normal calculators and computers. The exponent is 31 bits, which allows for numbers up to 4.197·10323228496. Handy when you want to calculate the factorial of 40000000.

Disclaimer

The Calc Java program is supplied "AS IS", without any guarantee of operation, and without any responsibility for damages which may result from usage. To summarize: I might be stupid. You too.

Download

You can download Calc into your phone or MIDP device using one of these links:
http://midp-calc.sf.net/Calc.jad, or
http://midp-calc.sf.net/Calc.jar

Different versions for different phones: The Nokia version gives a fullscreen window and better control of the command keys for "ENTER" and "+". The middle joystick button is also handled correctly, so "dial" can instead be used as a "clear" key. Many phones, such as SonyEricsson, support the Nokia version and I actually prefer using this version on my K700i. The MIDP 2.0 version only gives access to the fullscreen mode so far, and this works rather poorly, but you might prefer to switch to fullscreen e.g. before you draw a graph. The Siemens version (only version 3.00 at this point) is created by Michael Schierl and remaps keys (as documented here) for the Siemens A65. It might work on other Siemens phones as well.
http://midp-calc.sf.net/CalcNokia.jad, -.jar
http://midp-calc.sf.net/CalcMIDP2.jad, -.jar
http://midp-calc.sf.net/CalcSiemens.jad, -.jar

Download instructions: If you have an internet (or wap) enabled cell-phone, enter one of the above URL's while surfing. Try the ".jad" URL first, if that doesn't work, then try the ".jar". If your device is not internet enabled, you need a computer link with synchronization software for your device. Download one of the above URL's to the computer and add it to the synchronization software before synchronizing. In the latter case I would probably try the ".jar" URL first.

I have noticed one thing when upgrading with my SonyEricsson K700i, which might apply to other phones as well. After downloading, the phone says "The new version may be from another source. Trust source?". If I don't answer "yes", the program memory is cleared.

→ → Older versions

Hardware compatibility

From version 3.00, the size of Calc exceeds 64kB. This means that on some old phones, Calc won't work. For those users, there is always version 2.08. Since I don't know what phones from the old compatibility list work after version 3.00, I have made a new list. I'll fill it up as I get feedback from you!

The following MIDP phones/devices have been tested with Calc v3.00 and later versions: 1 works with the normal Midp 1.0 version
2 works with the Midp 2.0 version
N works with the Nokia version
S works with the Siemens version
(if nothing is specified, I have not received detailed enough information)

Please drop me a note about your experiences if you have tested Calc on a device that is not on the list, or if your experiences were different than what is listed. Remember that nearly all devices can have different versions of "firmware" (the "operating system"), and that upgrading the firmware at your local repair shop may improve many compatibility issues.

(The phones are not sorted in any specific order)

User manual

Table of contents:
Keys
Setup
RPN logic
Menu
Operations
Basic
Math
Trigonometric
Bitwise operations
Special
Stack
Memory
Statistical
Financial
Conversions and constants
Time and date
Metric conversions
Scientific constants
Mode
Number
Programming
Base
Monitoring
System
Notes
Abnormal results
Complex arithmetic
Matrix arithmetic
Financial calculation
Date calculation
Constants
Programming
Graph drawing
Binary representation
Monitor editing mode

Keys

Read this section at least. To be able to navigate efficiently through operation menus, Calc is best operated on a phone with a 5-way "joystick" or equivalent arrow keys, plus a "clear" key, 12 number keys and two soft-keys (those configurable keys below the display). The keys are mapped as follows:

Setup

To be able to use Calc on devices with fewer keys than the T610 (most Nokias, that is), a couple of setup dialogs may appear the first time Calc is started. If you don't answer these dialogs correctly the first time, you can get to the setup dialogs again using the "reset" command.

First, to make sure that "ENTER" and "+" is immediately available, Calc will rotate through a set of command-key mappings until you answer "yes" to the question if you see "no" mapped to the left soft-key and "yes" mapped to the right soft-key simultaneously (These keys are located left and right directly below the display). Some phones may for instance map "yes" and "no" to a menu named "Options" on the left side, with nothing on the right side. If you select "yes" when such a mapping is active, your "ENTER" and "+" key will be accessible in the same cumbersome manner. (In the Nokia version, this screen is skipped.)

Second, to make sure that a "clear" or "c" key is available (and recognizable by the application), you will be asked to press it. If you do not have a "clear" key, press "#" instead - this will be your clear key, and "*" will be used to magically enter both minus sign, decimal point and exponent marker. On some Motorola phones the "menu" button can be used as "clear".

(If you have downloaded the Nokia version, be extra careful at this point. If your phone has a "joystick" or direction keys with an extra button in the center, you can use "dial" (the green button) as the clear key. In that case press "dial". If you don't have a button in the center of your direction keys, you must use "dial" as a replacement for the center button. In that case you don't have a clear key, so press "#". You might be tempted to try pressing "hangup" (the red button) to use that as a clear key, but in most cases that just exits the application immediately, leaving the setup unfinished. In that case, you can use the "mode/sys/reset" to access the setup again.)

The third setup item is font selection. For color devices, Calc uses sub-pixel anti-aliasing to improve the visibility of numbers displayed on screen. However, some phones uses different pixel ordering (BGR instead of RGB), and then the numbers may look strange. Select the font that looks best on your device (beware that the commands "left" and "right" may be mapped to the right and left command key respectively, if you chose that setting in the first screen). Some phones may have a 90 degrees rotated screen where the red, green and blue color cells are stacked vertically instead of horizontally. There is no support for such screens, so on these devices the numbers will always look bit strange, unless you select the "system" font.

If your phone does not have a 5-way joystick, most times on Nokia you can use the "dial" button instead of the middle joystick button. If you only have a two-way joystick or none at all, the number keys 2, 4, 5, 6 and 8 will work as joystick keys once a menu is activated. In that case, you can only hope that the menu will be activated by "dial" or some other button, otherwise you will be stuck.

RPN logic

If you are familiar with RPN logic, e.g. from a HP calculator, skip forward to the next section.

The basis for implementing RPN logic in this calculator is a stack of numbers. The stack is initially empty, and when you write a number and "ENTER" it on the stack, the stack grows upwards with the latest entered number at the bottom of the stack. If you start to enter another number, the numbers already on the stack jump up to make room for the new number. To make the stack shrink, you can either clear the lowest element on the stack using the "clear" key, or you can combine the two lowest elements on the stack using a mathematical operation.

The lowest element on the stack is called "x". In operations with one argument, such as "sin", x is used as input and is replaced by the result. The rest of the stack remains the same. The element above x on the stack is called "y". In operations with two arguments, such as +,-,* and /, the x and y stack elements are removed from the stack and the result is placed on the stack instead, as the new x. The rest of the stack moves down one step. Sometimes the element above y is called "z".

For instance, to calculate 3+7, one would press the following sequence of keys: 3, ENTER, 7, +. The result, 10, will now be the lowest element on the stack, ready for further calculations. To calculate 3*(2+4), one would press the following sequence of keys: 3, ENTER, 2, ENTER, 4, +, *. (To access the "*" operator, you really need to press the key "↑" to enter the "basic" arithmetic menu, followed by "←", to select the multiplication operator.)

This is what the display will look like as you enter the sequence of keys above, assuming that you start with an empty stack:
Keystrokes:     "3"   "ENTER"     "2"   "ENTER"     "4"      "+"      "*"
Stack:     |        |        |        |        |        |        |        |
           |        |        |        |        |   3.00 |        |        |
y:         |        |        |   3.00 |   3.00 |   2.00 |   3.00 |        |
x:         | 3_     |   3.00 | 2_     |   2.00 | 4_     |   6.00 |  18.00 |

Notice that you don't need to press "ENTER" after the "4" (but you could), because the following "+" operation makes it clear that you are finished keying the number. As you press "+", the 2 and the 4 are added to produce 6, and the 3 jumps down, ready for the "*" operation.

A more thorough RPN tutorial can be found here, except that the "ENTER" key works as in the HP RPL system.

Menu

Pressing the middle of the joystick activates the menu. You select sub-menus by pressing one of the 5 joystick directions up, left, right, down or middle. The next sub-menu will replace the previous menu as you proceed. The following illustration shows the main menu (light blue titled "menu") and the first level of sub-menus (minus the "mode" sub-menu). In the case of the "special" sub-menu, the three subsequent sub-menus activated by the right joystick button are shown. Sub-menu entries are displayed in normal text and actual operations are displayed in bold text. Through this hierarchical system, more than 200 operations can be reached.

↑

←
→
↓

→
→
→


Once you've familiarized yourself with the layout, you don't need to press the middle joystick button to activate the main menu. Pressing up/down/right/left on the joystick without activating the main menu first activates the corresponding sub-menu directly. In this way, you can reach the most used "ENTER" and "+" operations in one keyclick (they are not on the menu, but on soft-keys), and the rest of the most basic operations, "-", "*", "/" and "+/-" in just two keyclicks.

Some operations require a number argument ("STO", "FIX", etc). When such an operation is activated, a two-level number menu is entered, enabling the selection of a number between 0 and 15. When this number menu is active, you can access the numbers 0-9 directly using the number keys.

Since the middle joystick button can be a bit difficult to press, care has been taken not to place the most used operations and sub-menus on the middle button. Pressing "clear" (the button, not one of the menu entries) while navigating the menus backtracks up one level of menus.

Operations

The following operations are available through the menu system. Some of the operations are explained more thoroughly in the notes section.

Basic

Math

Trigonometric

Bitwise operations (available instead of math/trig in HEX/OCT/BIN mode)

Special

Mode

Notes

Abnormal results

The calculator implements infinities and nan following the IEEE754 logic. It is impossible to enter abnormal numbers through the keyboard, but they are easily obtained by calculation. If an operation produces a result larger than the largest representable number, an infinity value is generated, and "inf" or "-inf" is displayed. If an operation produces a result smaller than the smallest representable number, zero is generated. To be able to use this result properly in further calculations, the number "-0" may also be produced. If an operation is undefined, a nan value is produced and "nan" is displayed (not-a-number).

Abnormal numbers are often fine to use in further calculations. In most cases where the final result would be meaningful, abnormal numbers accomplish this. For instance, atan(inf)=pi/2, 1/inf=0, etc. In most cases where the final result is not meaningful, a nan will be produced. Additionally, nan is used to indicate "bad input parameters" or "failure to obtain a valid result" from an algorithm implemented in the calculator, e.g. factorizing.

Examples of operations with abnormal numbers are:
1/0 = inf
1+inf = inf
1*inf = inf
0/0 = nan
0*inf = nan
inf/inf = nan
inf-inf = nan
1/inf = 0
-1*0 = -0
Any operation involving nan produces nan, except nan to the power of 0:
nan^0 = 1

Complex arithmetic

The calculator creates complex numbers automatically when you try to use the "√x" operation on a negative number, or when another operation requires a complex result. Alternatively, a complex number can be created from x and y using the "r→cplx" operation.

Most operations that logically extends to complex arguments have been implemented for complex numbers, i.e. all basic operations, all simple operations except "%chg", all power operations and all trigonometric operations. For convenience, integer operations (rounding and truncation) work on the real and imaginary part of the complex number separately.

All stack and memory operations handle complex numbers transparently. Financial and statistical modules cannot store complex numbers, so with these modules only the real part of the numbers are stored/used. Any operations that are undefined for complex numbers or that have not been implemented yet, returns nan when used with complex input(s).

If either x or y contains a complex number, any operation in the "coord" sub-menu is undefined (the sub-menu dealing with rectangular/polar coordinates). In this case the "coord" sub-menu is exchanged with a sub-menu called "cplx" for dealing with complex numbers.

Complex operations work strictly in radians, so when the input is complex (i.e. it has a non-zero imaginary part), operations involving the angle of the complex number (i.e. most trigonometric and power functions) will automatically cause a switch from degrees (DEG) or grads (GRAD) to radians (RAD).

Complex numbers are displayed on one line as e.g. 2+3i. Since two numbers are displayed simultaneously, the display may not be wide enough to display both numbers if you are using a large font and the numbers have large exponents. Instead "*****" will be displayed. Don't worry, the number is still there, but you have to switch to a smaller font or perform a "cplx→r" operation on the complex number to view it.

Matrix arithmetic

The calculator creates matrices using the "matrix/new" operation or when you stack or concat two normal numbers.

Most operations that logically extends to matrix arguments have been implemented for matrices, i.e. all basic operations, "1/x" and "x²", and yx for integer x.

All stack and memory operations handle matrices transparently. Financial and statistical modules cannot store matrices, so with these modules a matrix is treated as nan. Any operations that are undefined for matrices or that have not been implemented yet, returns nan when used with matrix input(s).

Matrices are displayed on one line as e.g. M:[3x4]. This indicates a matrix of 3 rows and 4 columns. A 1x1 matrix is automatically converted to a normal number.

There are two methods for filling a matrix with numbers. In the first method, you enter the two first numbers of the matrix and then either "matrix/concat" or "matrix/stack" the two numbers into a row or column vector. Continue concating or stacking more numbers until your first vector is complete. Then do the next vectors. Finally, you either stack together your row vectors or you concat together your column vectors until the matrix is complete. If you use the "repeat" operation on the basic menu this method requires the fewest button clicks.

Alternatively, you can create an empty matrix by "matrix/new", and then press "mode/monitor/matrix" to edit the matrix (see (*)). When monitoring is active you can go into the monitor area by pressing the middle button from the "basic" menu. If you enter a number on the stack before you go into the matrix, you can press the middle button again to move this number from the stack into the highlighted matrix element. This brings you out of matrix editing again and you can enter a new number. Repeat this (number, up-middle-middle) until the matrix is complete. This method requires a few more button clicks, but it is more visual.

Matrix limitations: There are a few limits to the size of the matrices that can be used in the calculator. You cannot create matrices with "new" with more than 65536 rows or columns. Even if you manage to create an even larger matrix than this by concatenating or stacking such matrices, the matrix would not be saved when the calculator exited. Due to a limitation when storing programs, matrix element editing (through the matrix monitor) of elements beyond column 64 or row 128 will not be stored in a program.

Apart from these limitations in the program itself, it is the limitations of the host (i.e. you phone) that may be the most severe. When creating especially large matrices you may experience "Out of memory error". If you get this, is advised to exit the program to avoid further errors which may be caused by this. There may also be a limit to how much matrix data the calculator can save when you exit. If the calculator was unable to save all the matrices, some of your matrices will be replaced by nan when you start up again.

Matrices are stored by reference, so copying a matrix many times on the stack or in memory does not consume memory, it only copies the reference. However, changing a matrix will create a new matrix, even for such a simple operation as "+/-". Since the old matrix is still backed up in "LAST x" you are temporarily using twice as much memory as with just the one matrix.

Financial calculation

Remember to use negative values for owed balances and money paid to the account, positive values for balances in your favor and money withdrawn from the account. Also enter the interest rate per period, not per year. If you are making monthly payments and have an annual interest rate, divide the annual rate by 12 (*). Thus, one period of an 8% annual rate is 8/12=0.6666%.

[* This business of dividing an interest rate by 12 is not mathematically correct, but since the banks use this procedure it is wise to do it also, otherwise your numbers will not agree with those of the bank. To calculate the nominal monthly interest rate from an effective annual interest rate, use the "y%/x" operation, which actually calculates 100·(x√1+y/100 - 1).]

If you solve repeatedly and successively for each of the financial registers, the values may start to drift away from the original values because of inaccuracies during the calculations.

Date calculation

The calendar implemented by the DH.MS operations is strictly Gregorian, which did not take effect until 1582 in Catholic states and not until 1752 in Britain and her colonies (including the United States). Dates before these years will be extrapolations of the Gregorian calendar and will not match the Julian calendar of the time.

When converted to hours, a date is represented by the number of hours since the imaginary date January 1st year 0 (in the extrapolated Gregorian calendar). Negative dates are not interpreted as years BC, but are instead represented as a negative amount of time equal in magnitude to the date interpreted as a positive number. In this way, you can subtract dates by entering a negative date and using "DH.MS+". However, it is impossible to extrapolate the Gregorian calendar to years BC.

When converting from date-time format (yyyymmddHH.MMSS) to hours, several checks are performed. If year (yyyy) is zero (i.e. input is less than 1000000), the date-time format is instead interpreted as the days-time format ddddHH.MMSS, where dddd is the number of days. When you convert from hours back to date-time format, it is enough that the number of hours is greater than 8784 (i.e. 24 hours times 366, number of days in year 0) for the converter to switch back to yyyymmddHH.MMSS format. This means that for dddd between 366 and 9999, converting from ddddHH.MMSS to hours and back again will not yield the original input.

Beware that you must specify the year with all four digits. If you specify a year with two digits only, you will be calculating dates in a Gregorian calendar extrapolated to the years AD 1-99 (*). As an intermediate result such dates are fine (e.g. a time interval, resulting from a DH.MS+ operation with one negative operand), but the result should be converted to hours or added to a proper date before it is meaningful. If an intermediate result like this represents a time interval less than one year, it will be converted to the form ddddHH.MMSS, where dddd is the number of days. Do not worry, this form will interpreted unambiguously in further calculations with DH.MS+.

[* leap years in this period matches leap years in the period 1900-1999, so you may get away with it. On the other hand, the year 100 (in the extrapolated Gregorian calendar) was not a leap year while the year 2000 was.]

If year is nonzero, and month (mm) is zero, the month will be interpreted as 1 (January). If day (dd) is zero, it is interpreted as 1 (the 1st of the month). If seconds (SS) is greater than 59, the number is interpreted as that many seconds into the next minute. If minutes (MM) is greater than 59, the number is interpreted as that many minutes into the next hour. If hours (HH) is greater than 23, the number is interpreted as that many hours into the next day. If day (dd) is greater than the number of days in a month, the number is interpreted as that many days into the next month (or the months after). If month is greater than 12, the number is interpreted as that many months into the next year(s) (unspecified how many days there are in each of those months). E.g. the number 2003000000 is understood as January 1st, 2003, at 00:00.00. The number 1403.5901 is understood as 14 days, 3 hours, 59 minutes and 1 second. Unfortunately, the number 1.9999 is understood as 1 hour, 99 minutes and 99 seconds, actually 2.6775 hours, considerably more than 2 hours (if that was intended).

Because a date-time value is represented with many digits, inexact intermediate representation may cause inaccuracies to escalate. To alleviate this, some magic rounding has been implemented so that e.g. 99 minutes and 99.999 seconds is instead interpreted as 1 hour, 0 minutes and 0.000 seconds. This will catch a majority of the problems that may occur.

The calendar conversions routines were taken from http://www.fourmilab.ch/documents/calendar/

Relation to Unix time

Unix time measures seconds since midnight (00:00 UTC) on January 1st, 1970. Many operating systems and languages (including Java) use this time scale, although many use a local time zone instead of UTC. Use "DH.MS→unix" and "unix→DH.MS" to convert dates to/from this time scale.

Relation to Julian Days

Astronomers often use Julian Day or Modified Julian Day as a practical format for doing arithmetic with dates. The Julian Day is the number of days elapsed since noon on Monday, January 1st 4713 BC (in the Julian calendar). Use "DH.MS→JD" and "JD→DH.MS" to convert dates to/from this time scale.

The Modified Julian Day is the number of days elapsed since midnight (00:00 UTC) on November 17, 1858. Use "DH.MS→MJD" and "MJD→DH.MS" to convert dates to/from this time scale.

Beware that this calculator has no notion of time zones, it takes whatever value the Java environment returns (through System.currentTimeMillis()). If you are in a different time zone than UTC, you may have to add or subtract some hours to get a perfect unix, JD or MJD time value.

Constants

The constants were found at http://physics.nist.gov/cuu/Constants and the metric conversions at http://www.free-definition.com. Constants given using "≡" are as accurate as the internal precision of Calc. Constants given using "≈" are not precisely known by science, but are as up-to-date as the CODATA internationally recommended values of 2002.

Monitor editing mode

When monitoring is active, the usual repeat operation in the "basic" menu is exchanged with the symbol [→]. Selecting this operation lets you enter the monitor area in the upper part of the screen, where one monitor element will be highlighted. You can then move about in the monitor area using the arrow keys. The normal commands, "ENTER" and "+" will be replaced with "STO" and "RCL".

Pressing "STO" in this mode will copy x into the current monitor element. Pressing "RCL" in this mode extracts the current monitor element and pushes it on the stack. Pressing the middle joystick button pops one element off the stack, stores it in the current monitor element, and exits the editing mode so you can enter or calculate the next number. All these operations also have the side effect of advancing to the next monitor element below (or in the next column if you are at the bottom). Pressing "clear" will exit the editing mode.

Programming

(Programming is found on the "mode" menu because it was added last and I couldn't find a spot for it anywhere else. Despite this, not all operations reached from this menu are "mode-like".)

As of version 4.00, Calc is fully programmable with control flow and looping. When program recording has been activated (i.e. after executing "prog/new" or "prog/append"), all activity is recorded in the current program, but the calculator looks and behaves exactly as before except a "PRG" indicator to the upper right. There is no limit to the size of a program, but beware, do not leave Calc in programming mode (look for the "PRG" indicator), because Calc will eventually run out of memory, giving the "Out of memory error".

Using the "undo" operation does not remove any statements from the program, it only adds the "undo" operation to the program as well. Instead, use the program editing mode described below to remove an operation. Advice: If your program is complex, plan the steps beforehand on a piece of paper.

Programs can be viewed or edited using the program editing monitor command: "monitor/prog":

The program editing monitor can be used to view or edit programs. Note that the program editing monitor can only be accessed in the programming mode and as usual the number of lines to display have to be chosen. As the other monitor modes, it has a display mode and an editing mode (accessed by the [→] command). In the display mode, the active line is marked by an ">" after the line number. In the display mode, all commands recorded will be inserted at this marked position. After activating the editing mode, the inseration mark is at the end of the program, so all new instructions will be appended to the program. When the editing mode is entered, the mark can be moved using the joystick (up/down, left=page up, right=page down). In the editing mode, the softkeys have the following meanings: DEL removes the marked current instruction and SST executes the marked current instruction and advances the mark. Note that the availability of commands you want to insert depends on the current state of the calculator, e.g. if you want to use complex number operations, there has to be a complex number on the stack at x. As usual the instructions recorded at the insert position are executed immediately, not necessarily in the order of the finished program. So if you want to insert an instruction and review an example calculation in parallel, it could be a good idea to run the program from the beginning using the SST up to the point where you want to extend your program -- then the calculator would be in the same state as when running the program offering all appropriate commands in the main menu. As all monitor modes, the monitor mode can be activated by setting it to display 0 lines. However, when the program editing is finished using the "prog/finish" command, the program monitor is deactivated and it is reactivated with the same number of lines next time the "new" or "append" commands are issued, even if a different monitor mode was active.

A program is called a function if it uses the x on the stack as input, and produces a new number on the stack as output. The value left in the x register when the program finishes is used as the function value f(x). During graph drawing, integration, differentiation, solving, minimizing or maximizing, a program is called repeatedly with different x values placed on the stack. If the program does not clutter the stack (i.e. it does not leave more values on the stack than the result), the input parameters will remain on the stack when the operation is finished.

When drawing graphs, you must first enter the ranges along the x axis and y axis that you want to see during drawing. When drawing functions as y=f(x), if a program returns a complex value, the graph will split into two lines of different color. This is a neat way to display two (non-complex) graphs at once, placing both graph values in x and y and using "r→cplx". See note on graph drawing.

When integrating, you must enter the range over which you want to integrate, and the accuracy you desire from the result. When the operation is finished, the result is placed on the stack. If the program returns inf or nan values during the operation, the result will be nan. If the algorithm fails to produce the desired accuracy, the unfinished result is placed on the stack and a message is shown. The algorithm may handle integration through a singularity, but in this case the algorithm works better if the singularity is at x=0 and the first integration limit is also 0. The accuracy of the result will most often be of the same magnitude as the input accuracy, but depending on the difficulty of the function to be integrated, it may be much better or worse than this.

When differentiating, you must enter the x for which you want to differentiate. When the operation is finished, the result is placed on the stack. If the program returns inf or nan values during the operation, the result will be nan. The accuracy of the result is at most 13 digits.

When solving, you must enter two limits that "straddle" the solution, i.e. two x values for which the corresponding function values have opposite sign. When the operation is finished, the result is placed on the stack. If the program returns complex, inf or nan values during the operation, the result will be nan. The accuracy of the result is in most cases a full 19 digits, but this depends largely on the accuracy of the operations used in the program.

When minimizing or maximizing, you must enter two limits in such a way that the calculator can decide if it should do minimization or maximization. To decide, it inspects the function value midway between the limits. If this value is greater than the function value at both limits, the operation will be maximization. If the value is less than at both limits, the operation will be minimization. If the value lies in-between, the criterion is undecided and the result will be nan. When the operation is finished, the result placed on the stack. If the program returns complex, inf or nan values during the operation, the result will be nan. The accuracy of the result is much worse than for solving because of the flatness of a curve at a minima/maxima, in most cases only about 10 digits.

Caveat I: If you make a program that runs forever, e.g. a sequence of "LBL 0" followed by "GTO 0", when executing the program execution can be stopped by pressing "Break" as explained in Graph drawing below. However, if you do anything else with the program, i.e. drawing, differentiating, itegrating, solving, maximizing or minimizing, execution can only be stopped between indivitual runs of the program, so it will not be possible to stop e.g. integration of a program that runs forever. In the worst case you may have to turn off the entire device (i.e. phone) and lose everything that has changed in the last session. If you are unsure whether your program runs forever or not, try it once using the plain "prog/run" command.

Caveat II: Since the calculator can represent very small numbers (i.e. 2.383e-323228497), solving or min/max-ing trivial cases when the answer is exactly zero can take forever, since the result always approaches zero but never gets there. Examples are "solve" on the "sgn" function, and "min/max" on the "abs" function.

Graph drawing, integration, differentiation, solving, min/max-ing and calling other programs recursively cannot be programmed, as well as commands on the "System menu".

Here are some programming examples.

Graph drawing

While drawing a graph, as explained in the previous note, Calc will continue calculating new graph points and improving the graph indefinitely, until "Break", "clear", or "#" is pressed. Do not leave the program in this state, it will eat your battery.

To save battery, you can stop program drawing using the "*" key when you are satisfied with the look of the graph. If some parts of the axes are obscured by the graph, the axes can be refreshed using the "0" key. If drawing is stopped, another hit on the "0" key draws the numbers along the axes as well.

When drawing is stopped, the graph can be zoomed using direction keys (or the corresponding number keys). Zoom in using the middle button or "5". Zoom out using "1". To restart drawing, press "*" again. Zooming can also be used when drawing statistics. After the zoom function has been used, the values xmin, xmax, ymin and ymax on the stack are changed accordingly.

Binary representation

In binary modes (HEX, OCT and BIN), fractional numbers are not displayed as integers, but are instead displayed with the fraction visible in exactly the same manner as decimal numbers, depending on the number format (normal, FIX, SCI and ENG). If a number is displayed with an exponent, the exponent itself is still displayed in decimal form.

Negative numbers are displayed as a generalized form of "twos complement", with the following interpretation: Negating the number inverts all bits, including an infinite number of 1-bits before the radix point and an infinite number of 1-bits after the radix point. The infinite number of 1-bits before the radix is represented by an "f" prefix (or 7 or 1 in OCT and BIN modes). The infinite number of 1-bits after the radix is rounded upwards producing an infinite number of 0-bits, until the first 0-bit is encountered which will be switched to a 1 (rounded or not, these two forms are mathematically equivalent). For example, the number "1", inverted, will become (in binary mode) ...1111110.111111.... Rounding of the infinite number of 1's after the radix gives the number ...1111111.000000..., which is exactly the way we usually see "-1" as two's complement.

Bitwise operations with negative numbers (and, or, xor and bic) use the generalized "twos complement" representation of the number when interpreting the bits. However, beware that normal rounding that occurs when the display cannot display all the significant digits of a number may cause inexact values to appear different in the display than their internal representation.