Calculator Help
| Name: | Calculator |
| Version: | 1.1.1 |
| Last update: | 2019-11-27 14:12:48 |
Abstract
Alpha has its own calculator. This is a
sophisticated RPN stack calculator, which works on both signed and unsigned
decimals, hex integers, and floating point. (You might wonder, What does 'RPN' mean? ...)
It can also serve as an Equation Editor.
This Calculator Example hyperlink will return the result
of typing
1<Space>1<Space>+4.2*
or
1
Space
1
Space
+
4.2
*
It first adds "1, 1" to the stack, adds them, and then calculates
(1 + 1) * 4.2 and displays the result 8.4.
Basic Usage, RPN modes
The first four Calculator modes use the RPN stack method:
| Signed Decimal |
| Unsigned Decimal |
| Unsigned Hexadecimal |
| Floating Point |
Here is the basic sequence of operations:
- Open the calculator by selecting Tools ↣ Calculator.
- The default mode is Floating Point.
- The cursor is waiting in the User Input field.
- Enter some value, and press
Space, Enter, or Return to add it to the stack.
- Enter a new value, and then an operator key (such as +, -, *, / ...)
As you perform additional operations, they are recorded in the History
section at the bottom of the window, and the User Input field is cleared for
the next entry. Click on the Clear hyperlink to reset the current Value,
Input, or to remove all history items.
As you perform operations, any value in the Current Input field is used as
the primary operator value. For example, enter 123 and select the menu
item Calculator ↣ Other Math Functions ↣ sqrt and you will get
sqrt(123.0) 11.09053651
If the operation requires two values, then the Current Input and the last
item in the stack will be used. For example, if your Calculator looks like
Stack : «Clear»
44
_______________________
Input : «Clear»
123
_______________________
History : «Clear»
Pushed Stack : 44.0
and you press "/" (for divide) then you will get
Stack : «Clear»
0.3577235772
_______________________
Input : «Clear»
_______________________
History : «Clear»
Pushed Stack : 44.0
44.0 / 123.0 0.3577235772
If, however, the Input field is empty when you perform a binary operation
requiring two values, then the last two values in the stack will be used. For
example, if the stack contains
Stack : «Clear»
22
44
87
_______________________
then pressing "/" (with the Input field empty) will produce this:
Stack : «Clear»
22
0.5057471264
_______________________
Input : «Clear»
_______________________
History : «Clear»
Pushed Stack : 22.0
Pushed Stack : 44.0
Pushed Stack : 87.0
44.0 / 87.0 0.5057471264
If you have never used an RPN stack calculator before, this might seem a bit
inintuitive at first, but this method is really very flexible. For example,
if you wanted to calculate
(4 + 5) * (78 - 6)
you would use these keystrokes:
4
Space (or Enter or Return)
5
+
78
Space
6
-
*
In this case, your final Calculator History section would look like
History : «Clear»
Pushed Stack : 4.0
4.0 + 5.0 9
Pushed Stack : 78.0
78.0 - 6.0 72
9.0 * 72.0 648
If you want to remove the last item in the stack, move the cursor to the
start of the Input field and press Delete.
If this still seems confusing, you might rather use the Equation Editor
mode for the Calculator as described below.
These are some of the basic operations, where y indicates the current
value, and x indicates the entry in the User Input field.
+,-,*,/,|,&,% | Calculates "<Value> <Operation> <Input>" |
~ | bitwise NOT |
^ | y to the power of x |
< | x << y |
> | x >> y |
n | change y's sign |
Additional utility items include
q | Place the current y value in the User Input field. |
i | Swap x and y, i.e. the current value and input fields. |
Space/Enter | Enter the current input value. |
m | Switch amongst signed/unsigned/hex/floating-point modes. |
x | Show the current mode in the status bar. |
h or ? | Open this window. |
More Keyboard Shortcuts
The Calculator menu includes a number of operations with their own special
Keyboard Shortcuts. Whenever you attempt to call one of these menu commands
or type something outside of the User Input field, the cursor will be
returned to the input line without performing any further operation.
The Calculator Window
When you move or re-size the Calculator window, the current
geometry (i.e. the left, top, right, bottom boundaries) are saved and used
the next time that the Calculator window is created. There are no
preferences to set here, this is done automatically.
There are, however, some preferences that you can adjust
- Include History Section
- If turned on, every operation will be recorded in a History section at the
bottom of the Calculator window. Click the Clear hyperlink to reset it.
- Include Function Hyperlinks
- If turned on, most of the Calculator menu items will be displayed in the
window with hyperlinks. Clicking on them will execute the menu item (in RPN
modes) or insert the function text (in Equation Editor mode.)
- Include Keypad Hyperlinks
- This is a Very Clever feature that has little utility, unless you are
addicted to the mouse and never want to use your keyboard or keypad to enter
numerical values or the common "+ - * /" binary function operators.
You can also change the default font and font size used for the window.
Calculator Modes
The default mode for this calculator is Floating Point.
Select the Calculator Menu ↣ Calculator Mode ↣ Change Mode command to
change the current mode. When the Calculator window is active and in an RPN
mode, you can press x to display the current mode in the status bar, and
m to change it. Options include
| Signed Decimal |
| Unsigned Decimal |
| Unsigned Hexadecimal |
| Floating Point |
| Equation Editor |
All calculations are performed in signed decimal in integer modes. Floating
point numbers can be entered as -1.0e-5 : use Control - (⌃-Minus) to
get the minus sign.
In Floating Point and Equation Editor modes the Display Precision
preference determines when the stack values are presented in scientific
notation. Select the Calculator Menu ↣ Calculator Prefs menu item to
change this value.
The Calculate Precision preference is used internally by the Tcl functions
that perform the operations.
(More information needs to be added for the other RPN modes...)
Equation Editor
When the Calculator mode is Equation Editor, it no longer uses RPN, and
the Value field no longer maintains a stack.
Instead, you can add an equation in the Input Field to have
it evaluated using the Tcl command [expr] . While you
are in Equation Editor mode, all of the special keyboard
shortcuts are disabled. For example, pressing the m key will now
insert a real m and not offer the dialog to change the Calculator mode. Similarly, pressing Return will insert a
carriage return and open a new line: in order to execute an expression,
you have to press either the Enter key (if there is one on your
keyboard) or the Equal ('=') key.
The supported mathematical functions in expressions include
| abs | exp | round |
| acos | floor | sin |
| asin | fmod | sinh |
| atan | hypot | sqrt |
| atan2 | int | srand |
| ceil | log | tan |
| cos | log10 | tanh |
| cosh | pow | wide |
| double | rand |
Here are some very simple examples (press Enter or = to
evaluate the expressions):
History :
----------------------------------------------
1 + abs(-10)
11.0
----------------------------------------------
rand()
0.151567682229
----------------------------------------------
rand()
0.398035219125
----------------------------------------------
(45*90)/10
405.0
----------------------------------------------
(45*90)/10 + cos(66)
404.000352544
----------------------------------------------
(1+sqrt(5.0))/2
1.618033988749895
The string $V (without the quotes) or $v or ${V} or ${v} will be
substituted with the current Value field, as in
----------------------------------------------
1 + 3
4.0
----------------------------------------------
1 + 3 * $V
1 + 3 * 4.0
13.0
----------------------------------------------
1 + (3 * ${V})
1 + (3 * 13.0)
40.0
----------------------------------------------
${V} + (3 * $V)
40.0 + (3 * 40.0)
160.0
'International' Users
Most of the Keyboard Shortcuts should be automatically adjusted for your
current Alpha Keyboard preference. Click here to display the International Preferences panel.
If this is not the case, please inform the maintainer of this package about
the changes that need to be made.
Users of non-American keyboards need to type a space after the dead
keys to get ~ and ^. Note that "," is interpreted as a "."
decimal point for all calculations. This reflects the anglo-centrism of
Tcl, not Alpha.
What does 'RPN' mean?
In the 1920s, Jan Lukasiewicz developed a formal logic system that allowed
mathematical expressions to be specified without parentheses by placing the
operators before (prefix notation) or after (postfix notation) the operands.
For example the (infix notation) expression
(4 + 5) * 6
could be expressed in prefix notation as
* 6 + 4 5
or
* + 4 5 6
and could be expressed in postfix notation as
4 5 + 6 *
or
6 4 5 + *
Prefix notation also came to be known as Polish Notation in honor of
Lukasiewicz. HP adjusted the postfix notation for a calculator keyboard,
added a stack to hold the operands and functions to reorder the stack. HP
dubbed the result Reverse Polish Notation (RPN) also in honor of
Lukasiewicz.
https://www.hpmuseum.org/rpn.htm
Known problems
Please report any problem or bug you encounter to
Alpha's Bug Tracker.
License and Disclaimer
Copyright (c) 1996-2019, Pete Keleher and Contributors.
Contributors: Craig Barton Upright, Dominique d'Humieres, Vince Darley.
All rights reserved.
The Calculator package is free software and distributed under
the terms of the new BSD license:
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 Pete Keleher 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 PETE KELEHER OR THE 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.