ECKERT 2017 10 Users Manual

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Engineering Calculator with KEyboard
and Refined Tools

ECKERT
Console User Interface
(Scientific stack calculator)

User’s manual
For version 2017-10
Oct 25, 2017
© 2014-2017 Yuishin Kikuchi

INDEX

INDEX
NOTICE
This is the user’s manual of ECKERT.

0. Introduction ............................................................................................... 1
0-1. What is ECKERT...................................................................................................................1
0-2. Audiences ..............................................................................................................................1
0-3. Supporting functions..............................................................................................................2
0-4. Operating environments ........................................................................................................2
0-5. Disclaimer ..............................................................................................................................2

1. Preparation................................................................................................. 2
1-1. Installation and Uninstallation ...............................................................................................2
1-2. How to read this manual ........................................................................................................2
1-3. Format of this manual ............................................................................................................3

2. Display and Operation............................................................................... 4
2-1. Launch and End .....................................................................................................................4
2-2. Display of calculation mode ..................................................................................................4
2-3. Calculation mode and states display ......................................................................................6
2-4. Stack display ..........................................................................................................................8
2-5. Message display................................................................................................................... 11
2-6. Configuration mode display ................................................................................................12
2-7. Fundamental operation ........................................................................................................13
2-8. Input numeric values ...........................................................................................................14
2-9. Examples of value input ......................................................................................................16
2-10. When the error message is displayed .................................................................................17

3. Settings .................................................................................................... 18
3-1. Settings in configuration mode ............................................................................................18
3-2. Settings in calculation mode ................................................................................................20
3-3. Next/previous pages in stack ...............................................................................................27
3-4. Next/previous pages in register ...........................................................................................28
3-5. View full string of data ........................................................................................................30
3-6. Version display ....................................................................................................................31

4. Fundamental operations ~ four arithmetics............................................. 32
4-1. Elementary stack operation..................................................................................................32
4-2. Four arithmetics ...................................................................................................................35

INDEX

4-3. Multiple arithmetics .............................................................................................................38
4-4. Elementary functions ...........................................................................................................40

5. Mathematical functions ........................................................................... 41
5-1. How to use math functions ..................................................................................................41
5-2. Exponent and logarithm.......................................................................................................41
5-3. Trigonometric functions ......................................................................................................42
5-4. Hyperbolic functions ...........................................................................................................43
5-5. Stats functions......................................................................................................................44
5-6. Integer roundings .................................................................................................................44
5-7. Functions for integers ..........................................................................................................45

6. Useful functions ...................................................................................... 46
6-1. Percent calculations .............................................................................................................46
6-2. Time conversion ..................................................................................................................47
6-3. DMS conversion ..................................................................................................................48
6-4. Whole stack calculations .....................................................................................................48
6-5. Multiply by prefix ................................................................................................................50
6-6. Divide by prefix ...................................................................................................................51
6-7. Angle conversion .................................................................................................................52
6-8. Angle calculation .................................................................................................................52
6-9. Ratio ....................................................................................................................................52
6-10. Random numbers ...............................................................................................................53
6-11. Cast ....................................................................................................................................53
6-12. Calculations for engineers .................................................................................................54
6-13. Health calculations ............................................................................................................54

7. Complex calculations .............................................................................. 55
7-1. Display of complex numbers ...............................................................................................55
7-2. How to make complex numbers ..........................................................................................56
7-3. Complex calculations ..........................................................................................................58
7-4. Disassemble complex ..........................................................................................................59
7-5. Complex functions ...............................................................................................................59

8. Logical calculations................................................................................. 60
8-1. Unsigned decimal and Boolean ...........................................................................................60
8-2. Bit length .............................................................................................................................60
8-3. N-ary number switching ......................................................................................................61
8-4. Input binary and Boolean ....................................................................................................61
8-5. Fundamental logical calculations ........................................................................................62

INDEX

8-6. Bit shift ................................................................................................................................63
8-7. Rotate ...................................................................................................................................63
8-8. Other functions that support unsigned integer .....................................................................64
8-9. Whole-stack logical calcultions ...........................................................................................64

9. Vector calculations .................................................................................. 65
9-1. Display of vectors ................................................................................................................65
9-2. Making of vector .................................................................................................................65
9-3. Extract element from tuple ..................................................................................................68
9-4. Four arithmetics of vectors ..................................................................................................70
9-5. Inner / outer product ............................................................................................................70
9-6. Norms of vectors .................................................................................................................71
9-7. Transpose vectors ................................................................................................................71

10. Matrix calculations ................................................................................ 72
10-1. Display of matrices ............................................................................................................72
10-2. Making of matrices ............................................................................................................72
10-3. Get element or tuple from matrix ......................................................................................75
10-4. Four arithmetics of matrices ..............................................................................................78
10-5. Determinant and inverse matrix .........................................................................................79
10-6. Transpose matrix................................................................................................................79
10-7. Other matrix functions .......................................................................................................79

11. Register operations ................................................................................ 80
11-1. What is register ..................................................................................................................80
11-2. Register display .................................................................................................................81
11-3. Store to selected register ....................................................................................................82
11-4. Load from selected register................................................................................................84
11-5. Delete selected register ......................................................................................................86
11-6. Register calculation............................................................................................................87
11-7. Register clear .....................................................................................................................89
11-8. Strings and registers ...........................................................................................................89

12. Stack operations .................................................................................... 90
12-1. Special stack operations.....................................................................................................90
12-2. Fundamental stack operations............................................................................................90
12-3. Order changing functions ..................................................................................................90
12-4. Duplicate and overwrite functions .....................................................................................95
12-5. Removal functions ........................................................................................................... 101
12-6. Other stack operations ..................................................................................................... 105

iii

INDEX

13. Unit conversions .................................................................................. 106
13-1. Supporting units ............................................................................................................... 106
13-2. How to use unit conversion function ............................................................................... 106
13-3. Units of length ................................................................................................................. 107
13-4. Units of length inverse ..................................................................................................... 108
13-5. Units of area..................................................................................................................... 109
13-6. Units of are inverse .......................................................................................................... 110
13-7. Units of volume ............................................................................................................... 111
13-8. Units of volume inverse ................................................................................................... 112
13-9. Units of time .................................................................................................................... 113
13-10. Units of time inverse ...................................................................................................... 113
13-11. Units of mass ................................................................................................................. 114
13-12. Units of velocity ............................................................................................................ 114
13-13. Units of acceleration ...................................................................................................... 115
13-14. Units of force ................................................................................................................. 115
13-15. Units of pressure ............................................................................................................ 116
13-16. Units of energy .............................................................................................................. 116
13-17. Units of temperature ...................................................................................................... 117

14. Math / Scientific constants .................................................................. 118
14-1. Input constants ................................................................................................................. 118
14-2. Math constants ................................................................................................................. 118
14-3. Fundamental physical constants ...................................................................................... 118
14-4. Electromagnetics ............................................................................................................. 119
14-5. Nuclear physics................................................................................................................ 119
14-6. Physicochemistry ............................................................................................................. 122
14-7. Agreement value .............................................................................................................. 123
14-8. Planck unit ....................................................................................................................... 123
14-9. Astronomy ....................................................................................................................... 123

15. Other functions .................................................................................... 124
15-1. All clear ........................................................................................................................... 124
15-2. All reset ............................................................................................................................ 124
15-3. Undo / redo ...................................................................................................................... 124
15-4. JSON output .................................................................................................................... 125
15-5. Macro function ................................................................................................................ 125
15-6. Test precisions ................................................................................................................. 127
15-7. Special startup.................................................................................................................. 127

INDEX

16. Messages ............................................................................................. 128
16-1. Error messages ................................................................................................................. 128
16-2. Notice messages .............................................................................................................. 129
16-3. Confirm messages............................................................................................................ 129

17. Technical information.......................................................................... 130
17-1. Data types ........................................................................................................................ 130
17-2. Calculation precision ....................................................................................................... 130
17-3. Mathematical definitions ................................................................................................. 131

18. Troubleshootings ................................................................................. 133
18-1. I have no idea to operate this software ............................................................................ 133
18-2. I’d like to view full data................................................................................................... 133
18-3. I’d like to change rational or floating display .................................................................. 133
18-4. I’d like to change complex display .................................................................................. 133
18-5. I’d like to view all values in the stack and the registers .................................................. 133
18-6. I saw doubtful calculation result ...................................................................................... 134
18-7. Stopped by errors ............................................................................................................. 135
18-8. I found doubtful behaviors............................................................................................... 135

0. Introduction

0. Introduction
0-1. What is ECKERT
ECKERT is a calculator software with keyboard interface, whose name is short for Engineering
Calculator with KEyboard and Refined Tools.

Watching the display, type keywords or values to calculate. This software adopts RPN (Reverse
Polish Notation), so you do not have to type parenthnesses to determine calculation priorities.

0-2. Audiences
ECKERT is recommended for following users:
Physical or Chemical scientists, electrical scientists, machine engineer, architect, civil engineer,
medical scientists, pharmacists, sologists and so on.

0. Introduction

0-3. Supporting functions
ECKERT has many functions such as following:
SI prefix, binary prefix [1]

Percent calculation

Logical calculations

Rational calculations

Include/exclude tax

Vector calculations

Complex calculations

Multiply/divide by prefix

Matrix calculations

Exponent and logarithm

Multiply/divide by 2π

Trigonometric func

Decibel conversion

Unit conversions [3]

Hyperbolic func

Base conversion

Math/sci constants [3]

[1] Numeric formats such as ‘12k’ (12 kilos) or ‘32u’ (32 micros) and so on.
[2] You can store data from stack to register, also can load/delete from register.
[3] 2014 CODATA

0-4. Operating environments
Windows 7, Windows 8, Windows 8.1 and the latter versions.

0-5. Disclaimer
This software and the manual of this software is copyrighted to Yuishin Kikuchi.
ECKERT is free for use and no warranty.
If you find bugs or unnatural specifications, please send messages to me.
ECKERT introduction page
http://sfoftime.web.fc2.com/eckert
E-mail to:
only.my.truth@gmail.com

I NEED YOUR HELP
This user’s manual was translated from Japanese version. If you find the English in the document
something wrong, please send reports to me, thanks.
これは日本語からの翻訳です。不自然な英語表現にお気づきの際はご連絡ください。

1. Preparation

1. Preparation
1-1. Installation and Uninstallation
You can find eckert86.exe and eckert64.exe in the package. The both are executable file.
The file eckert86.exe is for 32-bit Windows system and the file eckert64.exe is for 64-bit
Windows system. Please check your system.
Each exe file is independent so you can delete unnecessary one. This software does not change
registories in your system. Thus, this is portable.
The installation of thie software is just copying.
The uninstallation is just delete. You can also delete the config file.

1-2. How to read this manual
This manual explains whole functions of ECKERT and it is just user’s manual so the fundmental
mathematical definitions are omitted.
If it is the first time to use RPN calculator, please read chapter 2 and 4. If you get used to the
operations, read chapter 5, 6, 7 and 11.
If you know about RPN calculator, you can read chapter 4 diagonally to make comprehension of
the operations of this software.
To configurate display digits or value format, please read chapter 3.

1. Preparation

1-3. Format of this manual
This manual uses following format:
IMPORTANT

Important thngs

NOTICE

Things to notice

Input>

(Notation)

Type the right text and press enter.
This software uses stack concept, which is one of data storage structures. (Please read chapter 3 to
get more information about stack). This manual uses tables following to describe a state of a stack.
#

TYPE

VALUE

4
Z

Suuplementary

Integer

Floating

1.5

explanation

The column TYPE means data type and the column VALUE means data value.
This document uses list in following format to show functions.
Function
Add
Subtract

Keyword
ADD
+
SUB
-

Computation

𝑌+𝑋

𝑌−𝑋

The column Function means function name and the column Keyword means command to call
corresponding function.
Please refer chapter 4 to get more information about reading list above.

2. Display and Operation

2. Display and Operation
2-1. Launch and End
Just double click the executable file to launch.
Type “EXIT”, “QUIT”, or “Q” and press enter to terminate the program. Inputs are non-capitalsensitive except for numerical value input.
Function

Keyword
EXIT

Terminate

QUIT
Q

Special start up is available. Please refer chapter 15.

2-2. Display of calculation mode
The following chart is the display of calculation mode:

2. Display and Operation

The first two lines mean name of this software and the copyright of it.

Following a split line, calculation config and states display.

Below a doubly split line, you can find stack display there.

The right column is data number, the center is data type, and the left is value.
Below the stack display is 2-line message are.

The bottom of the display is input field.

Go on to the next section to make comprehension of reading the display.

2. Display and Operation

2-3. Calculation mode and states display
You can find 2-line calculation mode and states display.

In the first line, you can notice symbols in the following table:
Symbol

Meaning

Class

(AD)

Auto Decimal display

(FD)

Force Decimal display

(FF)

Force Fractional display

(Deg)

Degree mode

(Rad)

Radian mode

(Gra)

Grade mode

(Bin)

Binary display

(Oct)

Octal display

(Sdec)

Signed decimal display

(Udec)

Unsigned decimal display

(Hex)

Hexadecimal display

(Byte)

8-bit mode

(Word)

16-bit mode

Logical

(Dword)

32-bit mode

calculation

(Qword)

64-bit mode

[Reg]

[Eul]

Euler display

[Eul(Pi)]

Euler display (π radian)

[i.a/b]

Mixed fractional display

Decimal
display

Angle mode

Unsigned
integer display

(Symbol) selected in each class is always displayed.
[Symbol] is displayed if the mode is enabled.

You can see display above and you get force fractional display, radian, hexadecimal display, 32-bit
and mixed fractional display mode.

2. Display and Operation

There are three sections in the second line. The first consists of decimal display mode and display
digits.
Symbol

Mode

Std

Standard display

Fix

Fixed display

Sci

Scientific display

Eng

Engineering display

The fraction “Int/Int” in the first section means this: the first means the current display digits and
the second is the number of max digits you can set in the selected display mode. To change the number
of digits, please read chapter 3.

If you see above, you get that the decimal display mode is standard display mode and the current
number of selected (standard) display digits is 6 and the maximum number of digits you can set is 15.
The second is the number of elements in the stack. If the number is zero, Empty is displayed.

If you see like above, there are 11 elements in the stack.
The third is history display.
Display

Meaning

OFF

History is disabled

Init

Initial state

Int/Int

(Discribed later)

The fraction “Int/int” in the second section means this: the first integer is the times that you have
called undo and the second integer is the items in the history.

You see above display and you get that you have undo 4 times and the number of items in the stack
is 10, so you can redo 10 times totally.

2. Display and Operation

2-4. Stack display
Learn the concept of stack.

Stack is one of the data containers. This software has one stack.
In each line in the stack display contains item number, data type and value. A data type means a
kind of a number. If a data type is integer, Integer is displayed in the TYPE column and if the type
is rational number, Rational is displayed.
This manual shows the stack like below:
#

TYPE

VALUE

4
Z
Y

Integer

Floating

1.5

IMPORTANT
The stack size is unlimited.
X is the bottom of the stack. Y is the second bottom and Z is the third bottom. After that, the data
numbers are displayed as integers such as 4, 5…. The data in X is called just X, the data in Y is just Y,
and so on.
Go on to the next page and make comprehension of stack graphically.

2. Display and Operation

You can see a stack like a pile of cards. You draw one by one from the top of the pile and you put
into the pile one by one.
Please look at the left chart. There are some cards. You put a
card ‘1’ and card ‘2’ in turn.
This situation is expressed like below:
#

TYPE

VALUE

Z
Y

Integer

The next chart means the top of the pile is removed from the
previous chart. In other words, X is dropped from the stack.
#

TYPE

VALUE

Z
Y
X

Integer

See addition with stack.
You draw 2 cards from the top
and you put the value of 1 + 2 on
the top.
This is the fundamental flow of
calculation with stack.

TYPE

VALUE

Z
Y

Integer

Addition

operated

→

Y
X

TYPE

Integer

There are 3 fundamental operations: add (push), remove (drop) and execution.

VALUE

2. Display and Operation

Here is the type of data types:
Display

Meaning

Error

String value means error

String

String value

Integer

Floating

Floating point number

Rational

Rational number

Infinity

Complex

Complex number

Boolean

Boolean (true of false)

Byte

8-bit unsigned integer

Word

16-bit unsigned integer

Dword

32-bit unsigned integer

Qword

64-bit unsigned integer

Tuple[Row]

Row vector

Tuple(Col)

Column vector

Matrix

2. Display and Operation

2-5. Message display
In the message display, the last called function and error / notice / confirm message are displayed.

In the first line is called function and the second line is the other messages.
If unoperatable commands such as division by zero is input, the operation is stopped and an error
message is displayed in the second line.

If there is error or notice message, the message is displayed second line with a symbol in the first
line.
Symbol

Meaning

[!]

Operation is terminated by error

[i]

Unordinal operation

[C]

Waiting input or confirm

For more information, please read chapter 16.
If [?] is displayed, it means that there are software bugs. Please send me a bug report.

2. Display and Operation

2-6. Configuration mode display
Type “CONFIG” to go to configuration display.

Maximum history size, display width and the number of stack display lines are shown. Please read
chapter 3 to configurate these.

Those are command for config management.

2. Display and Operation

2-7. Fundamental operation
Input keywords or values to operate. Only half-width (one byte) characters are supported.
Type one or several space-splitted keywords or values and hit enter to calculate or configurate. If
the number of tokens, which are keywords or numerical values, is not single, each token is processed
in turn.
This way, "type and enter" is the flow of the operations. Please notice that the display changes only
pressing enter. Then, only SI or binary prefixes are case-sensitive, the others are not.
This software supports only printable characters input.
For instance, type like below to operate ‘add’ and ‘multiply’ in turn.
Input> + *
Some keywords are aliases, in other words, some ones are connected with the same function. And
more, there are some keywords depend on calculation modes.
Type numerical values to input. You can put space-splitted values in order.
Input> 1 2
You can even mix values and keywords.
Input> 2 5 /
Go on to the next section to get how to input numeric values.

2. Display and Operation

2-8. Input numeric values
This section shows how to input numeric values in this software.
2-8-1. Integer
Just type an integer value.
2-8-2. Decimal
Type a value with decimal point.
You can omit integer part (like “.2”) or decimal part (like “1.”).
2-8-3. Exponential
Type a decimal value and append 'E' and a decimal exponent.
For instance, 6.02 × 10−23 is expressed like “6.02E-23” and 1.01325 × 105 is expressed
like “1.01325E5”.
2-8-4. Imaginary unit
Positive imaginary unit is “i” or “+i” and negative imaginary unit is “-i”.
Non-case-sensitive.
2-8-5. Imaginary number
Type integer, decimal or exponential with prefix ‘i’.
Non-case-sensitive.
2-8-6. Infinity
Positive infinity is “INF”, “+INF” or “+INFINITY”.
Negative infinity is “-INF” or “-INFINITY”.
2-8-7. Boolean
True value is “TRUE” or “T” and false value is “FALSE” or “F”.
2-8-8. Unsigned decimal value
Type “u” and postfix non-signed integer.
2-8-9. Binary value
Type “0b” and postfix binary expression using 0 and 1.

2. Display and Operation

2-8-10. Octal value
Type “0o” and postfix octal expression using 0 to 7.
2-8-11. Hexadecimal value
Type “0x” and postfix hexadecimal expression using 0 to 9 and A to F.
2-8-12. Value with SI or binary prefix
You can append SI or binary prefix to integer, decimal, exponential and imaginary value. SI
and binary prefixes are case-sensitive.
Value

Value

Name

Symbol

DECA

1.0E+01

1.0E-01

DECI

HECTO

1.0E+02

1.0E-02

CENTI

K, k

KILO

1.0E+03

1.0E-03

MILLI

MEGA

1.0E+06

1.0E-06

MICRO

GIGA

1.0E+09

1.0E-09

NANO

TERA

1.0E+12

1.0E-12

PICO

PETA

1.0E+15

1.0E-15

FEMTO

EXA

1.0E+18

1.0E-18

ATTO

ZETTA

1.0E+21

1.0E-21

ZEPTO

YOTTA

1.0E+24

1.0E-24

YOCTO

Ki, ki

KIBI

1024^1

Mi, mi

MEBI

1024^2

Gi, gi

GIBI

1024^3

Ti, ti

TEBI

1024^4

Pi, pi

PEBI

1024^5

Ei, ei

EXBI

1024^6

Zi, zi

ZEBI

1024^7

Yi, yi

YOBI

1024^8

SI prefix less than 1

Name

SI prefix greater than 1

Symbol

Binary prefix

You can use binary prefixes alias.

2. Display and Operation

2-9. Examples of value input
Examples here:
Integer

Input> -3

Infinity

Input> -inf

Prefixed

Input> 3k

Boolean

Input> t

Exponential

Input> 2.998e8

Unsigned

Input> u65536

Imaginary unit

Input> -i

Binary

Input> 0b1010

Imaginary num Input> i12

Octal

Input> 0o100

Imag with sign

Hexadecimal

Input> 0xFFFE

Input> -i5

You can also input math or scientific constants with keywords. Please read chapter 14 to get more
information.
Name

Keyword

Value

3.141 592 653 589 79

Napier’s constant

2.718 281 828 459 05

Euler-Mascheroni constant

0.577 215 664 901 533

In addition to these, you can input string value. Use double quotation to input string value.
String

Input> "This is test"

You can use string to put memos in the register or use macro function.

2. Display and Operation

2-10. When the error message is displayed
When the error occurs while operating some functions, the operating and the left unoperated
functions are cancelled. This means, the state is the before one cancelled operation. And then, the error
messages are shown.
If you see error messages, you can operate as usual. Input commands and if the operations are
successful, error messages are disappeared.
Even if operating space-splitted tokens, the functions called one by one, so this software do not stop
the operations if no errors.
Input> 5 0 /
(You can make sense of the notation if you read chapter 4.)
For instance, if you input like above, the error “division by zero” occurs. But the push operations
are done, so the value 5 and the value 0 is added into the stack and the division cancelled with the
stack keeped.
If the error messages are shown, undo and redo are recommended. Please read chapter 15 to get
more information.
If you look at the list of error messages, please read chapter 16.
When unsupported inputs are detected, the error message below is displayed:

If you see this, please check the spelling.
And then, even if the keyword is supported, you can see this when the calculation mode or state is
not inappropriate, or greater than one settings-changing keywords.

3. Settings

3. Settings
IMPORTANT
Please read this chapter after making comprehension of fundamental operations.

3-1. Settings in configuration mode
You can set max history size, display width and the number of lines of stack display in configuration
mode.
Please type the keyword “CONFIG” to go to config mode. Input keyword “HOMURA” or “CALC” to
return to calculation mode.
3-1-1. Max history size
Type “HIST” and an integer. You can input splited-tokens like “hist 10”. You can set the
size to 0 to disable history function.
The default max history size is 10.
Type below to set the max history size to 20.
Input> hist 20
3-1-2. Display width
Type “WIDTH” and an integer. You can input splited-tokens like “width 79”. If the value is
less than the least width, the least width is set.
The default display width is 79 and the least size is 60.
Type below to set the display width to 69.
Input> width 69
3-1-3. Number of stack lines
Type “LINES” and an integer. You can input splited-tokens like “lines 11”. If the value is
less than the least number, the least number is set.
The default number of stack lines is 11 and the least is 4.
Type below to set the number of stack lines to 20.
Input> lines 20

3. Settings

3-1-4. Management of config
You can save configurations as a config file. You can use the following functions to manage
config file.
Function

Keyword

Load config file

LOAD

Save config file

SAVE
RESET

Reset config

RST

If the config file exists, this software loads it on startup. So the max history size and display
width are restored automatically.
You can load config file explicitly with “LOAD” function.
The function “RESET” sets all settings in config mode to default. However, this function does
not save or change a config file.
3-1-5. Functions in configuration mode
Here is the list of keywords for configuration mode:
Function

Keyword

Config mode

CONFIG
CALC

Calculation mode

HOMURA

History size

HIST

Display width

WIDTH

Number of stack lines

LINES

Load config file

LOAD

Save config file

SAVE
RESET

Reset config

RST

3. Settings

3-2. Settings in calculation mode
Angle mode, type display and number of display digits can be changed in calculation mode.
3-2-1. Rational display mode
When the decimal display is set to standard, you can choose rational number display following:


Audo Decimal display
If a rational number can be displayed as finite decimal display, show a decimal. In other
cases, show a fraction.



Force Decimal display
All rational numbers are displayed as decimal.



Force Fractional display
All rational numbers are displayed as fraction.

To choose mode, use the followingkeywords:
Mode

Keyword

Symbol

Auto Decimal display

(AD)

Force Decimal display

(FD)

Force Fractional display

(FF)

The default rational display mode is Force Decimal.
3-2-2. Angle mode
You can choose angle unit with setting angle mode. Angle mode affects trigonometric functions.
To choose mode, use the keywords below:
Mode

Keyword

Symbol

Degree

DEG

(Deg)

Radian

RAD

(Rad)

Grade

GRAD
GRA

This mode is connected with “SIN”, “ARG” and so on.
The default angle mode is Radian.

(Gra)

3. Settings

3-2-3. N-ary number display mode
You can select the display of 8-bit ,16-bit, 32-bit and 64-bit data.
To choose mode, use the following keywords:
Mode

Keyword

Symbol

Binary display

BIN

(Bin)

Octal display

OCT

(Oct)

Signed decimal display

SDEC

(Sdec)

Unsigned decimal display

UDEC

(Udec)

Hexadecimal display

HEX

(Hex)

The default N-ary number display mode is Hexadecimal.
3-2-4. N-bit input mode
You can choose the binary size to input from 8, 16, 32 or 64 bits. If unsigned decimal with ‘u’
is detected, the value is generated as selected bit mode.
To choose mode, use the keywords below:
Mode
8-bit mode
(byte)
16-bit mode
(word)
32-bit mode
(dword)
64-bit mode
(qword)

Keyword

Symbol

BYTE

(Byte)

WORD

(Word)

DWORD

(Dword)

QWORD

(Qword)

The default size is 32-bit.
3-2-5. Type display
You can switch the type display in the stack display on/off. Input “TYPE” without any other
keywords to switch.
The default type display is enabled.

3. Settings

3-2-6. Register display
You can enable or disable the register display. Use the keywords “REG” or “REGISTER” to
switch the display. Register is displayed above the stack. If the register display is enabled, the
stack display gets smaller.
When register display is enabled, the symbol [Reg] is displayed.
The default setting is disabled.
3-2-7. Euler display
You can switch the complex number display: 𝑎 + 𝑖𝑏 (rectangular) or 𝑟 exp(𝑖𝜃) (polar)
style. Use the keyword “EULER” or “EUL” to switch.
If the Euler display is enabled, the symbol [Eul] is displayed.
The argument of Euler display is depends on angle mode.
Mode

Expression

Rectangular

5 + 12𝑖

Polar
(Degree)
Polar
(Radian)
Polar
(Grade)

13∠67[deg]
13∠1.3[rad]
13∠75[gra]

Display
5 + i12
13 exp(+i67.d)
13 exp(+i1.3)
13 exp(+0.37 Pi)
13 exp(+i75.g)

If you select radian, you can convert the argument to 𝜋 radians. To switch the display, type
“PIRAD” or “PRAD”. When 𝜋 radian mode is enabled and Euler display is also enabled, then
the symbol [Eul(Pi)] is displayed.
The default setting is disabled.

3. Settings

3-2-8. Mixed fractional display
You can get mixed fractional display. Use “FRACTION” or “FRAC” to enable/disable mixed
fractional display.
The display of rational number is below:
Value

Provisional

Mixed

Decimal

+ 3⁄2

3/2

1.1/2

1.5

− 6⁄5

-6/5

-1.1/5

-1.2

If the mode is enabled, the symbol [i.a/b] is displayed.
The default setting is disabled.
3-2-9. Decimal display
You can choose decimal display mode. There are four modes: standard, fixed, exponential and
engineering.


Standard display
Value display changes flexibly.
Rational number display depends on the rational display mode.



Fixed display
Fix the digits of decimal part.
Integer and rational number is displayed as decimal.



Scientific display
All scalars are displayed as scientific notation such as “1.2E+10”. The range of mantissa
m is 0 ≤ m < 10.
Integer and rational number is displayed as decimal.



Engineering display
All scalars are displayed as scientific notation such as “12E+10”. The range of mantissa
m is 0 ≤ m < 1000.
Integer and rational number is displayed as decimal.

3. Settings

To choose display mode, use the following keywords:
Display

Keyword

Symbol

Standard display

STD

Std

Fixed display

FIX

Fix

Scientific display

SCI

Sci

Engineering display

ENG

Eng

Rational number is displayed as decimal without in standard mode.
The default display mode is standard.
3-2-10. Decimal digits
You can change the digits of decimal. Here is the list of “digit” meaning:
Mode

Meaning of “digits”

Standard

Significant digits

Fixed

Digits of decimal part

Scientific

Significant digits

Engineering

Significant digits

Use the keyword “DISP” or “DIGIT” and input an integer to set the number of digits.
If you would set to 3 digits, type below:
Input> digit 3
You can set digits in each mode.
The maximum number of digits exists in each mode. Too large number is read as max and too
small number does as minimum.
Mode

Minimum

Maximum

Standard

Fixed

Scientific

Engineering

3. Settings

Example: 10 times of 𝜋 (31.4159265358979)
Std: 5/15

31.416

Fix: 5/15

31.41593

Sci: 5/15

3.1416E+01

Eng: 5/15

31.416E+00

The default numbers of digits are all 9.
And then, if you put other tokens after digit settings like “disp 10 36”, these are ignored.

3. Settings

3-2-11. Keywords of settings in calculation mode
Here is the list of keywords of settings in calculation mode:
Mode

Keyword

Symbol

Auto Decimal display

(AD)

Force Decimal display

(FD)

Force Fractional display

(FF)

Degree mode

DEG

(Deg)

Radian mode

RAD

(Rad)

GRA

Grade mode

GRAD

(Gra)

Binary display

BIN

(Bin)

Octal display

OCT

(Oct)

Signed decimal display

SDEC

(Sdec)

Unsigned decimal display

UDEC

(Udec)

Hexadecimal display

HEX

(Hex)

8-bit mode

BYTE

(Byte)

16-bit mode

WORD

(Word)

32-bit mode

DWORD

(Dword)

64-bit mode

QWORD

(Qword)

Type display

TYPE

REG
EULER

Euler display

EUL
PIRAD

π radian argument display

PRAD
FRACTION

Mixed fraction display

FRAC

[Reg]
[Eul]
[Eul(Pi)]

[i.a/b]

Standard decimal display

STD

Std

Fixed decimal display

FIX

Fix

Scientific decimal display

SCI

Sci

Engineering decimal display

ENG

Eng

DISP

Set number of digits

DIGIT

3. Settings

3-3. Next/previous pages in stack
If there are many elements in the stack, you cannot see the all data.

If you need to see unshown data, use stack page function. There are 8 data in stack but only 6 is
shown in the chart above.
Use the keyword “NEXT” or “N” to turn to the next page.

Use the keyword “PREV” or “P” to turn to the previous page.
If you would like to return to first page, use the keyword “FIRST” or “FST”.
If a stack-changing function is called, the page is set to first.

3. Settings

Here is the list of stack page-flipping:
Function

Keyword
NEXT

Next page of stack

N
PREV

Previous page of stack

P
FIRST

First page of stack

FST

3-4. Next/previous pages in register
This software has registers which is used for saving location of data. There are 26 registers in this
software: RA to RZ. You can not view all registers at once without changing the number of stack lines.
Look at the following chart. RA to RC are displayed but the others are not.

3. Settings

You can change the register page.
Type “REGNEXT” or “RN” to change to next page of registers.

On the other hand, type “REGPREV” or “RP” to change to previous page of registers.
The keyword “REGFIRST” or “RF” is for returning to first page of the registers.
Here is the list of register page functions:
Function

Keyword
REGNEXT

Next page of registers

Previous page of registers

REGPREV
RP
REGFIRST

First page of registers

3. Settings

3-5. View full string of data
In case of the value display is too long, only the left part is displayed. The following chart is the
stack which has a complex number consists of 2 rationals but the right part is omited.

To view full data, use the keywords “VIEW” or “V”.
Function

Keyword
VIEW

View full data

View mode shows data, which are displayed in calculation mode.
Press Enter to return to calculation mode.

3. Settings

3-6. Version display
Type the keyword “VER” or “VERSION” to display current version.
Function

Keyword
VERSION

Version display

VER

If you find bugs in this app, please send reports to me with the version.

4. Fundamental operations ~ four arithmetics

4. Fundamental operations ~ four arithmetics
IMPORTANT
This chapter includes the most important things about operating this software, such as RPN. So
please read carefully.

4-1. Elementary stack operation
First of all, let’s input an integer.
Input> 12
#

TYPE

VALUE

4
Z
Added into

Y
X

Integer

the bottom

12 is added into X in the stack display area.
Next, type one more integer.
Input> 9
#

TYPE

VALUE

4
Z
Y

Integer

The data 9 is added into X.
This way, addition is executed into X.

Added into
the bottom

4. Fundamental operations ~ four arithmetics

The next, input decimals.
Input> 1.6 6.0e-23
#

TYPE

VALUE

Integer

Floating

1.6

Floating

6E-23

Added in turn

This way, just write numbers to add into the stack. The addition into the bottom of the stack is called
push.
Type “DROP” or “¥” to remove the data at the bottom of the stack. The removal of the bottom of
the bottom of the stack is called drop.
Input> ¥
#

TYPE

VALUE

4
Z

Integer

Floating

The bottom is

1.6

Just hit enter without any input to duplicate the bottom of the stack (X) and push.
The keywords “COPY”, “C” and “DUP” call the same function.

removed

4. Fundamental operations ~ four arithmetics

Input> (Just hit Enter)
#

TYPE

VALUE

Integer

Floating

1.6

Floating

1.6

Duplicated

Type “CLEAR” or “CLR” to empty the stack.
Input> clear
#

TYPE

VALUE

4
Z
Y

Emptied

X
Here is the list of keywords described in this section:
Function

Keyword

Push
Drop
Duplicate
[1]
Clear stack

DROP
¥

N>0

COPY
C
DUP
CLEAR
CLR

[1] You can call the function just hitting enter without any input.
Let us calculate four arithmetics after getting this section.

4. Fundamental operations ~ four arithmetics

4-2. Four arithmetics
The four arithmetics are the basics of calculating with this software.
Use following keywords to calculate the four arithmetics:
Function

Keyword
ADD

Add

Subctract
Multiply
Divide
Modulo

SUB
MUL
*
DIV
/
MOD
%

Computation

𝑌+𝑋

𝑌−𝑋

𝑌×𝑋

𝑌 ⁄𝑋

𝑌 mod 𝑋

Let us try following the tutlrial.
The first step is a simple addition. Challenge “2 + 3”. Push 2 numbers as following:
Input> 2 3
#

TYPE

VALUE

4
Z
Y

Integer

Added in turn

4. Fundamental operations ~ four arithmetics

Input> +
#

TYPE

VALUE

4
Z
Y
X

Integer

Addition
requires
2 data.
2 dropped.
1 result
pushed.

You can see X is 5, which is the the result of Y+X (2+3). The previous Y and X are removed. Your
inputs mean the pushing 2 and 3 before adding.
Following this, try this:
Input> 9 #

TYPE

VALUE

4
Z

Push and

subtraction at

Integer

-4

one time.

You get X is −4. You have pushed 9 and called subtraction. You can see this software calculates
with using the bottom of the stack.
Function
Add

Keyword
ADD
+

Computation

𝑌+𝑋

This manual uses tables like above one. The column R is the number of required data. If you call
the function without the stack containing enough data, error messages are displayed. The column D is
the number of dropped data.
Addition requires 2 data. Once the function is called, 2 data are dropped and the result of 𝑌 + 𝑋 is
pushed. The other arithmetics are similar with addition.

4. Fundamental operations ~ four arithmetics

In the case of not-enough data, you see error messages like following:

4. Fundamental operations ~ four arithmetics

4-3. Multiple arithmetics
Let us try higher-level.
Calculate the area of the trapezoid: the upper base is 2, the lower is 1, the hight is 5. The formula of
of calculating this is:
5 × (2 + 1) ÷ 2
You can read this like the multiplication of 5 and (2 + 1). First, push 5 and the result of 2 + 1,
and call multiply. The final step is halfing.
Type as following to calculate at one time.
Input> 5 2 1 + * 2 /
However, this expression is difficult for the beginners. I divided this into the steps: (1) ~ (5). Read
carefully and operate to understand easily.
(1) Push 5, 2 and 1
Input> 5 2 1
#

TYPE

VALUE

4
Z

Integer

TYPE

Pushed in
turn

(2) Add
Input> +
VALUE

Unused value
remains

4
Z
Y

Integer

Addition

Integer

requires 2.

4. Fundamental operations ~ four arithmetics

(3) Multiply
Input> *
#

TYPE

VALUE

4
Z
Multiplication

Y
X

Integer

TYPE

requires 2.

(4) Push 2
Input> 2
VALUE

4
Z
Y

Integer

Pushed into

Integer

the bottom

TYPE

(5) Divide
Input> /
VALUE

4
Z
Division

Y
X

Rational

15/2

requires 2.

You can calculate with pushing and calling functions in appropriate order without parentheses.

4. Fundamental operations ~ four arithmetics

4-4. Elementary functions
Here is the list of elementary functions without the four arithmetics:
Function
Quotient and
remainder
Increment
Decrement
Absolute value
Negate
Invert (incl. matrix)

Keyword
QM
INC
++
DEC
-ABS
PM
NEG
INV

Computation

𝑋+1

𝑋−1

|𝑋|

−𝑋

𝑋 −1

𝑌 ←𝑌÷𝑋
𝑋 ← 𝑌 mod 𝑋

You can increment or decrement only integers. Increment is adding 1 and decrement is adding -1.
For example, type this to find the inverse of 5:
Input> 5 inv
These functions require 1 argument.

5. Mathematical functions

5. Mathematical functions
5-1. How to use math functions
This software supports many math functions. Please notice that the usages of these functions are
similar with the usage of the ones of four arithmetics. Push first and call functions.
Some functions have restricted domains.

5-2. Exponent and logarithm
Use the following keywords with operating exponents and logarithms.
Function

Keyword

Computation

Square

𝑋2

Square root

SQRT

√𝑋

Cubic root

CBRT

Hypotenuse

HYPOT

√𝑌 2 + 𝑋 2

𝑌𝑋
𝑋

√𝑋

POW
Power

^
**

N-th root

NRT

Exponent

EXP

exp(𝑋)

Power of 10

TPOW

10𝑋

Power of 2

BPOW

2𝑋

Logarithm of X to base Y

LOGB

log𝑌 (𝑋)

Natural logarithm

log𝑒 (𝑋)

Common logarithm

LOG

log10(𝑋)

Binary logarithm

log2(𝑋)

EX 1 log10 3000

√𝑌

EX 3 log3 22

Input> 3000 log

Input> 3 22 logb
EX 4 exp(− 32⁄2)

EX 2 √52 + 122
Input> 5 sq 12 sq + sqrt

Input> 3 sq 2 / pm exp

5. Mathematical functions

5-3. Trigonometric functions
Here is the list of trigonometric and inverse trigonometric functions:
Function

Keyword

Computation

Sine

SIN

sin(𝑋)

Cosine

COS

cos(𝑋)

Tangent

TAN

tan(𝑋)

Arcsine

ASIN

arcsin(𝑋)

Arccosine

ACOS

arccos(𝑋)

Arctangent

ATAN

arctan(𝑋)

These keywords depend on the angle mode. If you input “sin” in degree mode, this software calls
“sin (degree)”.
The radian trigonometric functions are here:
Function

Keyword

Computation

Sine (Radian)

SINR

sin(𝑋[rad])

Cosine (Radian)

COSR

cos(𝑋[rad])

Tangent (Radian)

TANR

tan(𝑋[rad])

Arcsine (Radian)

ASINR

arcsin(𝑋)[rad]

Arccosine (Radian)

ACOSR

arccos(𝑋) [rad]

Arctangent (Radian)

ATANR

arctan(𝑋) [rad]

The degree trigonometric functions are here:
Function

Keyword

Computation

Sine (Degree)

SIND

sin(𝑋[deg])

Cosine (Degree)

COSD

cos(𝑋[deg])

Tangent (Degree)

TAND

tan(𝑋[deg])

Arcsine (Degree)

ASIND

arcsin(𝑋)[deg]

Arccosine (Degree)

ACOSD

arccos(𝑋) [deg]

Arctangent (Degree)

ATAND

arctan(𝑋) [deg]

5. Mathematical functions

The grade trigonometric functions are here:
Function

Keyword

Computation

Sine (Grade)

SING

sin(𝑋[gra])

Cosine (Grade)

COSG

cos(𝑋[gra])

Tangent (Grade)

TANG

tan(𝑋[gra])

Arcsine (Grade)

ASING

arcsin(𝑋)[gra]

Arccosine (Grade)

ACOSG

arccos(𝑋) [gra]

Arctangent (Grade)

ATANG

arctan(𝑋) [gra]

EX 1 sin(30) (mode dependent)

EX 2 cos(52[deg])

Input> 30 sin

Input> 52 tand

5-4. Hyperbolic functions
Use following keywords to calculate hyperbolic functions:
Function

Keyword

Computation

Hyperbolic sine

SINH

sinh(𝑋)

Hyperbolic cosine

COSH

cosh(𝑋)

Hyperbolic tangent

TANH

tanh(𝑋)

Inverse hyperbolic sine

ASINH

asinh(𝑋)

Inverse hyperbolic cosine

ACOSH

acosh(𝑋)

Inverse hyperbolic tangent

ATANH

atanh(𝑋)

cosh(1.2)
Input> 1.2 cosh

5. Mathematical functions

5-5. Stats functions
Stats functions are here:
Function

Keyword

Computation

Beta function

BETA

Β(𝑌, 𝑋)

Gamma function

GAMMA

Γ(𝑋)

Logarithm of gamma function

LNGAMMA

loge |Γ(𝑋)|

Error function

ERF

erf(𝑋)

Complementary error function

ERFC

1 − erf(𝑋)

EX 1 Β(0.5, 1.6)

EX 2 Γ(2)

Input> 0.5 1.6 beta

Input> 2 gamma

5-6. Integer roundings
Integer roundings are here:
Function
Floor function
Ceiling function
Round

Keyword

Computation

⌊𝑋⌋

CEIL

⌈𝑋⌉

ROUND

RND

FLOOR
FLR

EX 1 ⌊−2.2⌋

⌊𝑋 + 0.5⌋

EX 2 ⌈𝜋⌉

Input> -2.2 flr

Input> pi ceil

5. Mathematical functions

5-7. Functions for integers
Functions for integers such as GCD and LCM are here:
Function
Factorial

EX 1

Keyword
FACT
!

Computation

𝑋!

Greatest common divisor

GCD

GCD(𝑌, 𝑋)

Least common multiple

LCM

LCM(𝑌, 𝑋)

Permutations

PERM

𝑌P𝑋

Combinations [binomial coefficient]

COMB

𝑌 C𝑋

EX 2 LCM(12, 50)

5P2

Input> 5 2 perm

Input> 12 50 lcm

𝑌
=( )
𝑋

6. Useful functions

6. Useful functions
6-1. Percent calculations
Percent calculations such as including tax are here:
Function
X percent of Y
Delta percent between Y and X

Keyword
PERC
PC
DPERC
DP

Computation

𝑋−𝑌
× 100
𝑌

𝑌×

𝑋
100

Include tax

INTAX

𝑌×

100 + 𝑋
100

Exclude tax

EXTAX

𝑌×

100
100 + 𝑋

These functions support only scalars.
EX 1 3% of 5.15

EX 3 Include 8% tax to 1250

Input> 5.15 3 pc

Input> 1250 8 intax

EX 2 Delta percent between 1.2 and 1.3

EX 4 Exclude 8% tax from 120

Input> 1.2 1.3 dp

Input> 120 8 extax

6. Useful functions

6-2. Time conversion
Conversions between sec, min, hour, day and week are here.
Function

Keyword

Computation

Seconds to ninutes

STOM

𝑋⁄60

Seconds to hours

STOH

𝑋⁄3600

Seconds to days

STOD

𝑋⁄86400

Seconds to weeks

STOW

𝑋⁄604800

Minutes to seconds

MTOS

𝑋 × 60

Minutes to hours

MTOH

𝑋⁄60

Minutes to days

MTOD

𝑋⁄1440

Minutes to weeks

MTOW

𝑋⁄10080

Hours to seconds

HTOS

𝑋 × 3600

Hours to minutes

HTOM

𝑋 × 60

Hours to days

HTOD

𝑋⁄24

Hours to weeks

HTOW

𝑋⁄168

Days to seconds

DTOS

𝑋 × 86400

Days to minutes

DTOM

𝑋 × 1440

Days to hours

DTOH

𝑋 × 24

Days to weeks

DTOW

𝑋 ⁄7

Weeks to seconds

WTOS

𝑋 × 604800

Weeks to minutes

WTOM

𝑋 × 10080

Weeks to hours

WTOH

𝑋 × 168

Weeks to days

WTOD

𝑋×7

These functions support only scalars.
EX 2 45 mins to hours

EX 1 65536 secs to days

Input> 45 mtoh

Input> 65536 stod

6. Useful functions

6-3. DMS conversion
DMS conversion divides a scalar value into degrees / minutes / seconds.
Inverse DMS conversion combines degrees / minutes / seconds into a value.
Function

Keyword

Computation
𝑍←𝐷

Decimal deg to deg/min/sec

TODMS

𝑌←𝑀

𝑋←𝑆
Deg/min/sec to decimal deg

DMSTO

𝑍+

𝑌
𝑋
+
60 3600

These functions support only scalars.
EX 2 30°20′10′′ to degrees

EX 1 4096 sec to h:m:s
Input> 4096 stoh todms

Input> 30 20 10 dmsto

6-4. Whole stack calculations
You can find sum or infinite product in the stack.
Function

Keyword

Computation
𝑛

Sum

SUM

N>1

∑

Infinite product

PROD

N>1

∏

Arithmetic average

AVR

N>1

Geometric average

GAVR

N>1

HAVR

N>1

Harmonic average

𝑥𝑖

𝑖=1
𝑛

𝑥𝑖

𝑖=1

𝑛
1
∑ 𝑥𝑖
𝑛
𝑖=1

𝑛

√∏

𝑛

𝑥𝑖

𝑖=1

𝑛
∑𝑛𝑖=1 𝑥𝑖 −1

If there are errors in the process of the functions, the calculation is cancelled and the stack keeps on.

6. Useful functions

Other versions available:
Function

Keyword

Partial sum

PSUM

N>2

M+1

Partial product

PPROD

N>2

M+1

Partial arithmetic average

PAVR

N>2

M+1

Partial geometric average

PGAVR

N>2

M+1

Partial harmonic average

PHAVR

N>2

M+1

Sum without drop

SUMW

N>1

Infinite product without drop

PRODW

N>1

Arithmetic average without drop

AVRW

N>1

Geometric average without drop

GAVRW

N>1

Harmonic average without drop

HAVRW

N>1

Partial sum without drop

PSUMW

N>2

Partial product without drop

PPRODW

N>2

Partial arithmetic average without drop

PAVRW

N>2

Partial geometric average without drop

PGAVRW

N>2

Partial harmonic average without drop

PHAVRW

N>2

Computation

6. Useful functions

6-5. Multiply by prefix
Multiplication by prefix means the removal of prefix. For instance, if you have to get meter from
kilometer, multiply by 1000, which means kilo.
Here is the list of multiplications by prefix:
Function

Keyword

Computation

Multiply by yocto

YOCTO

𝑋 × 10−24

Multiply by zepto

ZEPTO

𝑋 × 10−21

Multiply by atto

ATTO

𝑋 × 10−18

Multiply by femto

FEMTO

𝑋 × 10−15

Multiply by pico

PICO

𝑋 × 10−12

Multiply by nano

NANO

𝑋 × 10−09

Multiply by micro

MICRO

𝑋 × 10−06

Multiply by milli

MILLI

𝑋 × 10−03

Multiply by centi

CENTI

𝑋 × 10−02

Multiply by deci

DECI

𝑋 × 10−01

Multiply by deca

DECA

𝑋 × 10+01

Multiply by hecto

HECTO

𝑋 × 10+02

Multiply by kilo

KILO

𝑋 × 10+03

Multiply by mega

MEGA

𝑋 × 10+06

Multiply by giga

GIGA

𝑋 × 10+09

Multiply by tera

TERA

𝑋 × 10+12

Multiply by peta

PETA

𝑋 × 10+15

Multiply by exa

EXA

𝑋 × 10+18

Multiply by zetta

ZETTA

𝑋 × 10+21

Multiply by yotta

YOTTA

𝑋 × 10+24

Multiply by kibi

KIBI

𝑋 × 210

Multiply by mebi

MEBI

𝑋 × 220

Multiply by gibi

GIBI

𝑋 × 230

Multiply by tebi

TEBI

𝑋 × 240

Multiply by pebi

PEBI

𝑋 × 250

Multiply by exbi

EXBI

𝑋 × 260

Multiply by zebi

ZEBI

𝑋 × 270

Multiply by yobi

YOBI

𝑋 × 280

6. Useful functions

6-6. Divide by prefix
Division by prefix means the addition of prefix. For instance, if you have to get millimeter from
meter, divide by 0.001, which means milli.
Here is the list of divisions by prefix:
Function

Keyword

Computation

Divide by yocto

TOYOCTO

𝑋⁄10−24

Divide by zepto

TOZEPTO

𝑋⁄10−21

Divide by atto

TOATTO

𝑋⁄10−18

Divide by femto

TOFEMTO

𝑋⁄10−15

Divide by pico

TOPICO

𝑋⁄10−12

Divide by nano

TONANO

𝑋⁄10−09

Divide by micro

TOMICRO

𝑋⁄10−06

Divide by milli

TOMILLI

𝑋⁄10−03

Divide by centi

TOCENTI

𝑋⁄10−02

Divide by deci

TODECI

𝑋⁄10−01

Divide by deca

TODECA

𝑋⁄10+01

Divide by hecto

TOHECTO

𝑋⁄10+02

Divide by kilo

TOKILO

𝑋⁄10+03

Divide by mega

TOMEGA

𝑋⁄10+06

Divide by giga

TOGIGA

𝑋⁄10+09

Divide by tera

TOTERA

𝑋⁄10+12

Divide by peta

TOPETA

𝑋⁄10+15

Divide by exa

TOEXA

𝑋⁄10+18

Divide by zetta

TOZETTA

𝑋⁄10+21

Divide by yotta

TOYOTTA

𝑋⁄10+24

Divide by kibi

TOKIBI

𝑋⁄210

Divide by mebi

TOMEBI

𝑋⁄220

Divide by gibi

TOGIBI

𝑋⁄230

Divide by tebi

TOTEBI

𝑋⁄240

Divide by pebi

TOPEBI

𝑋⁄250

Divide by exbi

TOEXBI

𝑋⁄260

Divide by zebi

TOZEBI

𝑋⁄270

Divide by yobi

TOYOBI

𝑋⁄280

6. Useful functions

6-7. Angle conversion
Angle conversions here:
Function

Keyword

Computation

Radian to degree

RTOD

180𝑋⁄𝜋

Radian to grace

RTOG

200𝑋⁄𝜋

Degree to radian

DTOR

𝜋𝑋⁄180

Degree to grade

DTOG

10𝑋⁄9

Grade to radian

GTOR

𝜋𝑋⁄200

Grade to degree

GTOD

9𝑋⁄10

Computation

6-8. Angle calculation
Complementary / supprementaly angle:
Function

Keyword

Complementary angle [1]

CANG

Complementary angle (Radian)

CANGR

𝜋 ⁄2 − 𝑋

Complementary angle (Degree)

CANGD

90 − 𝑋

Complementary angle (Grade)

CANGG

100 − 𝑋

Supplementary angle [1]

SANG

Supplementary angle (Radian)

SANGR

𝜋−𝑋

Supplementary angle (Degree)

SANGD

180 − 𝑋

Supplementary angle (Grade)

SANGG

200 − 𝑋

[1] Depends on angle mode

6-9. Ratio
Convert a rational number into two integers.
Function
Ratio

Keyword
RATIO

Computation
𝑌 ← 𝑁𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑋 ← 𝐷𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟

6. Useful functions

6-10. Random numbers
You can generate random numbers:
Function

Keyword

Computation

Random integer

RAND

Push Int

Random floating

FRAND

Push Flt

IMPORTANT
A random integer has 63 bits and random floating is generated from one.
The algorithm of random generator is mersenne twister.

6-11. Cast
You can cast data types:
Function

Keyword

Cast into integer

TOINT

Cast into floating

TOFLT

Cast into rational

TORAT

Cast into bool

TOBOOL

Cast into byte

TOBYTE

Cast into word

TOWORD

Cast into dword

TODWORD

Cast into qword

TOQWORD

Cast into word (Sign extend)

TOSWORD

Cast into dword (Sign extend)

TOSDWORD

Cast into qword (Sign extend)

TOSQWORD

IMPORTANT
You can approximate floating to rational with “cast into rational”.
The approximation is using continued fraction.

Computation

6. Useful functions

6-12. Calculations for engineers
These are useful calculations for engineers:
Function

Keyword

Computation
2𝜋𝑋

Multiply by 2𝜋

TPIX

Divide by 2𝜋

DTPI

𝑋⁄2𝜋
(𝑌 −1

+ 𝑋 −1 )−1

Parallel

PARA

To decibel

TODB

10 log10 |𝑋|

Decibel to

DBTO

1010

𝑋

6-13. Health calculations
These calculations are extras:
Function
Discomfort
index
Body mass
index

Keyword

Computation

DISCOM

0.81𝑌 − 0.01𝑋 × (0.99𝑌 − 14.3) + 46.3

BMI

𝑋⁄(𝑌⁄100)

7. Complex calculations

7. Complex calculations
7-1. Display of complex numbers
This software displays complex numbers as following:
Mode

Expression

Default

5 + 12𝑖

Euler
(degree)
Euler
(radian)
Euler
(grade)

Display
5 + i12

13∠67[deg]
13∠1.3[rad]
13∠75[gra]

13 exp(+i67.d)
13 exp(+i1.3)
13 exp(+0.37 Pi)
13 exp(+i75.g)

Type “EULER” or “EUL” to toggle Euler mode. If Euler mode is enabled, complex numbers are
shown as polar display.
The argument display depends on angle mode. Use the keywords “DEG”, “RAD” or “GRA” to
change angle mode.
If you select radian, you can convert the argument to 𝜋 radians. To switch the display, type “PIRAD”
or “PRAD”.
Function

Keyword
EULER

Euler display

EUL

Degree mode

DEG

Radian mode

RAD
GRAD

Grade mode

GRA
PIRAD

𝜋 radian mode

PRAD

When Euler display is on, even scalars are treated as complex numbers so its argument is displayed
if its value is not 0.

7. Complex calculations

7-2. How to make complex numbers
There are three ways to make complex numbers.
IMPORTANT
Real and imaginary part accept only scalars.
7-2-1. Input imaginary and add or subtract
Try to make “2+i3”.
Input> 2 i3 +
7-2-2. Make complex from real and imaginary part
Push real and imaginary part in turn and make complex. Use the keyword “MKCMP” or “MKC”
to make complex from rectangular.
Input> 2 3
#

TYPE

VALUE

4
Real.

Z
Y

Integer

TYPE

Imaginary.

Input> mkc
VALUE

4
Z

Complex

Y
X

Complex

2 + i3

generated.

7. Complex calculations

7-2-3. Make complex from absolute value and argument
Push absolute value and argument in turn and make complex. Use the keyword “MKE” to make
complex from polar.
This keyword depends on angle mode. For example, make 1.5∠30° in degree mode.
Input> 1.5 30
#

TYPE

VALUE

4
Absolute.

Z
Y

Floating

1.5

Integer

TYPE

Argument.

Input> mke
VALUE

4
Z

Complex

Y
X

Complex

1.29903811 + i0.75

Radian version is “MKER”.
Degree version is “MKED”.
Grade version is “MKEG”.

generated.

7. Complex calculations

You can generate complex with following keywords:
Function

Keyword
MKCMP

Make complex from rectangular

MKC

Computation

𝑌 + 𝑖𝑋

Make complex from polar

MKE

𝑌∠𝑋

Make complex from polar (radian)

MKER

𝑌∠𝑋[rad]

Make complex from polar (degree)

MKED

𝑌∠𝑋[deg]

Make complex from polar (grade)

MKEG

𝑌∠𝑋[gra]

7-3. Complex calculations
You can operate complex calculations:
Function

Keyword

Computation

Real part

Re(𝑋)

Imaginary part

Im(𝑋)

Complex argument

ARG

arg 𝑋

Complex argument (radian)

ARGR

arg 𝑋 [rad]

Complex argument (degree)

ARGD

arg 𝑋 [deg]

Complex argument (grade)

ARGG

arg 𝑋 [gra]

Complex conjugation

CONJ

conj(𝑋)

Complex magnitude is “ABS”.
EX 1 arg(1 + 𝑖2)

EX 3 conj(6 + 𝑖3)

Input> 1 2 mkc arg

Input> 6 3 mkc conj

EX 2 Re(15∠32°)
Input> 15 32 mked re

7. Complex calculations

7-4. Disassemble complex
You can disassemble complex numbers:
Function

Keyword

Real and imaginary

REIM

Magnitude and argument

MAGA

Magnitude and argument (radian)

MAGAR

Magnitude and argument (degree)

MAGAD

Magnitude and argument (grade)

MAGAG

EX 1 15∠32° to Re/Im part

This software supports complex functions:



Power, logarithm



Trigonometric functions



Hyperbolic functions

𝑋 ← Im(𝑋)
𝑌 ← |𝑋|
𝑋 ← arg 𝑋
𝑌 ← |𝑋|
𝑋 ← arg 𝑋 [rad]
𝑌 ← |𝑋|
𝑋 ← arg 𝑋 [deg]
𝑌 ← |𝑋|
𝑋 ← arg 𝑋 [gra]

Input> 5 3 mkc magad

7-5. Complex functions

Square root, cubic root

𝑌 ← Re(𝑋)

EX 2 5 + 𝑖3 to magnitude and arg (deg)

Input> 15 32 mked reim



Computation

Complex trigonometric functions are available only in radian.

8. Logical calculations

8. Logical calculations
8-1. Unsigned decimal and Boolean
This software displays unsigned decimal and Boolean as following:
Type/mode

Value

Boolean

Display

TRUE

FALSE

Binary mode

255

0b11111111

Octal mode

255

0377

Signed decimal mode

255

-1

Unsigned decimal mode

255

Hexadecimal mode

255

0xFF

8-2. Bit length
You can operate logical calculations in calculation mode.
This software supports 8, 16, 32, 64 bits. The bit length setting is shown in the display.
Switch the mode to change the bit length.
Mode
8-bit mode
(byte)
16-bit mode
(word)
32-bit mode
(dword)
64-bit mode
(qword)

Keyword

Symbol

BYTE

(Byte)

WORD

(Word)

DWORD

(Dword)

QWORD

(Qword)

Set bit length and the bit length symbol changes.
Please notice that if you input too large value for selected bit length, the software masks its lower
N-bit (N is selected length) and push the result.

8. Logical calculations

8-3. N-ary number switching
You can find N-ary number mode in the display.
Use the keywords to switch N-ary number display mode:
Mode

Keyword

Symbol

Binary display

BIN

(Bin)

Octal display

OCT

(Oct)

Signed decimal display

SDEC

(Sdec)

Unsigned decimal display

UDEC

(Udec)

Hexadecimal display

HEX

(Hex)

Set N-ary and the N-ary symbol changes.

8-4. Input binary and Boolean
Input value as binary (unsigned integer) to operate logical calculations.
Boolean:

True value is “TRUE” or “T” and false value is “FALSE” or “F”.

Unsigned:

Type "u" and postfix non-signed integer.

Binary:

Type “0b” and postfix binary expression using 0 and 1.

Octal value:

Type “0o” and postfix octal expression using 0 to 7.

Hex value:

Type “0x” and postfix hexadecimal expression using 0 to 9 and A to F.

The input data is shown as selected N-ary display mode. For example, input binary “0b1010” and
the display is “0x0000000A” in hexadecimal mode.
Input> 0b1010
#

TYPE

VALUE

4
Z
Y
X

Dword

0x0000000A

You can push binaries and Booleans at one time.

8. Logical calculations

Input> t f
#

TYPE

VALUE

4
Z

Dword

0x0000000A

Boolean

8-5. Fundamental logical calculations
Here is the list of fundamental logical calculations:
Function
Bitwise NOT
Bitwise AND
Bitwise OR

Keyword
NOT
~
AND
&
OR
|

Computation

𝑋̅

𝑌∧𝑋

𝑌∨𝑋

Bitwise XOR

XOR

𝑌⊕𝑋

Bitwise NAND

NAND

̅̅̅̅̅̅̅
𝑌∧𝑋

Bitwise NOR

NOR

̅̅̅̅̅̅̅
𝑌∨𝑋

EX 1 0x1234 & 0b0111

EX 2 not(65535)

Input> 0x1234 0b0111 and

Input> u65535 not

8. Logical calculations

8-6. Bit shift
Bit shifts are here:
Function

Keyword
SHL

Shift left

<<
SHR

Shift logical right

Shift arithmetic right

SAR
>>>

Computation

X << 1

X >> 1

X >>> 1

Shift Left (N times)

SHLC

X << N

Shift Right (N times)

SHRC

X >> N

SARC

X >>> N

Shift byte left

SBL

X << 8

Shift byte right

SBR

X >> 8

Shift nibble left

SNL

X << 4

Shift nibble right

SNR

X >> 4

Shift Arithmetic
Right (N times)

EX 1 0x1234 & 0b0111

EX 2 not(65535)

Input> 0x1234 0b0111 and

Input> u65535 not

8-7. Rotate
Bit rotates are here:
Function

Keyword

Computation

Rotate left

ROL

Rotate X Left

Rotate right

ROR

Rotate X Right

rol(31)
Input> u31 rol

8. Logical calculations

8-8. Other functions that support unsigned integer
Function
Increment
Decrement

Keyword
INC
++
DEC
-ADD

Add

Subtract
Multiply
Divide
Negate

SUB
MUL
*
DIV
/
NEG
PM

Computation

𝑋+1

𝑋−1

𝑌+𝑋

𝑌−𝑋

𝑌×𝑋

𝑌 ⁄𝑋

−𝑋

IMPORTANT
The addition of 2 Booleans is XOR, and the multiplication of 2 Booleans is AND. If you increment
Boolean, the result is always true.

8-9. Whole-stack logical calcultions
You can operate logical calculations for whole-stack.
Function

Keyword

Computation

All AND

ALLAND

N>1

𝑥1 ∧ 𝑥2 …

All OR

ALLOR

N>1

𝑥1 ∨ 𝑥2 …

All XOR

ALLXOR

N>1

𝑥1 ⊕ 𝑥2 …

9. Vector calculations

9. Vector calculations
9-1. Display of vectors
This software displays vectors as following:
Type

Math expr.

Horizontal [Row]

[1 2 3]
3
(2)
1

Vertical (Col)

Display
[1, 2, 3]
(3, 2, 1)

9-2. Making of vector
You can include scalars, complex numbers or even binaries in vectors.
The input of vectors is complicated. I recommend using register function. Please read chapter 11 to
get more information.
You can make vector with the following keywords:
Function

Keyword

Computation

Make row tuple

MRTUP

Push Tup.R

Make column tuple

MCTUP

Push Tup.C

There are three steps for making a vector:
1. Push elements of a vector
… Push data in turn.
2. Push the number of elements the vector contains
… Set the dimension of the vector.
3. Call making function
… The vector is pushed.
NOTICE
You can include integers, floatings, rationals, complexes, Booleans and unsigned integers in a vector.

9. Vector calculations

So, let us make row tuple [1 + 𝑖2 6].
(1) Push elements
Input> 1 2 mkc 6
#

TYPE

VALUE

4
Z
Y

Complex

1 + i2

Integer

Push in turn.

(2) Push number of elements
Input> 2
#

TYPE

VALUE

4
Z

Complex

1 + i2

Integer

TYPE

Dimension.

(3) Make row tuple
Input> mrtup
VALUE

4
Z
Make row

Y
X

Tuple[Row]

[1 + i2, 6]

Making column tuple is similar with this case.

tuple.

9. Vector calculations

You can make unit vectors easily.
Function

Keyword

Computation

Make row unit tuple

MRUTUP

Push Tup.R

Make column unit tuple

MCUTUP

Push Tup.C

These functions requires 2 arguments: a dimension and a position.
1. Push a integer as a dimension
2. Push a integer as a position (starting with 1)
3. Call making function
Make (0 1 0).
(1) Push the dimension
Input> 3
#

TYPE

VALUE

4
Z
Y
X

Integer

TYPE

Dimension.

(2) Push the position
Input> 2
VALUE

4
Z
Y

Integer

Position.

9. Vector calculations

(3) Make column unit tuple
Input> mcutup
#

TYPE

VALUE

4
Z
Y
X

Tuple(Col)

(0, 1, 0)

Generated.

9-3. Extract element from tuple
Use the keyword “TGET” to extract one element from a tuple.
Please make sure Y is a tuple and X is an integer as a position (starting with 1) to extract.
Function
Get element from tuple

Keyword
TGET

Computation

Extract

This function drops 2 data, so the vector from that you extract is dropped. I recommend storing the
tuple to a register and call to extract.
Please read chapter 11 to make comprehension of using register function.
You can crave a tuple into elements.
Function
Crave up

Keyword
CUT
CRAVE

The used tuple is dropped and the extracted elements are pushed in turn.

Computation

9. Vector calculations

Let us extract the second element from (6 9 12).
(0) Make sure that the tuple exists
#

TYPE

VALUE

4
Z
Y
X

Tuple[Col]

TYPE

(6, 9, 12)

(1) Set a position.
Input> 2
VALUE

4
Z
Y

Tuple[Col]

Integer

TYPE

(6, 9, 12)
2

Position.

(2) Extract
Input> tget
VALUE

4
Z
Y
X

Integer

Extracted.

9. Vector calculations

9-4. Four arithmetics of vectors
The four aritmetics keywords of vectors are same as those of scalars.
EX 1 (3 2 1) + (5 6 9)

EX 2 (3 2 1) × 9

Input> 3 2 1 3 mctup

Input> 3 2 1 3 mctup 9 *

Input> 5 6 9 3 mctup
Input> +
Please check that the calculations are defined.

9-5. Inner / outer product
Use the keywords to calculate inner / outer product:
Function
Inner product
Outer product

Keyword
INNER
DOT
OUTER
CROSS

Computation

⃗ ∙𝑋
𝑌

⃗ ×𝑋
𝑌

Outer product suppots only 3-dimensional tuples.
EX 1 (3 2 1) ∙ (7 8 9)

EX 2 (1 2 3) × (4 5 6)

Input> 3 2 1 3 mctup

Input> 1 2 3 3 mctup

Input> 7 8 9 3 mctup

Input> 4 5 6 3 mctup

Input> dot

Input> cross

9. Vector calculations

9-6. Norms of vectors
Here is the keywords of norms of vectors:
Function

Computation

NORM

√∑

Euclid norm squared

NSQ

∑

Lp-norm

PNORM

Euclid norm

Max norm

Keyword

MAXNORM

(∑

∞

|𝑥𝑖 |2

𝑖=1

∞

|𝑥𝑖 |2

𝑖=1

1⁄𝑥

|𝑦𝑖 |𝑥 )

𝑖=1

max(|𝑥1 |, |𝑥2 | … , |𝑥𝑛 |)

Euclid norm, Euclid norm squared ana maxnorm require one vector.
For example, type following to find the Euclid norm of [3 5 7]:
Input> 3 5 7 mrtup norm
Lp-norm requires one vector and an integer as a dimension.
Type following to find the third norm of [7 8 9]:
Input> 7 8 9 3 mrtup 3 pnorm

9-7. Transpose vectors
Use the keyword “TRANS” to transpose vectors.
Function
Transpose

Keyword
TRANS

This function supports matrices.

Computation

𝑋𝑇

10. Matrix calculations

10. Matrix calculations
10-1. Display of matrices
This software handles matrices as tuples of row tuples.
Math expr.
1 2 3
[4 5 6]
7 8 9

Display
[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

10-2. Making of matrices
This software supports matrix calculations. Matrices of this software can include scalars, complexes,
Booleans and unsigned integers.
The input of matrices is complicated. I recommend using register function. Please read chapter 11
to get more information.
Use the keyword “MKMAT” to make a matrix.
Function
Make matrix

Keyword
MKMAT

Computation

Push Mat

There are three steps for making a vector:
1. Prepare same dimensional and directional vectors.
…Make sure vectors are all row or all column.
2. Push an integer as a number of vectors.
…The integer must be greater than zero.
3. Call making function
…Make a matrix from vectors.
NOTICE
Matrices include row tuples. The data types that tuples cannot include are not supported in matrices.

10. Matrix calculations

Let us input matrix 𝐴:

1 2
𝐴=[
]
3 4

(1-1) Make two row vectors
Input> 1 2 2 mrtup 3 4 2 mrtup
#

TYPE

VALUE

4
Z
Y

Tuple[Row]

[1, 2]

Tuple[Row]

[3, 4]

Added in turn.

(1-2) Set a number of vectors
Input> 2
#

TYPE

VALUE

4
Z

Tuple[Row]

[1, 2]

Tuple[Row]

[3, 4]

Integer

TYPE

Number.

(1-3) Make matrix
Input> mkmat
VALUE

4
Z
Y
X

Matrix

[[1, 2], [3, 4]]

Generated.

10. Matrix calculations

(2-1) Push two column tuple
Input> 1 3 2 mctup 2 4 2 mctup
#

TYPE

VALUE

4
Z
Y

Tuple(Col)

(1, 3)

Tuple(Col)

(2, 4)

Pushed in
turn.

(2-2) Set a number of vectors
Input> 2
#

TYPE

VALUE

4
Z

Tuple(Col)

(1, 3)

Tuple(Col)

(2, 4)

Integer

TYPE

Number.

(2-3) Make matrix
Input> mkmat
VALUE

4
Z
Y
X

Matrix

[[1, 2], [3, 4]]

Make sure the sizes and directions of all vectors to make a matrix are same.

Generated.

10. Matrix calculations

You can make a unit matrix easily. Use the keyword “MKUMAT”.
Function
Make unit matrix

Keyword
MKUMAT

Computation

Push Mat

Set an integer as a dimension and call the function. For instance, input this to make 3-dim unit
matrix:
Input> 3 mkumat

10-3. Get element or tuple from matrix
Get a tuple or a element from matrix to use following keywords:
Function

Keyword

Computation

Get element from matrix

MGET

Extract

Get row tuple from matrix

MGETR

Extract

Get column tuple from matrix

MGETC

Extract

These functions drop a matrix. I recommend using register function.
Please read chapter 11 to get more information about registers.
You can crave up matrices.
Function
Crave up

Keyword
CUT
CRAVE

Computation

A matrix is craved up into row tuples and they are pushed in turn.
Go on to the next pages to get usages of “MGET”, “MGETR” and “MGETC”.

10. Matrix calculations

10-3-1. Get element from matrix
Use the keyword “MGET” to get an element from a matrix.
Make sure Z is matrix, Y is position i, X is position j. The position counting starts with 1.
Try to extract element (1, 2) from matrix [[1, 2], [3, 4]].
(0) Matrix is pushed
#

TYPE

VALUE

4
Z
Y
X

Matrix

[[1, 2], [3, 4]]

(1) Select a position of an element
Input> 1 2
#

TYPE

VALUE

Position i.

Matrix

[[1, 2], [3, 4]]

Integer

Position j.

(2) Get an element from matrix
Input> mget
#

TYPE

VALUE

4
Z
Y
X

Integer

Extracted.

10. Matrix calculations

10-3-2. Get tuple from matrix
You can get a tuple from a matrix. “MGETR” is the row tuple version and “MGETC” is the
column tuple version.
Make sure Y is matrix and X is position. The position counting starts with 1.
Try to extract second column tuple from [[1, 2], [3, 4]].
(0) Matrix is pushed
#

TYPE

VALUE

4
Z
Y
X

Matrix

[[1, 2], [3, 4]]

(1) Select a position
Input> 2
#

TYPE

VALUE

4
Z
Y

Matrix

Integer

[[1, 2], [3, 4]]
2

Position.

(2) Get a column tuple from matrix
Input> mgetc
#

TYPE

VALUE

4
Z
Y
X

Tuple(Col)

(2, 4)

Extracted.

10. Matrix calculations

10-4. Four arithmetics of matrices
The four arithmetics keywords are similar with those of scalars.
EX 1
3 7
2 6
[
]−[
]
9 5
2 4
Input> 3 7 2 mrtup 9 5 2 mrtup 2 mkmat
Input> 2 6 2 mrtup 2 4 2 mrtup 2 mkmat
Input> EX 2
1 2 5
[
]( )
3 4 6
Input> 1 2 2 mrtup 3 4 2 mrtup 2 mkmat
Input> 5 6 2 mctup
Input> *

10. Matrix calculations

10-5. Determinant and inverse matrix
Here is determinant and finding inverse matrix:
Function

Keyword

Computation

Determinant

DET

det 𝑋

Invert

INV

𝑋 −1

These functions support only square matrices. You cannot find inverse matrix of A if the determinant
of A is zero.
EX
−1

1
[√2
]
1 √2

Input> 2 sqrt 1 2 mrtup 1 2 sqrt 2 mrtup 2 mkmat inv

10-6. Transpose matrix
Here is the list of transpose functions:
Function
Transpose

Keyword
TRANS

Hermitian transpose

HTRANS
HCONJ

Computation

𝑋𝑇

conj(𝑋 𝑇 )

Hermitian transpose function transposes matrix or vector and conjugate each element in it.

10-7. Other matrix functions
Here is the list of other matrix functions:
Function
Trace

Keyword
TRACE

Trace function supports only square matrices.

Computation

tr(𝑋)

11. Register operations

11. Register operations
11-1. What is register
A register is kind of a memory. Each register in this software is independent of the stack. You can
calculate more quickly with register function. There are 26 registers: RA ~ RZ.

You can store one data to each register and can load or delete any time.
Even if the stack is changed or cleared, the registers keep on.
Registers can hold any data: scalars, vectors, errors even strings.
This manual uses following tables:
#

TYPE

VALUE
Registers

RA ~ RZ.

RB
Z
Y
X
This table shows X, Y and Z in a stack and RA and RB in registers.

11. Register operations

11-2. Register display
Type “REGISTER” or “REG” to switch register display.
If register display is enabled, the symbol [Reg] is displayed.
You can change display page of registers:
Function

Keyword
REGISTER

Switch register display

REG
REGNEXT

Next page of registers

Previous page of registers

REGPREV
RP
REGFIRST

First page of registers

See also chapter 3 and chapter 4.
IMPORTANT
Switching register display function and register page changing functions do not affect registers. So
you can use registers without displaying registers.

11. Register operations

11-3. Store to selected register
You can store X to selected register. Then X is dropped.
Use the following keywords to storing functions:
Function

Keyword

Store to RA

STRA

Store to RB

STRB

…

Store to RZ

STRZ

Use the format “STR?” and replace “?” by one alphabet.
Let us store the integer 5 to RA.
(1) Push
Input> 5
#

TYPE

VALUE

RA
RB
Z
Store from

Y
X

Integer

TYPE

only X.

(2) Store to RA
Input> stra

VALUE

Integer

RB
Z
Y
X

Stored.

11. Register operations

If the selected register has data, the data is overwritten.
(1) Initial state
#

VALUE

Already

Integer

stored.

Integer

TYPE

RB
Z
Y

(2) Push
Input> 9

VALUE

Integer

Store from

Integer

only X.

TYPE

RB
Z

(3) Overwrite RA
Input> stra

VALUE

Integer

RB
Z
Y
X

Cases of RB - RZ are similar with this.

Overwritten

11. Register operations

11-4. Load from selected register
You can load from selected register to X. The selected register keeps its data. If it has no data, error
message is displayed.
Use the following keywors to load:
Function

Keyword

Load RA

LDRA

Load RB

LDRB

…

Load RZ

LDRZ

Use the format “LDR?” and replace “?” by one alphabet.
Try to add RA and RB.
(1) Initial state
#

TYPE

VALUE

Integer

Stored.

Z
Y
X
(2) Load RA
Input> ldra
#

TYPE

VALUE

Integer

Z
Load RA

Y
X

Integer

to X.

11. Register operations

(3) Load RB
Input> ldrb
#

TYPE

VALUE

Integer

TYPE

Load RB
to X.

(4) Add
Input> +
VALUE

Integer

Z
Addition

Y
X

Integer

Cases of RC ~ RZ are similar with this.

requires 2.

11. Register operations

11-5. Delete selected register
You can remove data in selected register.
Use the following keywords to delete selected register:
Function

Keyword

Delete RA

DELRA

Delete RB

DELRB

…

Delete RZ

DELRZ

Use the format “DELR?” and replace “?” by one alphabet.
(1) Initial state
#

TYPE

VALUE

Integer

Stored.

Z
Y
X
(2) RA をデリート
Input> delra
#

TYPE

VALUE

RA
RB

Deleted.
Integer

Z
Y
X

11. Register operations

11-6. Register calculation
You can calculate with selected register and store the result to it.
Here is the list of register calculations:
Function
Register increment
Register decrement

Keyword
IR?
++R?
DR?
--R?
ADDR?

+R?

SUBR?
-R?
MULR?
*R?
DIVR?

/R?

Computation

𝑅 ←𝑅+1

𝑅 ←𝑅−1

𝑅 ←𝑅+𝑋

𝑅 ←𝑅−𝑋

𝑅 ←𝑅×𝑋

𝑅 ← 𝑅 ⁄𝑋

Operate register calculations to drop one data and overwrite selected register with the result.
Example: register addition and register increment
(1) Initial state
#

TYPE

VALUE

Integer

Z
Y
X

Stored.

11. Register operations

(2) Increment RA
Input> ira
#

TYPE

VALUE

Integer

Incremented.

Z
Y
X
(3) Push
Input> 1.2
#

TYPE

VALUE

Integer

Z
Operate with

Y
X

Floating

TYPE

1.2

(4) Increment RB
Input> +rb
VALUE

Integer

Floating

5.2

Z
Y
X

Added.

11. Register operations

11-7. Register clear
You can clear all registers:
Function
Register clear

Keyword
REGCLEAR
RCLR

Computation

If you would like to delte one or some registers, use delete functions.
IMPORTANT
You can clear registers and stack with the keyword “AC”. It is all clear function.

11-8. Strings and registers
The registers accept strings. You can put a landmark to registers with strings.
The macro and registers combo is very affective.
See also chapter 15.

12. Stack operations

12. Stack operations
12-1. Special stack operations
You can remove, insert or duplicate data or change the order of elements in the stack.
There are many special stack operations.

12-2. Fundamental stack operations
Here is the list of fundamental stack operations:
Function
Drop

Keyword
DROP
¥

N>0

COPY
Duplicate [1]

C
DUP

Clear

CLEAR
CLR

[1] Press enter without any input to call the function

12-3. Order changing functions
Here is the list of order changing functions:
Function
Swap

Keyword
SWAP
$

Rotate

ROT

Unrotate

UNROT

Roll

ROLL

Roll D

ROLLD

The details are next pages:

12. Stack operations

12-3-1. Swap
Swap function swaps 2 data at bottom of the stack. This function requires 2 arguments.
The keywords are “SWAP” and “$”.
(1) Initial state
#

TYPE

VALUE

4
Z

Integer

256

Integer

Rational

9/4

(2) Swap
Input> swap
#

TYPE

VALUE

4
Z

Integer

256

Rational

9/4

Integer

12. Stack operations

12-3-2. Rotate
Rotate function rotates Z, Y and X. This function requires 3 arguments.
𝑍
𝑌
(𝑌 ) → (𝑋)
𝑋
𝑍
The keyword is “ROT”.
(1) Initial state
#

TYPE

VALUE

4
Z

Integer

256

Integer

Rational

TYPE

9/4

(2) Rotate
Input> rot
VALUE

4
Z

Integer

256

Rational

9/4

Integer

12. Stack operations

12-3-3. Unrotate
Rotate function rotates Z, Y and X reversely. This function requires 3 arguments.
𝑍
𝑋
(𝑌 ) → ( 𝑍 )
𝑋
𝑌
The keyword is “UNROT”.
12-3-4. Roll
Roll function rotates data from selected position through X. The selected data is moved to X.
The keyword is “ROLL”.
(1) Initial state
#

TYPE

VALUE

4
Z

Integer

256

Integer

Rational

TYPE

Integer

256

Rational

9/4

Integer

9/4

(2) Set a position
Input> 3
VALUE

12. Stack operations

(3) Roll
Input> roll
#

TYPE

VALUE

4
Z

Integer

Rational

9/4

Integer

256

12-3-5. Roll D
Roll function rotates data from selected position through X reversely. X is moved to selected
position.
The keyword is “ROLLD”.

12. Stack operations

12-4. Duplicate and overwrite functions
Here is the list of duplicate and overwrite functions:
Function

Keyword
OVER

Over

Pick

PICK

Unpick

UNPICK

XY
Duplicate last 2 items

YX
DUP2
DUPDUP

Duplicate twice

Duplicate last N-1 items and push N
The details are next pages:

NDUPN

12. Stack operations

12-4-1. Over
Over function duplicates Y and push it.
The keywords are “OVER” and “O”.
(1) Initial state
#

TYPE

VALUE

4
Z
Y

Integer

TYPE

(2) Over
Input> o
VALUE

4
Z

Integer

12. Stack operations

12-4-2. Pick
Pick function duplicates data in selected position.
The keyword is “PICK”.
(1) Initial state
#

TYPE

VALUE

4
Z

Integer

256

Integer

Rational

TYPE

Integer

256

Integer

Rational

Integer

9/4

(2) Set a position
Input> 3
VALUE

9/4
3

(3) Pick
Input> pick
#

TYPE

VALUE

Integer

256

Integer

Rational

9/4

Integer

256

12. Stack operations

12-4-3. Unpick
Unpick function replaces data in selected position X by Y.
The keyword is “UNPICK”.
(1) Initial state
#

TYPE

VALUE

4
Z
Y

Integer

256

Integer

TYPE

(2) Push
Input> 64
VALUE

4
Z

Integer

256

Integer

TYPE

Integer

256

Integer

(3) Push a position
Input> 2
VALUE

12. Stack operations

(4) Unpick
Input> unpick
#

TYPE

VALUE

4
Z
Y

Integer

12-4-4. Duplicate last 2 items
Duplicate last 2 items function duplicates Y and X and push them in turn.
The keywords are “XY”, “YX” and “DUP2”.
(1) Initial state
#

TYPE

VALUE

4
Z
Y

Integer

(2) Duplicate last 2 items
Input> xy
#

TYPE

VALUE

Integer

12-4-5. Duplicate twice
Duplicate twice function operate duplicate function twice. The keywords are “dupdup” and
“dd”.

12. Stack operations

12-4-6. Duplicate last N-1 items and push N
Duplicate last N-1 items and push N function drops X and duplicate Y X times and then push
X.
The keyword is “NDUPN”.
(1) Initial state
#

TYPE

VALUE

4
Z
Y

Integer

(2) Set a number of items
Input> 2
#

TYPE

VALUE

4
Z

Integer

(3) Duplicate last N-1 items and push N
Input> ndupn
#

TYPE

VALUE

Integer

100

12. Stack operations

12-5. Removal functions
Here is the list of removal functions:
Function

Keyword
DROP2

Drop 2 items

¥¥
DROP3

Drop 3 items

¥¥¥

N+1

Drop N items

DROPN

Nip

NIP

Nip N-th item

NIPN

The details are here:
12-5-1. Drop 2 items
Drop 2 items function drops 2 items.
The keywords are “DROP2” and “¥¥”.
12-5-2. Drop 3 items
Drop 3 items function drops 3 items.
The keywords are “DROP3” and “¥¥¥”.

101

12. Stack operations

12-5-3. Drop N items
Drop N items function drops X + 1 items.
The keyword is “DROPN”.
(1) Initial state
#

TYPE

VALUE

4
Z

Integer

256

Integer

Rational

9/4

(2) Push a number of items to drop
Input> 2
#

TYPE

VALUE

Integer

256

Integer

Rational

Integer

9/4
2

(3) Drop N items
Input> dropn
#

TYPE

VALUE

4
Z
Y
X

Integer

256

102

12. Stack operations

12-5-4. Nip
Nip function removes Y.
The keyword is “NIP”.
(1) Initial state
#

TYPE

VALUE

4
Z
Y

Integer

TYPE

(2) Nip
Input> nip
VALUE

4
Z
Y
X

Integer

103

12. Stack operations

12-5-5. Nip N-th item
Nip N function removes data in the position X-1.
The keyword is “NIPN”.
(1) Initial state
#

TYPE

VALUE

4
Z

Integer

TYPE

Integer

(2) Set a position
Input> 3
VALUE

(3) Nip N
Input> nipn
#

TYPE

VALUE

4
Z
Y

Integer

104

12. Stack operations

12-6. Other stack operations
Here is the list of ther stack operations:
Function

Keyword

Number of stack items

DEPTH

Number of stack items function pushes the number of data in stack.

105

13. Unit conversions

13. Unit conversions
IMPORTANT
See also chapter 6 to get more information about conversions.

13-1. Supporting units
This software supports the units as following:


length



volume



mass



pressure



inv of length



inv of volume



velocity



energy



area



time



acceleration



temperature



inv of area



inv of time



force

NOTICE
These conversion functions support only scalars.

13-2. How to use unit conversion function
Type “CONV” or “CV” to call unit conversion. Then type 2 units to convert. The keyword “REC” calls
previous conversion.
Function
Unit conversion
Unit conversion (redo)

Keyword
CONV
CV
REC

Computation

Unit conversion

You can convert X with calling the function and type “from unit” and “to unit”.
For example, type this to convert inches into centimeter.
Input> conv in cm
IMPORTANT
If the each unit has different dimension, the combination is error.

106

13. Unit conversions

13-3. Units of length
Here is the list of units of length:
Unit

Keyword

Ratio

Meter

[m]

Kilometer

[km]

1 E+03

Centimeter

[cm]

1 E-02

Millimeter

[mm]

1 E-03

Nautical mile [1]

[nmi]

NMI

1 852

Yard [1]

[yd]

0.914 4

Feet [1]

[ft]

0.304 8

Inch [1]

[in]

0.025 4

Mile [1]

[mi]

1 609.344

Fathom [2]

[fath]

FATH

1.828 8

Shaku [3]

SHAKU

Sun [3]

SUN

1/33

Ken [3]

KEN

20/11

Jou [3]

JOU

100/33

Chou [3]

CHOU

1200/11

Ri [3]

[1] International unit
[2] British fathom
[3] These are Japanese traditional units.

107

10/33

43200/11

13. Unit conversions

13-4. Units of length inverse
Here is the list of units of length inverse:
Unit

Keyword

Ratio

Per meter

[1⁄m]

Per kilometer

[1⁄km]

/KM

1 E-03

Per centimeter

[1⁄cm]

/CM

1 E+02

Per millimeter

[1⁄mm]

/MM

1 E+03

Per nautical mile

[1⁄nmi]

/NMI

1/1852

Per yard

[1⁄yd]

/YD

1250/1143

Per feet

[1⁄ft]

/FT

1250/381

Per inch

[1⁄in]

/IN

5000/127

Per mile

[1⁄mi]

/MI

125/201168

Per fathom

[1⁄fath]

/FATH

625/1143

Per Shaku

/SHAKU

Per Sun

/SUN

Per Ken

/KEN

0.55

Per Jou

/JOU

0.33

Per Chou

/CHOU

Per Ri

/RI

108

3.3

11/1200
11/43200

13. Unit conversions

13-5. Units of area
Here is the list of units of area:
Unit

Keyword

Ratio

Square meter

[m2 ]

Square kilometer

[km2 ]

KM2

1 E+06

Square centimeter

[cm2 ]

CM2

1 E-04

Square millimeter

[mm2 ]

MM2

1 E-06

Are

[a]

ARE

1 E+02

Hectare

[ha]

1 E+04

Acre

[ac]

ACRE

Square yard

[yd2 ]

YD2

0.836 127 36

Square feet

[ft 2 ]

FT2

9.290 304 E-02

Square inch

[in2 ]

IN2

6.451 6 E-04

Square mile

[mi2 ]

MI2

2 589 988.110 336

4 046.856 422 4

Tsubo

TSUBO

Isse

ISSE

12000/121

Ittan

ITTAN

120000/121

Choubu

CHOUBU

1200000/121

109

400/121

13. Unit conversions

13-6. Units of are inverse
Here is the list of units of area inverse:
Unit

Keyword

Ratio

Per square meter

[1⁄m2 ]

/M2

Per square kilometer

[1⁄km2 ]

/KM2

1 E-06

Per square centimeter

[1⁄cm

/CM2

1 E+04

Per square millimeter

[1⁄mm2 ]

/MM2

1 E+06

Per are

[1⁄a]

/ARE

1 E-02

Per hectare

[1⁄ha]

/HA

1 E-04

Per acre

[1⁄ac]

/ACRE

78125/316160658

Per square yard

[1⁄yd

/YD2

1562500/1306449

Per square feet

[1⁄ft 2 ]

/FT2

1562500/145161

Per square inch

[1⁄in2 ]

/IN2

25000000/16129

Per square mile

/MI2

15625/40468564224

[1⁄mi

Per Tsubo

/TSUBO

Per Isse

/ISSE

121/12000

Per Ittan

/ITTAN

121/120000

Per Choubu

/CHOUBU

121/1200000

110

121/400

13. Unit conversions

13-7. Units of volume
Here is the list of units of volume:
Unit

Keyword

Ratio

Cubic meter

[m3 ]

Cubic kilometer

[km3 ]

KM3

1 E+09

Cubic centimeter

[cm3 ]

CM3

1 E-06

Cubic millimeter

[mm3 ]

MM3

1 E-09

[L]

1 E-03

Deciliter

[dL]

1 E-04

Kilolitter

[kL]

Millilitter

[mL]

1 E-06

Cubic yard

[yd3 ]

YD3

0.764 554 857 984

Cubic feet

[ft 3 ]

FT3

0.028 316 846 592

Cubic inch

[in3 ]

IN3

1.638 706 4 E−05

Cubic mile

[mi3 ]

MI3

4 168 181 825.440 579 584

Imperial gallon

[galimp ]

IMG

4.546 09 E-03

US gallon

[galus ]

USG

3.785 411 784 E-03

Gou

GOU

2401/13310000

Shou

SHOU

2401/1331000

Itto

ITTO

2401/133100

Koku

KOKU

2401/13310

Litter
(Cubic decimeter)

111

13. Unit conversions

13-8. Units of volume inverse
Here is the list of units of volume inverse:
Unit

Keyword

Ratio

Per cubic meter

[1⁄m3 ]

/M3

Per cubic kilometer

[1⁄km3 ]

/KM3

1 E-09

Per cubic centimeter

[1⁄cm

/CM3

1 E+06

Per cubic millimeter

[1⁄mm3 ]

/MM3

1 E+09

[1⁄L]

1 E+03

Per deciliter

[1⁄dL]

/DL

1 E+04

Per kilolitter

[1⁄kL]

/KL

Per millilitter

[1⁄mL]

/ML

1 E+06

Per cubic yard

[1⁄yd3 ]

/YD3

1953125000/1493271207

Per cubic feet

[1⁄ft3 ]

/FT3

1953125000/55306341

Per cubic inch

[1⁄in3 ]

/IN3

125000000000/2048383

Per cubic mile

/MI3

1953125/8140980127813632

Per litter
(Per cubic decimeter)

[1⁄mi

Per imperial gallon

[1⁄galimp ]

/IMG

100000000/454609

Per US gallon

[1⁄galus ]

/USG

125000000000/473176473

Per Gou

/GOU

13310000/2401

Per Shou

/SHOU

1331000/2401

Per Itto

/ITTO

133100/2401

Per Koku

/KOKU

13310/2401

112

13. Unit conversions

13-9. Units of time
Here is the list of units of time:
Unit

Keyword

Ratio

Second

[s]

SEC

Minute

[min]

MIN

Hour

[h]

HOUR

3 600

Day

[d]

DAY

86 400

Week

[wk]

WEEK

604 800

Normal year

[yr]

YEAR

31 536 000

Gregolian year

GYEAR

31 556 952

Julian year

JYEAR

31 557 600

13-10. Units of time inverse
Here is the list of units of time inverse:
Unit

Keyword

Per second

[1⁄s]

Per minute

[1⁄min]

Per hour

[1⁄h]

Per day

[1⁄d]

Per week

[1⁄wk]

Per normal year

[1⁄yr]

/SEC
/S
/MIN
/HOUR
/H
/DAY
/D
/WEEK
/WK
/YEAR
/YR

Ratio
1
1/60
1/3600

1/86400
1/604800
1/31536000

Per Gregolian year

/GYEAR

1/31556952

Per Julian year

/JYEAR

1/31557600

113

13. Unit conversions

13-11. Units of mass
Here is the list of units of mass:
Unit

Keyword

Ratio

Kilogram

[kg]

Gram

[g]

1 E-03

Milligram

[mg]

1 E-06

Metric ton

[t]

TON

1 E+03

Long ton

[l. t. ]

LTON

1 016.046 908 8

Short ton

[s. t. ]

STON

907.184 74

Ounce

[oz av]

0.028 349 523 125

Pound

[lb av]

0.453 592 37

Kan

KAN

Ryou

RYOU

3.75 E-02

Momme

MOMME

3.75 E-03

Kin

KIN

3.75

0.6

13-12. Units of velocity
Here is the list of units of velocity:
Unit

Keyword

Meter per second

[m⁄s]

Meter per minute

[m⁄min]

M/MIN

Kilometer per second

[km⁄s]

KM/S

Kilometer per hour

[km⁄h]

M/S

KM/H
KPH

Ratio
1
1/60
1 E+03
5/18

Inch per second

[ips]

IPS

0.025 4

Feet per second

[fps]

FPS

0.304 8

[mph]

MPH

0.447 04

[kn]

463/900

Mile per hour
Knot
(Nautical mile per hour)

114

13. Unit conversions

13-13. Units of acceleration
Here is the list of units of acceleration:
Unit

Keyword
[m⁄s2 ]

Meter per second per second
Kilometer per hour per second

[km⁄h⁄s]

Gal / Galileo

Ratio

M/S2
KM/H/S
KPH/S

1
5/18

[Gal]

GAL

1 E-02

Inch per second per second

[ips 2 ]

IPS2

0.025 4

Feet per second per second

[fps2 ]

FPS2

0.304 8

[mph⁄s]

MPH/S

0.447 04

[kn⁄s]

KN/S

463/900

(Centimeter per second per second)

Mile per hour per second
Knot per second
(Nautical mile per hour per second)

13-14. Units of force
Here is the list of units of force:
Unit

Keyword

Newton
(Kilogram meter per second per second)

Dynne

[N]

NEWTON

Ratio
1

[dyn]

DYN

1 E-05

Kilogram weight

[kgf]

KGF

9.806 65

Gram weight

[gf]

(Gram centimeter per second per second)

115

9.806 65
E-03

13. Unit conversions

13-15. Units of pressure
Here is the list of units of pressure:
Unit

Keyword

Pascal

Ratio

[Pa]

Hectopascal

[hPa]

HPA

1 E+02

Kilopascal

[kPa]

KPA

1 E+03

Megapascal

[MPa]

MPA

1 E+06

[bar]

BAR

1 E+05

[mmHg]

MMHG

101325/760

[inHg]

INHG

3 386.388 64

(Newton per square meter)

Bar
(Megadyne per square centimeter)

Millimeter of mercury
Inch of mercury

13-16. Units of energy
Here is the list of units of energy:
Unit
Joule

Keyword

Ratio

[J]

Kilojoule

[kJ]

1 E+03

Megajoule

[MJ]

1 E+06

Electronvolt

[eV]

1.602 176 620 8 E-19

Kilo-electronvolt

[keV]

KEV

1.602 176 620 8 E-16

Mega-electronvolt

[MeV]

MEV

1.602 176 620 8 E-13

Giga-electronvolt

[GeV]

GEV

1.602 176 620 8 E-10

Thermochemical calorie

[calth ]

CAL

4.184

Kilocalorie

[kcalth ]

KCAL

4 184

Ton of TNT

[t TNT ]

TTNT

4.184 E+09

Kilowatt hour

[kWh]

KWH

3.6 E+06

British thermal unit

[Btu]

BTU

1055.06

(Newton meter)

116

13. Unit conversions

13-17. Units of temperature
Here is the list of units of temperature:
Units

Keyword

Ratio

Zero

Kelvin

[K]

KEL

Celsius

[℃]

DEGC

-273.15

Rankine

[°R]

DEGR

5/9

Fahrenheit

[℉]

DEGF

5/9

-459.67

The values of absolute temperature of Celsius and Fahrenheit are not same.
For instance, conversion from Celcius to Fahrenheit is following:
9
𝜃[°C] = (𝜃 + 273.15) × − 459.67[°F]
5

117

14. Math / Scientific constants

14. Math / Scientific constants
14-1. Input constants
This software supports many math / scientific constants. Type a keyword to push a constant.
IMPORTANT
Scientific constants are from 2014 CODATA

14-2. Math constants
Here is the list of math constants:
Name

Keyword

Value

3.141 592 653 589 79

Napier’s constant

2.718 281 828 459 05

Euler-Mascheroni constant

0.577 215 664 901 533

14-3. Fundamental physical constants
Here is the list of fundamental constants in physics:
Name

Symbol

Keyword

Speed of light in vacum

𝑐0

[m⁄s]

LIGHT

Magnetic constant

𝜇0

[H⁄m]

MAGNETIC

Electric constant

𝜀0

[F⁄m]

ELECTRIC

Characteristic impedance of vacum

𝑍0

[Ω]

IMPEDANCE

Gravitation constant

𝐺0

[m3 ⁄kg⁄s 2 ]

Planck constant

ℎ

[J ∙ s]

PLANCK

Reduced Planck constant

ℏ

[J ∙ s]

RPLANCK

118

GRAVITATION

Value
299 792 458
1.256 637 061 436
E-06
8.854 187 817 620
E-12
376.730 313 461
6.674 08
E-11
6.626 070 040
E-34
1.054 571 800
E-34

14. Math / Scientific constants

14-4. Electromagnetics
Here is the list of constants in electromagnetics:
Name

Symbol

Keyword

Value
1.602 176 620 8

𝑒

[C]

ECHARGE

Magnetic flux quantum

Φ0

[Wb]

Q.FLUX

Conductance quantum

𝐺0

[S]

Q.CONDUCT

Resistance quantum

𝑅0

[Ω]

Q.RESIST

Josephson constant

𝐾𝐽

[Hz⁄V]

JOSEPHSON

von Klitzing constant

𝑅𝐾

[Ω]

KLITZING

Bohr magneton

𝜇𝐵

[J⁄T]

B.MAGNETON

Nuclear magneton

𝜇𝑁

[J⁄T]

N.MAGNETON

Elementary charge

E-19
2.067 833 831
E-15
7.748 091 731 0
E-05
12 906.403 727 8
483 597.852 5
E-09
25 812.807 455 5
927.400 999 4
E-26
5.050 783 699
E-27

14-5. Nuclear physics
Here is the list of constants in nuclear physics:
Name
Fine-structure constant

Symbol

Keyword

𝛼

FSTRUCT

Rydberg constant

𝑅∞

[m−1 ]

RYDBERG

Bohr radius

𝑎0

[m]

B.RADIUS

Hartree energy

𝐸ℎ

[J]

HARTREE

119

Value
7.297 352 566 4
E-03
10 973 731.568 508
0.529 177 210 67
E-10
4.359 744 650
E-18

14. Math / Scientific constants

Constants connected with electron:
Name

Symbol

Keyword

Mass of electron

𝑚𝑒

[kg]

E.MASS

Compton wavelength of electron

𝜆𝑒

[m]

E.COMPTON

Classical electron radius

𝑟𝑒

[m]

E.RADIUS

Magnetic moment of electron

𝜇𝑒

[J⁄T]

Gyromagnetic ratio of electron

𝛾𝑒

[s −1 T −1 ]

E.MAGNETIC
E.GYRO

Value
9.109 383 56
E-31
2.426 310 236 7
E-12
2.817 940 322 7
E-15
-928.476 462 0
E-26
1.760 859 644
E+11

Constants connected with proton:
Name

Symbol

Keyword

Mass of proton

𝑚𝑝

[kg]

P.MASS

Compton wavelength of proton

𝜆𝑝

[m]

P.COMPTON

Magnetic moment of proton

𝜇𝑝

[J⁄T]

P.MAGNETIC

Gyromagnetic ratio of proton

𝛾𝑝

[s −1 T −1 ]

120

P.GYRO

Value
1.672 621 898
E-27
1.321 409 853 96
E-15
1.410 606 787 3
E-26
2.675 221 900
E+08

14. Math / Scientific constants

Constants connected with neutron:
Name

Symbol

Keyword

Mass of neutron

𝑚𝑛

[kg]

N.MASS

Compton wavelength of neutron

𝜆𝑛

[m]

N.COMPTON

Magnetic moment of neutron

𝜇𝑛

[J⁄T]

N.MAGNETIC

Gyromagnetic ratio of neutron

𝛾𝑛

[s −1 T −1 ]

N.GYRO

Value
1.674 927 471
E-27
1.319 590 904 81
E-15
−0.966 236 50
E-26
1.832 471 72
E+08

Other constants in nuclear physics:
Name

Symbol

Keyword

Mass of muon

𝑚𝜇

[kg]

MU.MASS

Magnetic moment of muon

𝜇𝜇

[J⁄T]

MU.MAGNETIC

Mass of tauon

𝑚𝜏

[kg]

TAU.MASS

121

Value
1.883 531 594
E-28
-4.490 448 26
E-26
3.167 47
E-27

14. Math / Scientific constants

14-6. Physicochemistry
Here is the list of constants in physicochemistry:
Name

Symbol

Keyword

Boltzmann constant

𝑘

[J⁄K]

BOLTZMANN

Avogadro constant

𝑁𝐴

[mol−1 ]

AVOGADRO

Atomic mass constant

𝑚u

[kg]

DALTON

Faraday constant

𝐹

[C⁄mol]

FARADAY

Molar gas constant

𝑅

[J ∙ K −1 ∙ mol−1 ]

GAS

𝑉m

[m3 ⁄mol]

MOLV

𝑉m

[L⁄mol]

MOLVL

𝑛0

[m−3 ]

Molar volume [1]
(Cubic meter)
Molar volume [1]
(Litter)
Loschmidt’s constant [1]

LOSCHMIDT

Value
1.380 648 52
E-23
6.022 140 857
E+23
1.660 539 040
E-27
96 485.332 89
8.314 4598
22.413 962
E-03
22.413 962
2.686 7811
E+25

[1] In 0 degrees centigrade and standard atomospheric pressure (273.15K, 1 atm).
Here is the list of constants in thermal radiation:
Name

Symbol

Keyword

Stefan-Boltzmann constant

𝜎

[W ∙ m−2 ∙ K −4 ]

STEFAN

First radiation constant

𝑐1

[W ∙ m2 ]

F.RAD

Second radiation constant

𝑐2

[m ∙ K]

S.RAD

122

Value
5.670 367
E-08
3.741 771 790
E-16
1.438 777 36
E-02

14. Math / Scientific constants

14-7. Agreement value
Here is the list of agreement values:
Name

Symbol

Standard gravity
Standard atmosphere
Zero degrees Celsius in Kelvin

Keyword

Value

GRAVITY

9.806 65

𝑔𝑛

[m⁄s2 ]

1 atm

[Pa]

ATM

0°C

[K]

ZEROD

10 1325
273.15

14-8. Planck unit
Here is the list of Planck unit:
Name

Symbol

Keyword

Value
2.176 470

Planck mass

𝑚P

[kg]

Planck energy

𝐸P

[GeV]

Planck temperature

𝑇P

[K]

PL.TEMP

Planck length

𝑙P

[m]

PL.LENGTH

Planck time

𝑡P

[s]

PL.TIME

PL.MASS

E-08

PL.ENERGY

1.220 910
E+19
1.416 808
E+32
1.616 229
E-35
5.391 16
E-44

14-9. Astronomy
Here is the list of constants of astronomy:
Name

Symbol

Keyword

Astronomical unit

[m]

ASTRO

Parsec

[m]

PARSEC

Light year

[m]

LYEAR

123

Value
149 597 870 700
3.085 677 581
E+16
9 460 730 472 580 800

15. Other functions

15. Other functions
15-1. All clear
You can clear stack and registers with all clear function.
Function

Keyword

All clear

AC
CLEAR

Stack clear

CLR
REGCLEAR

RCLR

You can use undo after you call clear functions.

15-2. All reset
Type “RESET” or “RST” to reset all settings without those in config mode.
Call the function and type “YES” or “NO” to confirm.

15-3. Undo / redo
Undo and redo function is available:
Function

Keyword
UNDO

Undo

U
REDO

Redo

ECKERT 2017 10 Users Manual

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