## table of contents

ORPIE(1) | a console-based RPN calculator | ORPIE(1) |

# NAME¶

orpie - is a console-based RPN calculator with an interactive visual stack.

# SYNOPSIS¶

orpie

# QUICK START¶

CAUTION: while this manpage should be suitable as a quick reference, it may be subject to miscellaneous shortcomings in typesetting. The definitive documentation is the user manual provided with Orpie in PDF format.

This section describes how to use Orpie in its default configuration. After familiarizing yourself with the basic operations as outlined in this section, you may wish to consult the orpierc(5) manpage to see how Orpie can be configured to better fit your needs.

## OVERVIEW¶

The interface has two panels. The left panel combines status information with context-sensitive help; the right panel represents the calculator's stack. (Note that the left panel will be hidden if Orpie is run in a terminal with less than 80 columns.)

In general, you perform calculations by first entering data on to the stack, then executing functions that operate on the stack data. As an example, you can hit 1<enter>2<enter>+ in order to add 1 and 2.

## ENTERING REAL NUMBERS¶

To enter a real number, just type the desired digits and hit enter. The space bar will begin entry of a scientific notation exponent. The 'n' key is used for negation. Here are some examples:

_ Keypresses | Resulting Entry |

_ 1.23<enter> | 1.23 |

1.23<space>23n<enter> | 1.23e-23 |

1.23n<space>23<enter> | -1.23e23 |

_ |

## ENTERING COMPLEX NUMBERS¶

Orpie can represent complex numbers using either cartesian (rectangular) or polar coordinates. See PERFORMING BASIC COMMAND OPERATIONS to see how to change the complex number display mode.

A complex number is entered by first pressing '(', then entering the real part, then pressing ',' followed by the imaginary part. Alternatively, you can press '(' followed by the magnitude, then '<' followed by the phase angle. The angle will be interpreted in degrees or radians, depending on the current setting of the angle mode (see PERFORMING BASIC COMMAND OPERATIONS). Examples:

_ Keypresses | Resulting Entry |

_ (1.23, 4.56<enter> | (1.23, 4.56) |

(0.7072<45<enter> | (0.500065915655126, 0.50006591... |

(1.23n,4.56<space>10<enter> | (-1.23, 45600000000) |

_ |

## ENTERING MATRICES¶

You can enter matrices by pressing '['. The elements of the matrix may then be entered as described in the previous sections, and should be separated using ','. To start a new row of the matrix, press '[' again. On the stack, each row of the matrix is enclosed in a set of brackets; for example, the matrix

1 | 2 |

3 | 4 |

would appear on the stack as [[1, 2][3, 4]].

Examples of matrix entry:

_ Keypresses | Resulting Entry |

_ [1,2[3,4<enter> | [[1, 2][3, 4]] |

[1.2<space>10,0[3n,5n<enter> | [[ 12000000000, 0 ][ -3, -5 ]] |

[(1,2,3,4[5,6,7,8<enter> | [[ (1, 2), (3, 4) ][ (5, 6), (... |

_ |

## ENTERING DATA WITH UNITS¶

Real and complex scalars and matrices can optionally be labeled with units. After typing in the numeric portion of the data, press '_' followed by a units string. The format of units strings is described in the UNITS FORMATTING section.

Examples of entering dimensioned data:

_ Keypresses | Resulting Entry |

_ 1.234_N*mm^2/s<enter> | 1.234_N*mm^2*s^-1 |

(2.3,5_s^-4<enter> | (2.3, 5)_s^-4 |

[1,2[3,4_lbf*in<enter> | [[ 1, 2 ][ 3, 4 ]]_lbf*in |

_nm<enter> | 1_nm |

_ |

## ENTERING EXACT INTEGERS¶

An exact integer may be entered by pressing '#' followed by the desired digits. The base of the integer will be assumed to be the same as the current calculator base mode (see PERFORMING BASIC COMMAND OPERATIONS to see how to set this mode). Alternatively, the desired base may be specified by pressing space and appending one of {b, o, d, h}, to represent binary, octal, decimal, or hexadecimal, respectively. On the stack, the representation of the integer will be changed to match the current base mode. Examples:

_ Keypresses | Resulting Entry |

_ #123456<enter> | #123456`d |

#ffff<space>h<enter> | #65535`d |

#10101n<space>b<enter> | #-21`d |

_ |

Note that exact integers may have unlimited length, and the basic arithmetic operations (addition, subtraction, multiplication, division) will be performed using exact arithmetic when both arguments are integers.

## ENTERING VARIABLE NAMES¶

A variable name may be entered by pressing '@' followed by the desired variable name string. The string may contain alphanumeric characters, dashes, and underscores. Example:

_ Keypresses | Resulting Entry |

_ @myvar | @ myvar |

_ |

Orpie also supports autocompletion of variable names. The help panel displays a list of pre-existing variables that partially match the name currently being entered. You can press '<tab>' to iterate through the list of matching variables.

As a shortcut, keys <f1>-<f4> will enter the variables (``registers'') @ r01 through @ r04.

## ENTERING PHYSICAL CONSTANTS¶

Orpie includes definitions for a number of fundamental physical constants. To enter a constant, press 'C', followed by the first few letters/digits of the constant's symbol, then hit enter. Orpie offers an autocompletion feature for physical constants, so you only need to type enough of the constant to identify it uniquely. A list of matching constants will appear in the left panel of the display, to assist you in finding the desired choice.

The following is a list of Orpie's physical constant symbols:

_ Symbol | Physical Constant |

_ NA | Avagadro's number |

k | Boltzmann constant |

Vm | molar volume |

R | universal gas constant |

stdT | standard temperature |

stdP | standard pressure |

sigma | Stefan-Boltzmann constant |

c | speed of light |

eps0 | permittivity of free space |

u0 | permeability of free space |

g | acceleration of gravity |

G | Newtonian gravitational constant |

h | Planck's constant |

hbar | Dirac's constant |

e | electron charge |

me | electron mass |

mp | proton mass |

alpha | fine structure constant |

phi | magnetic flux quantum |

F | Faraday's constant |

Rinf | ``infinity'' Rydberg constant |

a0 | Bohr radius |

uB | Bohr magneton |

uN | nuclear magneton |

lam0 | wavelength of a 1eV photon |

f0 | frequency of a 1eV photon |

lamc | Compton wavelength |

c3 | Wien's constant |

_ |

All physical constants are defined in the Orpie run-configuration file; consult the orpierc(5) manpage if you wish to define your own constants or change the existing definitions.

## ENTERING DATA WITH AN EXTERNAL EDITOR¶

Orpie can also parse input entered via an external editor. You may find this to be a convenient method for entering large matrices. Pressing 'E' will launch the external editor, and the various data types may be entered as illustrated by the examples below:

_ Data Type | Sample Input String |

_ exact integer | #12345678`d, where the trailing letter is one of the base characters {b, o, d, h} |

real number | -123.45e67 |

complex number | (1e10, 2) or (1 <90) |

real matrix | [[1, 2][3.1, 4.5e10]] |

complex matrix | [[(1, 0), 5][1e10, (2 <90)]] |

variable | @myvar |

_ |

Real and complex numbers and matrices may have units appended; just add a units string such as ``_N*m/s'' immediately following the numeric portion of the expression.

Notice that the complex matrix input parser is quite flexible; real and complex matrix elements may be mixed, and cartesian and polar complex formats may be mixed as well.

Multiple stack entries may be specified in the same file, if they are separated by whitespace. For example, entering (1, 2) 1.5 into the editor will cause the complex value (1, 2) to be placed on the stack, followed by the real value 1.5.

The input parser will discard whitespace where possible, so feel free to add any form of whitespace between matrix rows, matrix elements, real and complex components, etc.

## EXECUTING BASIC FUNCTION OPERATIONS¶

Once some data has been entered on the stack, you can apply operations to that data. For example, '+' will add the last two elements on the stack. By default, the following keys have been bound to such operations:

_ Keys | Operations |

_ + | add last two stack elements |

- | subtract element 1 from element 2 |

* | multiply last two stack elements |

/ | divide element 2 by element 1 |

^T}&T{ raise element 2 to the power of element 1 | |

n | negate last element |

i | invert last element |

s | square root function |

a | absolute value function |

e | exponential function |

l | natural logarithm function |

c | complex conjugate function |

! | factorial function |

%T}&T{ element 2 mod element 1 | |

S | store element 2 in (variable) element 1 |

; | evaluate variable to obtain contents |

_ |

As a shortcut, function operators will automatically enter any data that you were in the process of entering. So instead of the sequence 2<enter>2<enter>+, you could type simply 2<enter>2+ and the second number would be entered before the addition operation is applied.

As an additional shortcut, any variable names used as function arguments will be evaluated before application of the function. In other words, it is not necessary to evaluate variables before performing arithmetic operations on them.

## EXECUTING FUNCTION ABBREVIATIONS¶

One could bind nearly all calculator operations to specific
keypresses, but this would rapidly get confusing since the PC keyboard is
not labeled as nicely as a calculator keyboard is. For this reason, Orpie
includes an *abbreviation* syntax.

To activate an abbreviation, press ''' (quote key), followed by the first few letters/digits of the abbreviation, then hit enter. Orpie offers an autocompletion feature for abbreviations, so you only need to type enough of the operation to identify it uniquely. The matching abbreviations will appear in the left panel of the display, to assist you in finding the appropriate operation.

To avoid interface conflicts, abbreviations may be entered only when the entry buffer (the bottom line of the screen) is empty.

The following functions are available as abbreviations:

_ Abbreviations | Functions |

_ inv | inverse function |

pow | raise element 2 to the power of element 1 |

sq | square last element |

sqrt | square root function |

abs | absolute value function |

exp | exponential function |

ln | natural logarithm function |

10^ | base 10 exponential function |

log10 | base 10 logarithm function |

conj | complex conjugate function |

sin | sine function |

cos | cosine function |

tan | tangent function |

sinh | hyperbolic sine function |

cosh | hyperbolic cosine function |

tanh | hyperbolic tangent function |

asin | arcsine function |

acos | arccosine function |

atan | arctangent function |

asinh | inverse hyperbolic sine function |

acosh | inverse hyperbolic cosine function |

atanh | inverse hyperbolic tangent function |

re | real part of complex number |

im | imaginary part of complex number |

gamma | Euler gamma function |

lngamma | natural log of Euler gamma function |

erf | error function |

erfc | complementary error function |

fact | factorial function |

gcd | greatest common divisor function |

lcm | least common multiple function |

binom | binomial coefficient function |

perm | permutation function |

trans | matrix transpose |

trace | trace of a matrix |

solvelin | solve a linear system of the form Ax = b |

mod | element 2 mod element 1 |

floor | floor function |

ceil | ceiling function |

toint | convert a real number to an integer type |

toreal | convert an integer type to a real number |

add | add last two elements |

sub | subtract element 1 from element 2 |

mult | multiply last two elements |

div | divide element 2 by element 1 |

neg | negate last element |

store | store element 2 in (variable) element 1 |

eval | evaluate variable to obtain contents |

purge | delete a variable |

total | sum the columns of a real matrix |

mean | compute the sample means of the columns of a real matrix |

sumsq | sum the squares of the columns of a real matrix |

var | compute the unbiased sample variances of the columns of a real matrix |

varbias | compute the biased (population) sample variances of the columns of a real matrix |

stdev | compute the unbiased sample standard deviations of the columns of a real matrix |

stdevbias | compute the biased (pop.) sample standard deviations of the columns of a matrix |

min | find the minima of the columns of a real matrix |

max | find the maxima of the columns of a real matrix |

utpn | compute the upper tail probability of a normal distribution |

uconvert | convert element 2 to an equivalent expression with units matching element 1 |

ustand | convert to equivalent expression using SI standard base units |

uvalue | drop the units of the last element |

_ |

Entering abbreviations can become tedious when performing repetitive calculations. To save some keystrokes, Orpie will automatically bind recently-used operations with no prexisting binding to keys <f5>-<f12>. The current autobindings can be viewed by pressing 'h' to cycle between the various pages of the help panel.

## EXECUTING BASIC COMMAND OPERATIONS¶

In addition to the function operations listed in the section EXECUTING BASIC FUNCTION OPERATIONS, a number of basic calculator commands have been bound to single keypresses:

_ Keys | Operations |

_ \T}&T{ drop last element | |

| | clear all stack elements |

<pagedown> | swap last two elements |

<enter> | duplicate last element (when entry buffer is empty) |

u | undo last operation |

r | toggle angle mode between degrees and radians |

p | toggle complex display mode between rectangular and polar |

b | cycle base display mode between binary, octal, decimal, hex |

h | cycle through multiple help windows |

v | view last stack element in a fullscreen editor |

E | create a new stack element using an external editor |

P | enter 3.14159265 on the stack |

C-L | refresh the display |

<up> | begin stack browsing mode |

Q | quit Orpie |

_ |

## EXECUTING COMMAND ABBREVIATIONS¶

In addition to the function operations listed in the section EXECUTING FUNCTION ABBREVIATIONS, there are a large number of calculator commands that have been implemented using the abbreviation syntax:

_ Abbreviations | Calculator Operation |

_ drop | drop last element |

clear | clear all stack elements |

swap | swap last two elements |

dup | duplicate last element |

undo | undo last operation |

rad | set angle mode to radians |

deg | set angle mode to degrees |

rect | set complex display mode to rectangular |

polar | set complex display mode to polar |

bin | set base display mode to binary |

oct | set base display mode to octal |

dec | set base display mode to decimal |

hex | set base display mode to hexidecimal |

view | view last stack element in a fullscreen editor |

edit | create a new stack element using an external editor |

pi | enter 3.14159265 on the stack |

rand | generate a random number between 0 and 1 (uniformly distributed) |

refresh | refresh the display |

about | display a nifty ``About Orpie'' screen |

quit | quit Orpie |

_ |

## BROWSING THE STACK¶

Orpie offers a *stack browsing mode* to assist in viewing and
manipulating stack data. Press <up> to enter stack browsing mode; this
should highlight the last stack element. You can use the up and down arrow
keys to select different stack elements. The following keys are useful in
stack browsing mode:

_ Keys | Operations |

_ q | quit stack browsing mode |

<left> | scroll selected entry to the left |

<right> | scroll selected entry to the right |

r | cyclically ``roll'' stack elements downward, below the selected element (inclusive) |

R | cyclically ``roll'' stack elements upward, below the selected element (inclusive) |

v | view the currently selected element in a fullscreen editor |

E | edit the currently selected element with an external editor |

<enter> | duplicate the currently selected element |

_ |

The left and right scrolling option may prove useful for viewing very lengthy stack entries, such as large matrices. The edit option provides a convenient way to correct data after it has been entered on the stack.

## UNITS FORMATTING¶

A units string is a list of units separated by '*' to indicate multiplication and '/' to indicate division. Units may be raised to real-valued powers using the '^'character. A contrived example of a valid unit string would be "N*nm^2*kg/s/in^-3*GHz^2.34".

Orpie supports the standard SI prefix set, {y, z, a, f, p, n, u, m, c, d, da, h, k, M, G, T, P, E, Z, Y} (note the use of 'u' for micro-). These prefixes may be applied to any of the following exhaustive sets of units:

_ String | Length Unit |

_ m | meter |

ft | foot |

in | inch |

yd | yard |

mi | mile |

pc | parsec |

AU | astronomical unit |

Ang | angstrom |

furlong | furlong |

pt | PostScript point |

pica | PostScript pica |

nmi | nautical mile |

lyr | lightyear |

_ |

_ String | Mass Unit |

_ g | gram |

lb | pound mass |

oz | ounce |

slug | slug |

lbt | Troy pound |

ton | (USA) short ton |

tonl | (UK) long ton |

tonm | metric ton |

ct | carat |

gr | grain |

_ |

_ String | Time Unit |

_ s | second |

min | minute |

hr | hour |

day | day |

yr | year |

Hz | Hertz |

_ |

_ String | Temperature Unit |

_ K | Kelvin |

R | Rankine |

_ |

Note: No, Celsius and Fahrenheit will not be supported. Because these temperature units do not share a common zero point, their behavior is ill-defined under many operations.

_ String | ``Amount of Substance'' Unit |

_ mol | Mole |

_ |

_ String | Force Unit |

_ N | Newton |

lbf | pound force |

dyn | dyne |

kip | kip |

_ |

_ String | Energy Unit |

_ J | Joule |

erg | erg |

cal | calorie |

BTU | british thermal unit |

eV | electron volt |

_ |

_ String | Electrical Unit |

_ A | Ampere |

C | Coulomb |

V | volt |

Ohm | Ohm |

F | Farad |

H | Henry |

T | Tesla |

G | Gauss |

Wb | Weber |

Mx | Maxwell |

_ |

_ String | Power Unit |

_ W | Watt |

hp | horsepower |

_ |

_ String | Pressure Unit |

_ Pa | Pascal |

atm | atmosphere |

bar | bar |

Ohm | Ohm |

mmHg | millimeters of mercury |

inHg | inches of mercury |

_ |

_ String | Luminance Unit |

_ cd | candela |

lm | lumen |

lx | lux |

_ |

Note: Although the lumen is defined by 1_lm = 1_cd * sr, Orpie drops the steridian because it is a dimensionless unit and therefore is of questionable use to a calculator.

_ String | Volume Unit |

_ ozfl | fluid ounce (US) |

cup | cup (US) |

pt | pint (US) |

qt | quart (US) |

gal | gallon (US) |

L | liter |

_ |

All units are defined in the Orpie run-configuration file; consult the orpierc(5) manpage if you wish to define your own units or change the existing definitions.

# LICENSING¶

Orpie is Free Software; you can redistribute it and/or modify it under the terms of the GNU General Public License (GPL), Version 3, as published by the Free Software Foundation. You should have received a copy of the GPL along with this program, in the file ``LICENSE.md''.

# CONTACT INFO¶

Orpie author: Paul Pelzl <pelzlpj@gmail.com>

Orpie website: **https://github.com/pelzlpj/orpie**

# SEE ALSO¶

28 August 2018 | a console-based RPN calculator |