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.

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:

l l . _ Keypresses Resulting Entry _ 1.23<enter> 1.23 1.23<space>23n<enter> 1.23e-23 1.23n<space>23<enter> -1.23e23 _

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:

l l . _ 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) _

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

l l . 1 2 3 4

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

Examples of matrix entry:

l l . _ 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), (... _

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:

l l . _ 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 _

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:

l l . _ Keypresses Resulting Entry _ #123456<enter> # 123456`d #ffff<space>h<enter> # 65535`d #10101n<space>b<enter> # -21`d _

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

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:

l l . _ 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>-<f12> will enter the variables (``registers'') @ r01 through @ r12.

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:

l l . _ Data Type Sample Input String _ integer constant #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.

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:

l l . _ Keys Operations _ + add last two stack elements - subtract element 1 from element 2 * multiply last two stack elements / divide element 2 by element 1 ^ 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 % 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.

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:

l l . _ 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.

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:

l l . _ Keys Operations _ \ 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 _

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:

l l . _ 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 _

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:

l l . _ 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.

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:

l l . _ 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 _

l l . _ 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 _

l l . _ String Time Unit _ s second min minute hr hour day day yr year Hz Hertz _

l l . _ 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.

l l . _ String Force Unit _ N Newton lbf pound force dyn dyne kip kip _

l l . _ String Energy Unit _ J Joule erg erg cal calorie BTU british thermal unit eV electron volt _

l l . _ String Electrical Unit _ A Ampere C Coulomb V volt Ohm Ohm F Farad H Henry T Tesla G Gauss Wb Weber Mx Maxwell _

l l . _ String Power Unit _ W Watt hp horsepower _

l l . _ String Pressure Unit _ Pa Pascal atm atmosphere bar bar Ohm Ohm mmHg millimeters of mercury inHg inches of mercury _