dCalc - manual


Introduction

Welcome to dCalc

Support: bob.hepple@gmail.com

Internet: https://gitlab.com/wef/gdcalc

Note: if you are using a locale other than English, please make sure you run gdcalc with the following command (thanks to Gösta):

LC_NUMERIC=en_US gdcalc &
      

Note: if you get a badly drawn border around windows in dcalc (curses-mode in a terminal) then try this:

        TERM=gnome dcalc # or:
        TERM=vte dcalc
      

Overview

dCalc is a calculator very similar to the venerable line of calculators that HP has sold for the last 50 years or so. Like the HP calculators it operates much more intuitively than calculators with an equals sign.

It features:

dCalc operates on real numbers with Scientific, Statistics and Financial functions or integers (for programmers).

Note that dCalc initially starts in algebraic mode - you can change to RPN mode in the Settings menu.

As well as the stack, which is always visible - a nice plus over an actual HP calculator - there are 10 integer and 10 real registers to store numbers.

All your numbers and settings are saved between sessions and dCalc works with other applications by supporting Cut and Paste into and out of the X register.

A full set of unit conversions including:

A Short RPN Tutorial

You can change to RPN mode using the Settings menu.

RPN is an easier way to use a calculator than the so-called algebraic method on so-called conventional calculators. It's just a shame that HP called it RPN, which means Reverse Polish Notation and that puts a lot of people off!

Think about how you do a sum on a piece of paper because that's how RPN works:

You write down the first number.

Then you write down the second number.

Then you do the sum.

Now, let's do it on dCalc. Type in the first number. You can use the BSP (backspace) key to correct any mistakes.

Now press the Enter key and the number jumps up into the Y register above X.

Now type the second number into the X register. When you've finished the second number press the key for the operation you want to do, for example, the + plus sign. There's your answer. Notice that the stack of registers drops down as numbers are used up - it's good old push and pop.

If you want to do another sum on the answer, just type in the new number and then the key for the operation, e.g. x, multiply.

Entering Numbers

In Real modes (FIN SCI STA) you can use the decimal point and 'E' key which allows you to enter powers of ten e.g. if you enter 1 E 5 you get 1.0x105 or 100,000.00

You change the sign of your number with CHS

You can use BSP to backspace at any time

You can use CLX to completely clear X.

INV CLX clears the stack.

Invalid characters will be simply ignored e.g.

In Real modes:

In PRO mode:

The Stack

Above the large numeric display (called X) there are four smaller numbers called Y, Z, T and L which make up the stack..

L is simply the last X value - every time the number in X is used, it is stored into L. You can exchange X and L by simple clicking the L register..

The stack (Y, Z and T) is connected to X. Every time you click Enter, the numbers in X, Y, Z and T propagate upwards. The number in Z moves to T, Y moves to Z and X moves to Y. The number which was in T is forgotten.

Numbers move down the stack as they are consumed in X - e.g. if you click + repeatedly, Y and X are added and put into X, Z moves down to Y and T moves down to Z. Try it.

You'll notice that the number in T stays put - it is copied when the stack is consumed at the bottom - this is really useful in repeated calculations

e.g. to work out how interest compounds every month just put in the interest rate percent (as a real number - 1.1 means 10%) and then press Enter until the interest rate reaches the T register. Then type in your principal, say 1000.00 (don't press Enter!) Then just keep pressing the X (multiply) key - every time the principal is compounded by 10%.

There are other keys to manipulate the stack, mentioned elsewhere in this help. The stack is your best friend and using it well is the secret to effective calculation with RPN.

RollDown

The ROLL stack operator rotates the stack downwards -

T->Z

Z->Y

Y->X and X goes back up to T.

Exchange X

You can exchange X and any other number in the stack by clicking on that number on the screen.

The X key exchanges X and Y.

The registers

There are 10 registers labelled 0-9. You can store X into a register by clicking STO. A menu of all the registers appears and you click on the register you want to use. Recall from registers is done in the same way (RCL key)

The registers are stored every time you exit so that the values are available next time.

You can add or subtract X to a register with ST+ and ST-

Cut/Paste

The usual shortcut keys Ctl-c and Ctl-v work in dCalc.

Ctl-c copies the X register into the clipboard which can then be used in a spreadsheet or Word processor. Similarly, if you are in another application and copy a number to the clipboard (with Ctl-x or Ctl-c) then you can paste it into X with Ctl-v.

Obviously, if it's not a number, you'll get an error message.

Main Modes

There are 4 main modes - Scientific, Financial, Statistics and Programming.

The first three operate on real (floating point) numbers and programming mode operates on integers. To change mode just use the buttons PRO FIN STA and SCI, the pull-down menus or the shortcut keys:

Ctl-s SCI scientific mode

Ctl-f FIN financial mode

Ctl-p PRO programming mode

Ctl-t STA statistics mode

PRO Mode

PRO mode can operate and display binary (BIN), octal (OCT), decimal (DEC), hexadecimal (HEX), Internet Protocol address (IP) and ascii (ASC) formats.

Ascii format shows the value of each byte as a printable glyph (a-z, A-Z, 0-9 etc) or as an control/alt keystroke e.g. ^-a means control a (decimal 1), a-b means alt-b which is 0x80 + 0x62. Note that Ctl- shortcuts are not available in Asc mode - they enter the appropriate ascii code instead.

Hex numbers are displayed with a leading 0x, octals with a leading 0.

IP address numbers are displayed as 4 decimal numbers in the range 0-255, corresponding to bits 0-7, 8-15, 16-23 and 24-31. The same bit manipulations can be made with IP numbers as for any other format eg.to calculate a subnet address using AND. The other arithmetic operations operate as before but are fairly meaningless on an IP address.

There is an indicator to the left of the log key showing the current display number base.

The usual suspects including AND, OR, XOR, MOD, left/right shift, complement.

The PF key calculates the prime factors of X.

32 bit integers are used.

Real Modes

Entering numbers should be fairly intuitive. For very large or small numbers, you can use exponent notation. For example, type:

1 E 15 CHS

for 1.0E-15. Notice that before the E is entered, the CHS button applies to the sign of the number. After E is put in, CHS applies to the sign of the exponent.

Angles for trig functions are normally expressed in decimal degrees, but a minor mode exists for radians - use the keyboard shortcut or the pull down menu.

There is an indicator to the right of the message window showing degrees or radians setting.

There is also an invert function INV which reverses the sense of some functions - for example, if INV is clicked before SIN then the asin function is called instead. Hopefully this is intuitive.

There is an indicator to the right of the message window showing the status of Invert.

In all real modes you have access to:

The Fix, Sci and Eng keys allow you to select the mode of real number display. Fix mode is the default and displays as e.g. 10.123. Very small or large numbers use scientific mode.

Sci real mode displays as 1.0123E+01 with a mantissa and exponent.

Eng mode restricts the exponent to be a power of 3 e.g. 10.1230E0

SCI mode

The trig functions SIN, COS, TAN and their inverse functions are provided as well as the hyperbolics Sinh, Cosh and Tanh and their inverses.

h.ms converts a decimal hours into sexadecimal hours, minutes and seconds (or back if Invert is pressed first). e.g., 2.56 hours converts to 2 hours 33 minutes and 36 seconds which is displayed as 2.3336.

The r->p button converts from rectangular coordinates to polar (or the inverse)

The d->r button converts from degrees to radians (or the inverse).

FIN mode

Compound interest and other financial calculations.

In these calculations we are interested in:

With any 4 of these values, we can calculate the fifth. E.g. if we know the initial value, the interest, the number of compounding periods and the regular payment, we can calculate the final value. Similarly, if we know the value of a mortgage, the interest rate and the repayment period, we can calculate the payment necessary to pay off the mortgage in the time given.

With all the financial functions, the method of data entry is optimised - if you type in a number and then press a key (e.g. PMT) then dCalc stores that number. If you press a financial function without entering a number, dCalc calculates that value. If you press a financial key and the number is entered instead of calculated, just press the key again to perform the calculation.

Finally, if you press INV before a function, the current value is retrieved to X. You can see all the current values at once by pressing RCL (and then Cancel to return to the calculator)

The financial keys are:

Note that cash flows (PMT, FV, PV) are negative for payments.

There is a global setting under Menu->Settings which when set, allows a payment to be made at the start of the investment. Otherwise, the first payment is calculated at the end of the first period.

The DYS function allows you to calculate the number of days between 2 dates. The dates must be entered as YYYY.MMDD.

If prefixed by INV, DYS calculates the number of days in a nominal month as 30 days in a 360 day year.

The TDY key is a shortcut for today's date.

Compound Interest Example:

let's invest $1000 for 3 years at 5% per annum paid monthly.

Type in:

3 Enter ×12 n ... 3 years is 36 months

1000 PV ... present value

5 Enter ÷12 i ... interest (5% per annum = 5/12 monthly)

0 PMT ... we are not making monthly payments

FV ... the final value is $1161.47 (shown as -1,161.47)

Another example: we have a $100,000 mortgage at 6% to be paid off completely after 20 years. What's the payment every month?

20 ×12 n ... 20 years

6 ÷12 i ... monthly interest

100000 PV ... present value

0 FV ... future value will be 0

PMT ... -716.43 per month.

Note the change of sign - the payment is a negative cash flow, and don't we know it!

The formula for these calculations is:

0=f+p(1+i)n + d((1+i)n - 1)(1+s.i) / i

where:

STA mode

Calculating sums, means and standard deviations is easy with these functions which operate on X and Y. The SUM key adds the current values in X and Y into the sum and increments the counter. Just keep entering your values and the running total is kept.

The m key gives the averages (means) of the X and Y values respectively.

StdD gives the standard deviation of both X and Y (into the X and Y registers). StdD, d is given by:

d² = (S(x²) - S(x)²/n)/(n-1)

where S(x) means the sum of x values

n displays the count.

Sum- subtracts the current X and Y from the total (e.g. if you entered a value incorrectly).

The statistics registers are:

x! predictably computes the factorial.

yPx and yCx calculate permutations and combinations for x <= y. The integer part of x and y are used.

LR calculates a linear regression using the least squares method on the values input as (X, Y) pairs by Sum. A best fit straight line is presented as the slope m in the X register, and the Y intersect c in the Y register. The correlation coefficent r² is provided in Z - a value of r² closer to 1 means a good fit to a straight line. r² close to zero means a poor fit.

You can display the current linear regression formula with INV LR.

The best fit line is given by the formula

y = my + c

S(x) means the sum of x values:

Dx = n.S(x²) - (S(x))²

Dy = n.S(y²) - (S(y))²

m = (n.S(xy) - S(x).S(y))/Dx

c = (S(x²)S(y) - S(x)S(xy))/Dx

r² = m.Dx/Dy

f(X) calculates a value for Y from X using the straight line calculated by LR. Use the INV function to calculate the value for X for a given value of Y.

Conversions

In real modes you can convert between a wide range of units. The conversions are arranged in groups:

Note that the units(1) program must be installed.

Keyboard shortcuts

Most of the keyboard keys operate the way you would expect, e.g. the numeric, Backspace (Del) and Enter keys.

Some shortcuts are:

Ctl-c Copies X to the clipboard

Ctl-d sets Degree mode

Ctl-f Financial mode

Ctl-p Programming mode

Ctl-q Exits

Ctl-r Radians

Ctl-s Scientific mode

Ctl-t sTatistics mode

Ctl-v paste to X

* multiply

/ divide

+ plus

- minus

< shift X left by 1 bit (prog mode)

> shift X right by 1 bit (prog mode)

~ complement X (prog mode)

, (comma) CHS (real modes where decimal point = .)

% percent

Copying

       GNU GENERAL PUBLIC LICENSE
           Version 2, June 1991

 Copyright (C) 1989, 1991 Free Software Foundation, Inc.
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