.----------------. .----------------. .----------------. .----------------. .----------------. .----------------. 
| .--------------. | .--------------. | .--------------. | .--------------. | .--------------. | .--------------. |
| |  ____  ____  | | |     _____    | | |   ______     | | |              | | |    ______    | | |   _______    | |
| | |_   ||   _| | | |    |_   _|   | | |  |_   __ \   | | |              | | |   / ____ `.  | | |  |  _____|   | |
| |   | |__| |   | | |      | |     | | |    | |__) |  | | |    ______    | | |   `'  __) |  | | |  | |____     | |
| |   |  __  |   | | |      | |     | | |    |  ___/   | | |   |______|   | | |   _  |__ '.  | | |  '_.____''.  | |
| |  _| |  | |_  | | |     _| |_    | | |   _| |_      | | |              | | |  | \____) |  | | |  | \____) |  | |
| | |____||____| | | |    |_____|   | | |  |_____|     | | |              | | |   \______.'  | | |   \______.'  | |
| |              | | |              | | |              | | |              | | |              | | |              | |
| '--------------' | '--------------' | '--------------' | '--------------' | '--------------' | '--------------' |
 '----------------' '----------------' '----------------' '----------------' '----------------' '----------------'

_{(ASCII art by patorjk.com)}

1. Introduction

What's this project?

HIP-35 is a calculator for hipsters. It emulates the RPN (reverse Polish notation) mode of HP-35 from 1972. It runs a terminal UI built with ncurses that displays the current result on a display.

⚫ Why RPN?

Because it genally involves less keystrokes and it's faster than algebraic notation calculations.

How? RPN makes it very easy to compute long expressions containing lots of brackets [1]. When using it, you don't need to think how terms are grouped anymore.

⚫ The memory

HP-35 had a stack-based memory of 4 registers X, Y, Z, T with X being the bottom (entry). That stack shifts (lifts or drops) automatically as calculations are performed. There are also 10 general registers labelled A to J that store values, acting as buffers.

HP-35	HIP-35

2. Usage

⚫ Dependencies

CMake is required to build the project and ncurses for the frontend. Also you need to make sure your compuler supports C++17 or higher. Install both packages by:

Arch-based	Debian-based
sudo pacman -S cmake ncurses	sudo apt install cmake libncurses5 libncursesw5

⚫ Compilation

The build system is based on CMake. To build the project run:

cmake . -Bbuild
cd build
make -j

or alternatively just execute the build.sh script:

./build.sh

The demo executable that runs the UI will be generated at

./build/demo/demo

That's it, have fun doing RPN calculations!

A unit test executable is also generated at ./build/test/testhip35.

⚫ The keys

Most keys are self-explanatory. However, some are less straightforward.

key	description	syntax	before	argument	after
CHS	change sign of X	CHS	4		-4
ENTER	duplicate X to Y	ENTER	T,Z,Y,X=1,2,3,4		T,Z,Y,X=2,3,4,4
LASTX	last X before operation	LASTX	4 E 20 + (X=24)		X=20
RDN	rotate stack down	RDN	T,Z,Y,X=1,2,3,4		T,Z,Y,X=4,3,2,1
STO	store to A-J e.g. A = X	STO a-j	X=3.14, A=0	a	X=3.14, A=3.14
RCL	recall to X e.g. X = A	RCL a-j	X=0, F=2.71	f	X=2.71, F=2.71
EEX	exponentiation of X	EEX N	7	3	7000
CLX	clear register X	CLX	12345		0
CLR	clear entire stack	CLR	T,Z,Y,X=1,2,3,4		T,Z,Y,X=0,0,0,0
q	quit application	q

Enter (<space>) needs to be pressed to separate two successive numbers. When running the UI, press q to quit. <Ctr-C> is not captured so q is the only way to quit. You can read more at the HP35 manual [4].

⚫ Project directory structure and source code

Implementations are found at lib/src and header files at lib/inc. The demo application is at demo/main.cpp and unit tests are found at test/test.cpp.

You can create an instance of the Hip35 class and run it either via the UI or without it (given a string) as follows:

#include "hip35.h"
//...
auto hp = std::make_unique<Ui::Hip35>(key::keypad);
// using the UI
hp->RunUI();
// or without it
auto result = hp->EvalString("430 ENTER 80 - 1.2 *");

3. Demo

Second order equation by using storage/recall:

second_order_eq.mp4

The fraction sqrt(2 + (sin(25) + pi/2)^2)/3:

fraction.mp4

4. Basic theory

⚫ What is RPN?

RPN allows a stack-based evaluation of numerical expressions, eliminating the need of brackets. There are two main ideas behind RPN:

1. operands (numbers) are pushed in a stack
2. it follows the postfix notation, i.e. each operator follows one or two operands preceeding it

Physical calculators need a way to separate successive numbers, accomplished with the enter (E) key.

For example:

+------------+---------------+-------------------+-----------------------------------------------+
| Algebrainc | RPN           | Physical          | Stack contents                                |
| expression | equivalent    | calculator        |                                               |
+------------+---------------+-------------------+-----------------------------------------------+
| 1 + 2      | 1 2 +         | 1 E 2 +           | [1], [1,1], [1,2], [3]                        |
+------------+---------------+-------------------+-----------------------------------------------+
| 1 + 2 - 3  | 1 2 3 + - or: | 1 E 2 E 3 + -     | ...[1,2], [1,2,2], [1,2,3], [1,-1], [0]       |
|            | 1 2 + 3 -     | 1 E 2 + 3 -       | ...[1,2], [3], [3,-3], [0]                    |
+------------+---------------+-------------------+-----------------------------------------------+
| (1+2)(3+4) | 1 2 + 3 4 + * | 1 E 2 + 3 E 4 + * | ...[1,2], [3], [3,3], [3,3,4], [3,7], [21]    |
+------------+---------------+-------------------+-----------------------------------------------+
| 13*sin(37) | 13 37 SIN *   | 13 E 37 SIN *     | [13], [13,13], [13,37] [13,s(37)], [13*s(37)] |
+------------+---------------+-------------------+-----------------------------------------------+

You can practise more with RPN by using the script docs/rpn.py which evaluates RPN expressions from a string. Numbers are separated by space in this script so you don't need to press enter.

⚫ HIP-35 additional features

HIP-35 includes some minor additions compared to HP-35:

• The display now has two rows, displaying the X and Y registers instead of just X.
• There is space on the right to display the 10 general registers. Back in the day users had to write down which register stores what.
• User can also enter negative numbers using the ~ as the unary minus. HP35 only supposed the CHS (change sign) operation for that.
• There is no ARC key. ARC key had to pressed to enable the SIN, COS, TAN keys to compute ASIN, ACOS, ATAN. The latter keys are directly implemented in HIP-35.
• The number format on the display is automatically adjusted based on the range the number is in.
• The LASTX key from HP-35s is ported as it makes certain calculations much faster.

You can read more at the wiki page, at HP museum or at the HP-35s manual, which is its successor.

⚫ Cool trivia

• HP35 was the first ever scientific pocket calculator. It was released in 1972. Before that, the only practical portable devices for performing trigonometric and exponential functions were slide rules [2]
• The co-founder of HP himself, Bill Hewlett, challenged his coworkers to create it as a "shirt-pocket sized HP-9100“ (HP-9100 was a scientific computer from the 60s).
• HP-35 calculators, were used by NASA's Skylab crew from 1973 to 1974 [3]. It's rumored to be the first calculator to ever fly into space. It helped the crew write programs that perform calculations related to the spacecraft's orbit around the moon (Lunar Orbital Rendezvous or LOR).
• It was able to perform calculations both in algebraic a RPN mode.

5. Future ideas

• Paste text into display
• In headless mode (parsing a string), throw an error instead of continuing when a token is unknown.
• (ambitious) write a compiler for the HP35/HP35s programming language and be able to write routines by pressing a key.

References

[1] Dr Marshall Leach Jr's page
[2] Interview with David Cochran
[3] History of Space Shuttle Rendezvous, Oct 2011
[4] HP35 manual