# Building a command line RPN calculator

By John Lekberg on May 22, 2020.

This week's post is about building a command line reverse Polish notation (RPN) calculator. You will learn:

- How to create a RPN calculator with a macro system.
- How to create advanced macros that can make medical calculations, like body mass index (BMI).

Reverse Polish notation means operators follow their operands. E.g.

(3 + 4) * 5

would be written as

3 4 + 5 *

# Script source code

rpncalc

```
#!/usr/bin/env python3
import decimal
import re
from decimal import Decimal as D
class RPNCalc:
"""A reverse polish notation (RPN) calculator.
Manages a stack of numbers.
Numbers are decimal.Decimal objects.
Supports the following operations:
| op | input | output |
|------|-----------|--------|
| + | x y + | x+y |
| - | x y - | x-y |
| * | x y * | x*y |
| / | x y / | x/y |
| ** | x y ** | x**y |
| drop | x drop | |
| swap | x y swap | y x |
| dup | x dup | x x |
| over | x y over | x y x |
| rot | x y z rot | y z x |
| nand | x y nand | !(x&y) |
| <= | x y <= | (x<=y) |
"""
def __init__(self):
"""Initialize the stack and supported operations."""
self._stack = []
def op(arity, f):
"""Turn a function like (lambda x, y: x + y)
into an operation that pops and pushes self._stack.
"""
def stack_f():
if len(self._stack) < arity:
raise IndexError(
"Stack too small for operation"
)
args = [
self._stack.pop() for _ in range(arity)
]
results = f(*reversed(args))
self._stack.extend(results)
return stack_f
self._operations = {
# Arithmetic
"+": op(2, lambda x, y: [x + y]),
"-": op(2, lambda x, y: [x - y]),
"*": op(2, lambda x, y: [x * y]),
"/": op(2, lambda x, y: [x / y]),
"**": op(2, lambda x, y: [x ** y]),
# Stack Manipulation
"drop": op(1, lambda x: []),
"swap": op(2, lambda x, y: [y, x]),
"dup": op(1, lambda x: [x, x]),
"over": op(2, lambda x, y: [x, y, x]),
"rot": op(3, lambda x, y, z: [y, z, x]),
# Boolean Logic
"nand": op(2, lambda x, y: [D(not (x and y))]),
# Inequality
"<=": op(2, lambda x, y: [D(x <= y)]),
}
@property
def stack(self):
"""Return a read-only version of the current
stack."""
return tuple(self._stack)
def execute(self, command):
"""Execute an RPN command.
Tokens are split on whitespace.
"""
for token in command.split():
try:
token = D(token)
self._stack.append(token)
except decimal.InvalidOperation:
if token in self._operations:
self._operations[token]()
else:
raise ValueError(
f"{token!r} not recognized as operation or number."
)
class RPNInterpreter:
"""Adds support for comments and macros on top of an
RPNCalc.
Comments are stripped from "#" to the end of the line.
Macro statements look like
macro NAME EXPANSION
E.g.
macro sqrt 0.5 **
SHOW statement shows the stack.
Also lower-cases the input, so "drop" can be written as
"DROP" or "Drop", etc.
"""
def __init__(self):
"""Initialize the underlying RPNCalc and the macro
table."""
self._calculator = RPNCalc()
self._macros = {}
def execute(self, line):
"""Execute a line by removing comments, then
- Processing macro-statements, OR
- Processing show-statements, OR
- Expanding all macros (exhaustively) and executing
the resulting line in the underlying RPNCalc.
Then return the top of the stack, or None if the
stack is empty.
"""
line = line.lower()
line = re.sub(r"#.*$", "", line)
match_macro = re.match(
r"macro\s+(?P<name>\S+)\s*(?P<expansion>.*)$",
line,
)
if match_macro:
self._macros[match_macro["name"]] = match_macro[
"expansion"
]
elif line.strip() == "show":
return [
float(x) for x in self._calculator.stack
]
else:
maybe_macro = lambda x: self._macros.get(x, x)
exhausted = False
while not exhausted:
old_line = line
line = re.sub(
"\S+", lambda m: maybe_macro(m[0]), line
)
exhausted = old_line == line
self._calculator.execute(line)
try:
return self._calculator.stack[-1]
except IndexError:
return
if __name__ == "__main__":
import argparse
parser = argparse.ArgumentParser()
parser.add_argument(
"scripts",
nargs="*",
help="execute these files before the REPL",
)
args = parser.parse_args()
interpreter = RPNInterpreter()
for script in args.scripts:
with open(script) as file:
for line in file:
try:
result = interpreter.execute(line)
except Exception as e:
print(f"ERROR in {script}, {e.args[0]}")
import readline
while True:
try:
line = input(" ")
except EOFError:
break
try:
result = interpreter.execute(line)
except Exception as e:
print("ERROR", e.args[0])
else:
if result is not None:
print(result)
print()
```

`$ ./rpncalc --help`

```
usage: rpncalc [-h] [scripts [scripts ...]]
positional arguments:
scripts execute these files before the REPL
optional arguments:
-h, --help show this help message and exit
```

# Using my calculator

```
$ ./rpncalc
```

I can use `rpncalc`

to calculate the square root of 2:

`2 .5 **`

```
1.414213562373095048801688724
```

I can also calculate the distance from the point (3, 4) to the point (0, 0):

`3 2 ** 4 2 ** + .5 **`

```
5.000000000000000000000000000
```

I think it's hard to read `2 **`

for squaring and `.5 **`

for square roots, so
I create macros for squaring and square rooting:

`macro ^2 2 ** macro sqrt .5 ** 3 ^2 4 ^2 + sqrt`

```
5.000000000000000000000000000
```

I think this would be easier to read if I could group some of the terms, so I like to have an "empty" macro that I just use for readability:

`3 ^2 , 4 ^2 , + sqrt`

```
5.000000000000000000000000000
```

Even though the macro system is simple, because this calculator uses a concatenative programming language I can create more advanced macros, such as unit conversions.

If I know that a 1 inch is 2.54 centimeters, then how many centimeters are in 6 feet 4 inches?

`macro cm macro in 2.54 * cm macro ft 12 * in macro ->cm 1 cm / 6 ft 4 in + ->cm`

```
193.04
```

# Building a "standard library" for my calculator

I have a few macros that I like to consistently use.
I have incorporated these into a standard library, a file named **stdlib.**

stdlib

```
# rpncalc Standard Library
macro ,
# Boolean.
macro not dup nand
macro and nand not
macro or not swap not nand
macro nor or not
# Equality and inequality.
macro > <= not
macro < swap >
macro >= swap <=
macro = over over <= rot rot >= and
macro != = not
# Multiplexing.
# a b s mux => like JavaScript "s ? b : a".
macro mux 0 != rot over not * rot rot * +
```

What are these macros?

`,`

is an empty macro, used for grouping terms and improving readability.`not`

,`and`

,`or`

, and`nor`

are logical operators. I derived them from the calculator's built-in`nand`

operation. (See "NAND logic" via Wikipedia for more information on deriving logical operators from`nand`

.)- I use the built-in "less-than" operator
`<=`

to derive the other inequality and equality operators:`>`

,`<`

,`>=`

,`=`

, and`!=`

. - The
`mux`

macro is a multiplexer that acts like an if-else statement. If the condition is true (non-zero), choose one value. If the condition is false (zero), choose the other value.

Here's an example of using **stdlib** to explore the golden ratio, φ:

`$ ./rpncalc stdlib macro abs dup 0 > -1 1 rot mux * macro ~ - abs 1e-8 < 0 0 ~`

```
1
```

`0.0000000000001 0 ~`

```
1
```

`macro sqrt .5 ** macro phi 5 sqrt 1 + 2 / phi`

```
1.618033988749894848204586834
```

`macro ^2 2 ** phi ^2`

```
2.618033988749894848204586833
```

`phi ^2 , phi 1 + , ~`

```
1
```

# Building a library for calculating body mass index (BMI)

Body mass index (BMI) is a measurement used to broadly classify a person's weight (given their height) into categories like "underweight", "normal weight", and "overweight".

I created a library, **bmi**, that allows me to make BMI calculations:

bmi

```
# rpncalc Body Mass Index (BMI) Library
#
# You MUST also load rpncalc stdlib.
# Units - Weight
macro kg
macro lb 0.453592 * kg
macro st 6.35 * kg
macro ->kg 1 kg /
# Units - Height
macro m
macro cm 100 / m
macro ft 0.3048 * m
macro in 12 / ft
macro ->m 1 m /
# BMI Formula
#
# height weight bmi
#
# E.g.
#
# 5 ft 7 in + , 175 lb , bmi
macro bmi ->kg swap ->m , 2 ** /
# BMI Classifications
#
# bmi *
#
# E.g.
#
# 33.3 obese
macro _range rot dup rot < rot rot <= and
macro underweight 18.5 <
macro normal-weight 18.5 25 _range
macro overweight 25 30 _range
macro obese 30 >=
# Classify BMI using a number:
# 1 - underweight
# 2 - normal-weight
# 3 - overweight
# 4 - obese
#
# E.g.
#
# 22.5 classify-bmi
macro classify-bmi _c1
macro _c1 dup underweight swap _c2 swap 1 swap mux
macro _c2 dup normal-weight swap _c3 swap 2 swap mux
macro _c3 dup overweight swap _c4 swap 3 swap mux
macro _c4 dup obese swap _c5 swap 4 swap mux
macro _c5 drop -1
```

I'll use this to look at the BMI of several people:

- 5ft 8in and 250lbs.
- 161cm and 14st 5lbs.
- 6ft 3in and 156lbs.

`$ ./rpncalc stdlib bmi macro bmi_1 5 ft 8 in + , 250 lb , bmi bmi_1`

```
38.01194886126796475046237290
```

`classify-bmi`

```
4
```

`bmi_1 obese`

```
1
```

`macro bmi_2 161 cm , 14 st 5 lb + , bmi bmi_2`

```
35.17146715018710697889741908
```

`classify-bmi`

```
4
```

`bmi_2 underweight`

```
0
```

`bmi_2 obese`

```
1
```

`macro bmi_3 6 ft 3 in + , 156 lb , bmi bmi_3`

```
19.49844710356087378841424350
```

`classify-bmi`

```
2
```

`bmi_3 underweight`

```
0
```

`bmi_3 overweight`

```
0
```

`bmi_3 normal-weight`

```
1
```

# How the script works

The `RPNCalc`

class manages the stack, and the `RPNInterpreter`

class manages
the macros.

I use Decimal objects for numbers because they have more accuracy than floating point numbers.

I represent the stack as a list and use list methods to push and pop from the stack.

The stack manipulation operations, like `dup`

, are taken from the Forth
programming language.

I tokenize strings using str.split, which does a simple split on whitespace. If I wanted to allow tokens containing whitespace, I might use the shlex module.

Macros are also implemented using simple text substitution. Because reverse Polish notation (RPN) lends itself to being a concatenative language, even simple text replacement macros can be used to construct advanced functions, like classifying BMI.

I use the built-in function input to get user input. I also import the readline module, to allow for more elaborate line editing and history features. (See the readline module for details.)

# In conclusion...

In this week's post you learned how to create a reverse Polish notation (RPN) calculator that supports macros. You also learned how to construct more advanced macros that converted between different units of measurement and calculated medical measurements, like body mass index (BMI).

My challenge to you:

Create macros for units of space and time (e.g. meters and seconds) and use them to convert speed values (e.g. convert 150 miles/hour to meters/second).

If you enjoyed this week's post, share it with your friends and stay tuned for next week's post. See you then!