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Shellfloat is copyright (c) 2020 by Michael Wood.
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the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<https://www.gnu.org/licenses/why-not-lgpl.html>.

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# Shellmath
Introducing decimal arithmetic libraries for the Bash shell, because
they said it couldn't be done... and because:
.
![image info](./image.png)
## Quick-start guide
Download this project and source the file `shellmath.sh` into your shell script,
then fire away at the shellmath API!
The ___basic___ API looks like this:
```
_shellmath_add arg1 arg2 [...] argN
_shellmath_subtract arg1 arg2 # means arg1 - arg2
_shellmath_multiply arg1 arg2 [...] argN
_shellmath_divide arg1 arg2 # means arg1 / arg2
```
The ___extended___ API introduces one more function:
```
_shellmath_getReturnValue arg
```
This function optimizes away the need for ___$(___ subshelling ___)___ in order to capture `shellmath`'s output.
To use this feature, just be sure to set `__shellmath_isOptimized=1` at the top
of your script. (You can find an example in `faster_e_demo.sh`.)
Operands to the _shellmath_ functions can be integers or decimal
numbers presented in either standard or scientific notation:
```
_shellmath_add 1.009 4.223e-2
_shellmath_getReturnValue sum
echo "The sum is $sum"
```
Addition and multiplication are of arbitrary arity; try this on for size:
```
_shellmath_multiply 1 2 3 4 5 6
_shellmath_getReturnValue sixFactorial
echo "6 factorial is $sixFactorial"
```
Subtraction and division, OTOH, are exclusively binary operations.
## The demos
For a gentle introduction to `shellmath` run the demo `slower_e_demo.sh`
with a small whole-number argument, say 15:
```
$ slower_e_demo.sh 15
e = 2.7182818284589936
```
This script uses a few `shellmath` API calls to calculate *e*, the mathematical
constant also known as [Euler's number](https://oeis.org/A001113). The argument
*15* tells the script to evaluate the *15th-degree* Maclaurin polynomial for *e*.
(That's the Taylor polynomial centered at 0.) Take a look inside the script to
see how it uses the `shellmath` APIs.
There is another demo script very much like this one but *different*, and the
sensitive user can *feel* the difference. Try the following, but don't blink
or you'll miss it ;)
```
$ faster_e_demo.sh 15
e = 2.7182818284589936
```
Did you feel the difference? Try the `-t` option with both scripts; this will produce
timing statistics. Here are my results
when running from my minGW64 command prompt on Windows 10 with an Intel i3 Core CPU:
```
$ for n in {1..5}; do faster_e_demo.sh -t 15 2>&1; done | awk '/^real/ {print $2}'
0m0.055s
0m0.051s
0m0.056s
0m0.054s
0m0.054s
$ for n in {1..5}; do slower_e_demo.sh -t 15 2>&1; done | awk '/^real/ {print $2}'
0m0.498s
0m0.594s
0m0.536s
0m0.511s
0m0.580s
```
(When sizing up these timings, do keep in mind that ___we are timing the
calculation of e from its Maclaurin polynomial. Every invocation of either
script is exercising the shellmath arithmetic subroutines 31 times.___)
The comment header in `faster_e_demo.sh` explains the optimization and shows
how to put this faster version to work for you.
## Runtime efficiency competitive with awk and bc
The file `timingData.txt` captures the results of some timing experiments that compare
`shellmath` against the GNU versions of the calculators `awk` and `bc`. The experiments
exercised each of the arithmetic operations and captured the results in a shell variable.
The result summary below shows that `shellmath` is competitive with `awk` and runs faster
than `bc` in these experiments. (One commenter noted that the differences in execution speed
can be partially explained by the fact that `shellmath` and `awk` use finite precision
whereas `bc` uses arbitrary precision. Another factor in these measurements is the need to
subshell 'awk' and 'bc' to capture their results, whereas 'shellmath' writes directly to
the shell's global memory.)
Here are the run times of `shellmath` as a percentage of the `awk` and `bc` equivalents:
```
versus awk versus bc
Addition: 82.2% 40.6%
Subtraction: 95.9% 50.5%
Multiplication: 135.9% 73.3%
Division: 80.3% 43.2%
```
Astute observers will note the experiments provide approximations to the sum, difference,
product, and quotient of *pi* and *e*. Unfortunately I did not gain insight as to which
of these values, if any, are
[transcendental](https://en.wikipedia.org/wiki/Transcendental_number#Possible_transcendental_numbers).
You can find a deeper discussion of shellmath's runtime efficiency
[here](https://github.com/clarity20/shellmath/wiki/Shellmath-and-runtime-efficiency).
## Background
The Bash shell does not have built-in operators for decimal arithmetic, making it
something of an oddity among well-known, widely-used programming languages. For the most part,
practitioners in need of powerful computational building blocks have naturally opted
for *other* languages and tools. Their widespread availability has diverted attention
from the possibility of *implementing* decimal arithmetic in Bash and it's easy to assume
that this ***cannot*** be done:
+ From the indispensable _Bash FAQ_ (on _Greg's Wiki_): [How can I calculate with floating point numbers?](http://mywiki.wooledge.org/BashFAQ/022)
*"For most operations... an external program must be used."*
+ From Mendel Cooper's wonderful and encyclopedic _Advanced Bash Scripting Guide_:
[Bash does not understand floating point arithmetic. Use bc instead.](https://tldp.org/LDP/abs/html/ops.html#NOFLOATINGPOINT)
+ From a community discussion on Stack Overflow, _How do I use floating point division in bash?_
The user's [preferred answer](https://stackoverflow.com/questions/12722095/how-do-i-use-floating-point-division-in-bash#12722107)
is a good example of _prevailing thought_ on this subject.
Meanwhile,
+ Bash maintainer (BDFL?) Chet Ramey sounds a (brighter?) note in [The Bash Reference Guide, Section 6.5](https://tiswww.case.edu/php/chet/bash/bashref.html#Shell-Arithmetic)
by emphasizing what the built-in arithmetic operators ***can*** do.
But finally, a glimmer of hope:
+ A [diamond-in-the-rough](http://stackoverflow.com/a/24431665/3776858) buried elsewhere
on Stack Overflow.
This down-and-dirty milestone computes the decimal quotient of two integer arguments. At a casual
glance, it seems to have drawn inspiration from the [Euclidean algorithm](https://mathworld.wolfram.com/EuclideanAlgorithm.html)
for computing GCDs, an entirely different approach than `shellmath`'s.
Please try `shellmath` on for size and draw your own conclusions!
## How it works
`shellmath` splits decimal numbers into their integer and fractional parts,
performs the appropriate integer operations on the parts, and recombines the results.
(In the spirit of Bash, numerical overflow is silently ignored.)
Because if we can get carrying, borrowing, place value, and the distributive
law right, then the sky's the limit! As they say--erm, as they ___said___ in Rome,
Ad astra per aspera.
## And now...
You can run your floating-point calculations directly in Bash!
## Please see also:
[A short discussion on arbitrary precision and shellmath](https://github.com/clarity20/shellmath/wiki/Shellmath-and-arbitrary-precision-arithmetic)

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#!/bin/env bash
###############################################################################
# Internal test engine functions
###############################################################################
RED='\033[0;31m'
GREEN='\033[0;32m'
NO_COLOR='\033[0m'
function _shellmath_assert_returnCode()
{
_shellmath_assert_functionReturn -c "$@"
return $?
}
function _shellmath_assert_returnString()
{
_shellmath_assert_functionReturn "$@"
return $?
}
function _shellmath_assert_functionReturn()
{
if [[ $# -lt 2 ]]; then
echo "USAGE: ${FUNCNAME[0]} [-c] returnStringOrCode functionName [ functionArgs ... ]"
echo " By default, asserts against the string output by the function."
echo " Use -c to assert against the numeric return code instead."
return "${__shellmath_returnCodes[FAIL]}"
fi
if [[ "${1,,}" == '-c' ]]; then
mode=RETURN_CODE
shift
else
mode=RETURN_STRING
fi
expectedReturn="$1"
func="$2"
shift 2
args=("$@")
# Exercise the function in optimized mode; it will run faster by avoiding
# subshelling. This also suppresses dumping of function output to stdout.
__shellmath_isOptimized=${__shellmath_true}
"$func" "${args[@]}"
returnCode=$?
__shellmath_isOptimized=${__shellmath_false}
# Fetch the return value(s)
local numReturnValues
declare -a actualReturn
_shellmath_getReturnValueCount numReturnValues
if ((numReturnValues == 1)); then
_shellmath_getReturnValue actualReturn[0]
else
# Multiple returns? Join them into one string
local _i evalString="_shellmath_getReturnValues"
for ((_i=0; _i<numReturnValues; _i++)); do
evalString+=" actualReturn[$_i]"
done
eval "$evalString"
fi
if [[ $mode == RETURN_STRING ]]; then
if [[ "${actualReturn[*]}" == "$expectedReturn" ]]; then
_shellmath_setReturnValue "${GREEN}ok${NO_COLOR} "
return "$__shellmath_SUCCESS"
else
_shellmath_setReturnValue "${RED}FAIL${NO_COLOR} (${actualReturn[*]}) "
return "$__shellmath_FAIL"
fi
elif [[ $mode == RETURN_CODE ]]; then
if [[ "$returnCode" == "$expectedReturn" ]]; then
_shellmath_setReturnValue "${GREEN}ok${NO_COLOR} "
return "$__shellmath_SUCCESS"
else
_shellmath_setReturnValue "${RED}FAIL${NO_COLOR} ($returnCode) "
return "$__shellmath_FAIL"
fi
fi
}

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#!/usr/bin/env bash
###############################################################################
# This script performs the same task as "slower_e_demo.sh" but with a major
# performance optimization. The speedup is especially noticeable on GNU
# emulation layers for Windows such as Cygwin and minGW, where the overhead
# of subshelling is quite significant.
#
# The speedup uses global storage space to simulate pass-and-return by
# reference so that you can capture the side effects of a function call without
# writing to stdout and wrapping the call in a subshell. How to use:
#
# Turn on "__shellmath_isOptimized" as shown below.
# Then instead of invoking "mySum = $(_shellmath_add $x $y)",
# call "_shellmath_add $x $y; _shellmath_getReturnValue mySum".
###############################################################################
source shellmath.sh
# Setting the '-t' flag will cause the script to time the algorithm
if [[ "$1" == '-t' ]]; then
do_timing=${__shellmath_true}
shift
fi
if [[ $# -ne 1 ]]; then
echo "USAGE: ${BASH_SOURCE##*/} [-t] *N*"
echo " Approximates 'e' using the N-th order Maclaurin polynomial"
echo " (i.e. the Taylor polynomial centered at 0)."
echo " Specify the '-t' flag to time the main algorithm."
exit 0
elif [[ ! "$1" =~ ^[0-9]+$ ]]; then
echo "Illegal argument. Whole numbers only, please."
exit 1
fi
__shellmath_isOptimized=${__shellmath_true}
function run_algorithm()
{
# Initialize
n=0; N=$1; zero_factorial=1
# Initialize "e" to its zeroth-order term
_shellmath_divide 1 $zero_factorial
_shellmath_getReturnValue term
e=$term
# Compute successive terms T(n) := T(n-1)/n and accumulate into e
for ((n=1; n<=N; n++)); do
_shellmath_divide "$term" "$n"
_shellmath_getReturnValue term
_shellmath_add "$e" "$term"
_shellmath_getReturnValue e
done
echo "e = $e"
}
if (( do_timing == __shellmath_true )); then
time run_algorithm "$1"
else
run_algorithm "$1"
fi
exit 0

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#!/bin/env bash
###############################################################################
# runTests.sh
#
# Usage: runTests.sh [testFile]
# where testFile defaults to testCases.in
#
# Processes a test file such as the testCases.in included with this package
###############################################################################
# Process one line from the test cases file. Invoked below through mapfile.
function _shellmath_runTests()
{
local lineNumber=$1
local text=$2
# Trim leading whitespace
[[ $text =~ ^[$' \t']*(.*) ]]
text=${BASH_REMATCH[1]}
# Skip comments and blank lines
[[ "$text" =~ ^# || -z $text ]] && return 0
# Check for line continuation
local len="${#text}"
if [[ ${text:$((len-1))} == '\' ]]; then
# Eat the continuation character and add to the buffer
__shellfloat_commandBuffer+="${text/%\\/ }"
# Defer processing
return
# No line continuation
else
# Assemble the command
local command=${__shellfloat_commandBuffer}${text}
__shellfloat_commandBuffer=""
words=($command)
# Expand first word to an assertion function
case ${words[0]} in
Code)
words[0]=_shellmath_assert_return${words[0]}
# Validate next word as a positive integer
if [[ ! "${words[1]}" =~ ^[0-9]+$ ]]; then
echo Line: "$lineNumber": Command "$command"
echo FAIL: \"Code\" requires integer return code
return 1
else
nextWord=2
fi
;;
String)
words[0]=_shellmath_assert_return${words[0]}
# Allow multiword arguments if quoted
if [[ ${words[1]} =~ ^\" ]]; then
if [[ ${words[1]} =~ \"$ ]]; then
nextWord=2
else
for ((nextWord=2;;nextWord++)); do
if [[ ${words[nextWord]} =~ \"$ ]]; then
((nextWord++))
break
fi
done
fi
else
nextWord=2
fi
;;
Both)
;;
*)
echo -e ${RED}FAIL${NO_COLOR} Line "$lineNumber": Command "$command": Code or String indicator required
return 2
;;
esac
# Expand the next word to a shellmath function name
words[nextWord]=_shellmath_${words[nextWord]}
if ! type -t "${words[nextWord]}" >/dev/null; then
echo "${RED}FAIL${NO_COLOR} Line $lineNumber: Command "$command": Syntax error. Required: String|Code value operation args..."
return 3
fi
# Run the command, being respectful of shell metacharacters
fullCommand="${words[*]}"
eval "$fullCommand"
local returnString
_shellmath_getReturnValue returnString
echo -e "$returnString" Line "$lineNumber": "$command"
fi
}
function _main()
{
source shellmath.sh
source assert.sh
# Initialize certain globals. As "public" functions, the arithmetic
# functions need to do this themselves, but there are some "private"
# functions that need this here when they are auto-tested.
_shellmath_precalc; __shellmath_didPrecalc=$__shellmath_true
# Process the test file line-by-line using the above runTests() function
mapfile -t -c 1 -C _shellmath_runTests -O 1 < "${1:-testCases.in}"
exit 0
}
_main "$@"

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#!/usr/bin/env bash
###############################################################################
# This script illustrates the use of the shellmath APIs to perform
# decimal calculations. Here we approximate the mathematical constant 'e'
# using its Maclaurin polynomials (i.e. its Taylor polynomials centered at 0).
###############################################################################
source shellmath.sh
# Setting the '-t' flag will cause the script to time the algorithm
if [[ "$1" == '-t' ]]; then
do_timing=${__shellmath_true}
shift
fi
if [[ $# -ne 1 ]]; then
echo "USAGE: ${BASH_SOURCE##*/} [-t] *N*"
echo " Approximates 'e' using the N-th order Maclaurin polynomial"
echo " (i.e. the Taylor polynomial centered at 0)."
echo " Specify the '-t' flag to time the main algorithm."
exit 0
elif [[ ! "$1" =~ ^[0-9]+$ ]]; then
echo "Illegal argument. Whole numbers only, please."
exit 1
fi
function run_algorithm()
{
# Initialize
n=0; N=$1; zero_factorial=1
# Initialize e to the zeroth-order term
term=$(_shellmath_divide 1 $zero_factorial)
e=$term
# Compute successive terms T(n) := T(n-1)/n and accumulate into e
for ((n=1; n<=N; n++)); do
term=$(_shellmath_divide "$term" "$n")
e=$(_shellmath_add "$e" "$term")
done
echo "e = $e"
}
if (( do_timing == __shellmath_true )); then
time run_algorithm "$1"
else
run_algorithm "$1"
fi
exit 0

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################################################################
# The general testcase syntax is
# assertionType expectedValue functionUnderTest [args ... ]
#
# where assertionType is either of:
# Code to indicate the (bash-style) integer return code
# String to indicate the string "printed" as a side effect
#
# and functionUnderTest is the function name
# with the "_shellmath_" prefix removed.
################################################################
################################
# Tests for SUPPORTING FUNCTIONS
################################
# Tests for getReturnCode()
Code 0 getReturnCode SUCCESS
Code 1 getReturnCode FAIL
Code 2 getReturnCode ILLEGAL_NUMBER
## Tests for validateAndParse():
## Validate a number, determine its type and sign, split it into parts
# Detect Invalid input
Code 2 validateAndParse NaN
String "" validateAndParse NaN
# Positive integers
String "4 0 0 0 0" validateAndParse 4
# Negative integers
String "9 0 1 0 0" validateAndParse -9
# Decimals
String "4 2 0 1 0" validateAndParse 4.2
# Negative decimals
String "4 2 1 1 0" validateAndParse -4.2
# Scientific / exponential notation: Check all code branches
String "340000 0 0 0 1" validateAndParse 3.4e5
String "344 4 0 1 1" validateAndParse 3.444e2
String "34567 0 0 0 1" validateAndParse 3.4567e4
String "0 003456 0 1 1" validateAndParse 3.456e-3
String "34 56 0 1 1" validateAndParse 345.6e-1
String "0 23011 0 1 1" validateAndParse 23.011e-2
String "23 011 0 1 1" validateAndParse 23.011e0
####################
# Tests for ADDITION
####################
String 4 add 4
String 9 add 4 5
# Same-length decimal tails with no leading zeros, no carry across decimal point
String 2.214 add 1.105 1.109
# Carry across decimal point
String 3.8 add 1.9 1.9
String -3.8 add -1.9 -1.9
# Different-length decimals, one with leading zero
String 2.195 add 1.105 1.09
String -2.195 add -1.105 -1.09
# Same-length tails having leading zeros
String 2.014 add 1.005 1.009
String -2.014 add -1.005 -1.009
# Different-length tails with and without leading zeros
String 3.31462 add 1.905 1.40962
String 2.01462 add 1.005 1.00962
# Subtraction
String 2.5 subtract 5.2 2.7
String -2.5 subtract 2.7 5.2
String 2.5 add 5.2 -2.7
# Integer part equal to 0
String 1.5 add 0.6 0.9
String 1.5 add .6 .9
String -0.3 add 0.6 -0.9
String -0.3 add .6 -.9
# Recursive/multiple addition
String 12 add 2 4 6
String 6.6 add 1.1 2.2 3.3
##########################
# Tests for MULTIPLICATION
##########################
String 4 multiply 4
String 20 multiply 4 5
String 21.32 multiply 4.1 5.2
String -21.32 multiply -4.1 5.2
# Carry-heavy products
String 98.901 multiply 9.9 9.99
# Leading zeros after decimal point:
# Track place value with zero-padding
String 1.0201 multiply 1.01 1.01
String 0.0001 multiply 0.01 0.01
String 0.0001 add 0 0.0001
# Staggered decimal precisions
String 0.000001 multiply 0.01 0.0001
# Interpret in base 10
String 2.2781 multiply 1.09 2.09
# Recursive multiplication
String 35.1384 multiply 1.1 2.2 3.3 4.4
####################
# Tests for DIVISION
####################
String 4 divide 4
String 4 divide 20 5
String 0.5 divide 1 2
String -0.5 divide -1 2
# Mixed fractions
String 34.54 divide 3454 100
# Non-terminating decimals
String 0.166666666666666667 divide 1 6
# Decimal arguments
String 0.25 divide 0.5 2
String 0.04165 divide 0.1666 4
###########################
# Tests for scientific math
###########################
String 8.8e4 add 1.1e4 7.7e4
String 4.239e1 add 1.224e1 3.015e1
String -6.6e4 add 1.1e4 -7.7e4
String -66000 add 11000 -77000
String 1.23123e2 add 1.23e2 1.23e-1
String 8.1403e7 multiply 2.03e5 4.01e2
String 1.0e-7 multiply 1.0e-3 1.0e-4
String 1.0e-7 multiply 1e-3 1e-4

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$ ######## Activate optimized mode as described in the README ########
$ __shellmath_isOptimized=1
$ ######## Addition ########
$ time { for ((i=0; i<100; i++)); do _shellmath_add 3.1415926 2.7182818; _shellmath_getReturnValue sum; done; }
real 0m0.196s
user 0m0.195s
sys 0m0.000s
$ time { for ((i=0; i<100; i++)); do sum=$(bc <<< "3.1415926+2.7182818"); done; }
real 0m0.488s
user 0m0.092s
sys 0m0.384s
$ ######## Subtraction ########
$ time { for ((i=0; i<100; i++)); do _shellmath_subtract 3.1415926 2.7182818; _shellmath_getReturnValue diff; done; }
real 0m0.236s
user 0m0.234s
sys 0m0.001s
$ time { for ((i=0; i<100; i++)); do diff=$(bc <<< "3.1415926-2.7182818"); done; }
real 0m0.461s
user 0m0.090s
sys 0m0.388s
$ ######## Multiplication ########
$ time { for ((i=0; i<100; i++)); do _shellmath_multiply 3.1415926 2.7182818; _shellmath_getReturnValue prod; done; }
real 0m0.340s
user 0m0.333s
sys 0m0.005s
$ time { for ((i=0; i<100; i++)); do prod=$(bc <<< "3.1415926*2.7182818"); done; }
real 0m0.465s
user 0m0.105s
sys 0m0.377s
$ ######## Division ########
$ time { for ((i=0; i<100; i++)); do _shellmath_divide 3.1415926/2.7182818; _shellmath_getReturnValue quot; done; }
real 0m0.196s
user 0m0.195s
sys 0m0.000s
$ time { for ((i=0; i<100; i++)); do quot=$(bc <<< "scale=8; 3.1415926/2.7182818"); done; }
real 0m0.463s
user 0m0.116s
sys 0m0.364s