12.8. Math Commands

Command Listing

factor

Decompose an integer into prime factors.

bash$ factor 27417
27417: 3 13 19 37
	      

bc, dc

These are flexible, arbitrary precision calculation utilities.

bc has a syntax vaguely resembling C.

dc uses RPN ("Reverse Polish Notation").

Of the two, bc seems more useful in scripting. It is a fairly well-behaved UNIX utility, and may therefore be used in a pipe.

Bash can't handle floating point calculations, and it lacks operators for certain important mathematical functions. Fortunately, bc comes to the rescue.

Here is a simple template for using bc to calculate a script variable. This uses command substitution.

	      variable=$(echo "OPTIONS; OPERATIONS" | bc)
	      

Example 12-28. Monthly Payment on a Mortgage

#!/bin/bash
# monthlypmt.sh: Calculates monthly payment on a mortgage.


# This is a modification of code in the "mcalc" (mortgage calculator) package,
# by Jeff Schmidt and Mendel Cooper (yours truly, the author of this document).
#   http://www.ibiblio.org/pub/Linux/apps/financial/mcalc-1.6.tar.gz  [15k]

echo
echo "Given the principal, interest rate, and term of a mortgage,"
echo "calculate the monthly payment."

bottom=1.0

echo
echo -n "Enter principal (no commas) "
read principal
echo -n "Enter interest rate (percent) "  # If 12%, enter "12", not ".12".
read interest_r
echo -n "Enter term (months) "
read term


 interest_r=$(echo "scale=9; $interest_r/100.0" | bc) # Convert to decimal.
                 # "scale" determines how many decimal places.
  

 interest_rate=$(echo "scale=9; $interest_r/12 + 1.0" | bc)
 

 top=$(echo "scale=9; $principal*$interest_rate^$term" | bc)

 echo; echo "Please be patient. This may take a while."

 let "months = $term - 1"
 for ((x=$months; x > 0; x--))
 do
   bot=$(echo "scale=9; $interest_rate^$x" | bc)
   bottom=$(echo "scale=9; $bottom+$bot" | bc)
#  bottom = $(($bottom + $bot"))
 done

 # let "payment = $top/$bottom"
 payment=$(echo "scale=2; $top/$bottom" | bc)
 # Use two decimal places for dollars and cents.
 
 echo
 echo "monthly payment = \$$payment"  # Echo a dollar sign in front of amount.
 echo


 exit 0

 # Exercises:
 #   1) Filter input to permit commas in principal amount.
 #   2) Filter input to permit interest to be entered as percent or decimal.
 #   3) If you are really ambitious,
 #      expand this script to print complete amortization tables.

Example 12-29. Base Conversion

:
##########################################################################
# Shellscript:	base.sh - print number to different bases (Bourne Shell)
# Author     :	Heiner Steven (heiner.steven@odn.de)
# Date       :	07-03-95
# Category   :	Desktop
# $Id: base.sh,v 1.2 2000/02/06 19:55:35 heiner Exp $
##########################################################################
# Description
#
# Changes
# 21-03-95 stv	fixed error occuring with 0xb as input (0.2)
##########################################################################

# ==> Used in this document with the script author's permission.
# ==> Comments added by document author.

NOARGS=65
PN=`basename "$0"`			       # Program name
VER=`echo '$Revision: 1.2 $' | cut -d' ' -f2`  # ==> VER=1.2

Usage () {
    echo "$PN - print number to different bases, $VER (stv '95)
usage: $PN [number ...]

If no number is given, the numbers are read from standard input.
A number may be
    binary (base 2)		starting with 0b (i.e. 0b1100)
    octal (base 8)		starting with 0  (i.e. 014)
    hexadecimal (base 16)	starting with 0x (i.e. 0xc)
    decimal			otherwise (i.e. 12)" >&2
    exit $NOARGS 
}   # ==> Function to print usage message.

Msg () {
    for i   # ==> in [list] missing.
    do echo "$PN: $i" >&2
    done
}

Fatal () { Msg "$@"; exit 66; }

PrintBases () {
    # Determine base of the number
    for i      # ==> in [list] missing...
    do         # ==> so operates on command line arg(s).
	case "$i" in
	    0b*)		ibase=2;;	# binary
	    0x*|[a-f]*|[A-F]*)	ibase=16;;	# hexadecimal
	    0*)			ibase=8;;	# octal
	    [1-9]*)		ibase=10;;	# decimal
	    *)
		Msg "illegal number $i - ignored"
		continue;;
	esac

	# Remove prefix, convert hex digits to uppercase (bc needs this)
	number=`echo "$i" | sed -e 's:^0[bBxX]::' | tr '[a-f]' '[A-F]'`
	# ==> Uses ":" as sed separator, rather than "/".

	# Convert number to decimal
	dec=`echo "ibase=$ibase; $number" | bc`  # ==> 'bc' is calculator utility.
	case "$dec" in
	    [0-9]*)	;;			 # number ok
	    *)		continue;;		 # error: ignore
	esac

	# Print all conversions in one line.
	# ==> 'here document' feeds command list to 'bc'.
	echo `bc <<!
	    obase=16; "hex="; $dec
	    obase=10; "dec="; $dec
	    obase=8;  "oct="; $dec
	    obase=2;  "bin="; $dec
!
    ` | sed -e 's: :	:g'

    done
}

while [ $# -gt 0 ]
do
    case "$1" in
	--)	shift; break;;
	-h)	Usage;;                 # ==> Help message.
	-*)	Usage;;
	*)	break;;			# first number
    esac   # ==> More error checking for illegal input would be useful.
    shift
done

if [ $# -gt 0 ]
then
    PrintBases "$@"
else					# read from stdin
    while read line
    do
	PrintBases $line
    done
fi

An alternate method of invoking bc involves using a here document embedded within a command substitution block. This is especially appropriate when a script needs to pass a list of options and commands to bc.

variable=`bc << LIMIT_STRING
options
statements
operations
LIMIT_STRING
`

...or...


variable=$(bc << LIMIT_STRING
options
statements
operations
LIMIT_STRING
)

Example 12-30. Another way to invoke bc

#!/bin/bash
# Invoking 'bc' using command substitution
# in combination with a 'here document'.


var1=`bc << EOF
18.33 * 19.78
EOF
`
echo $var1       # 362.56


#  $( ... ) notation also works.
v1=23.53
v2=17.881
v3=83.501
v4=171.63

var2=$(bc << EOF
scale = 4
a = ( $v1 + $v2 )
b = ( $v3 * $v4 )
a * b + 15.35
EOF
)
echo $var2       # 593487.8452


var3=$(bc -l << EOF
scale = 9
s ( 1.7 )
EOF
)
# Returns the sine of 1.7 radians.
# The "-l" option calls the 'bc' math library.
echo $var3       # .991664810


# Now, try it in a function...
hyp=             # Declare global variable.
hypotenuse ()    # Calculate hypotenuse of a right triangle.
{
hyp=$(bc -l << EOF
scale = 9
sqrt ( $1 * $1 + $2 * $2 )
EOF
)
# Unfortunately, can't return floating point values from a Bash function.
}

hypotenuse 3.68 7.31
echo "hypotenuse = $hyp"    # 8.184039344


exit 0
awk

Yet another way of doing floating point math in a script is using awk's built-in math functions in a shell wrapper.

Example 12-31. Calculating the hypotenuse of a triangle

#!/bin/bash
# hypotenuse.sh: Returns the "hypotenuse" of a right triangle.
#               ( square root of sum of squares of the "legs")

ARGS=2                # Script needs sides of triangle passed.
E_BADARGS=65          # Wrong number of arguments.

if [ $# -ne "$ARGS" ] # Test number of arguments to script.
then
  echo "Usage: `basename $0` side_1 side_2"
  exit $E_BADARGS
fi


AWKSCRIPT=' { printf( "%3.7f\n", sqrt($1*$1 + $2*$2) ) } '
#            command(s) / parameters passed to awk


echo -n "Hypotenuse of $1 and $2 = "
echo $1 $2 | awk "$AWKSCRIPT"

exit 0