Advanced Bash-Scripting Guide: Prev Chapter 16. External Filters, Programs and Commands Next

16.8. Math Commands"Doing the numbers"

factor

Decompose an integer into prime factors.

bash$ factor 2741727417: 3 13 19 37

Example 16-46. Generating prime numbers

#!/bin/bash# primes2.sh

# Generating prime numbers the quick-and-easy way,#+ without resorting to fancy algorithms.

CEILING=10000 # 1 to 10000PRIME=0E_NOTPRIME=

is_prime (){ local factors factors=( $(factor $1) ) # Load output of `factor` into array.

if [ -z "${factors[2]}" ]# Third element of "factors" array:#+ ${factors[2]} is 2nd factor of argument.# If it is blank, then there is no 2nd factor,#+ and the argument is therefore prime.then return $PRIME # 0else return $E_NOTPRIME # nullfi}

echofor n in $(seq $CEILING)do if is_prime $n then

printf %5d $n fi # ^ Five positions per number suffices.done # For a higher $CEILING, adjust upward, as necessary.

echo

exit

bc

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

Not just a versatile, arbitrary precision calculation utility, bc offers many of the facilities of a programming language. It has a syntax vaguely resembling C.

Since it is a fairly well-behaved UNIX utility, and may therefore be used in a pipe, bc comes in handy in scripts.

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

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

Example 16-47. 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 ABS Guide author).# http://www.ibiblio.org/pub/Linux/apps/financial/mcalc-1.6.tar.gz

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

bottom=1.0

echoecho -n "Enter principal (no commas) "read principalecho -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. # ^^^^^^^^^^^^^^^^^ Divide by 100. # "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) # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ # Standard formula for figuring interest.

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# ====================================================================

# -------------------------------------------------------------------- # Rick Boivie pointed out a more efficient implementation#+ of the above loop, which decreases computation time by 2/3.

# for ((x=1; x <= $months; x++))# do# bottom=$(echo "scale=9; $bottom * $interest_rate + 1" | bc)# done

# And then he came up with an even more efficient alternative,#+ one that cuts down the run time by about 95%!

# bottom=`{# echo "scale=9; bottom=$bottom; interest_rate=$interest_rate"# for ((x=1; x <= $months; x++))# do# echo 'bottom = bottom * interest_rate + 1'# done# echo 'bottom'# } | bc` # Embeds a 'for loop' within command

substitution.# --------------------------------------------------------------------------# On the other hand, Frank Wang suggests:# bottom=$(echo "scale=9; ($interest_rate^$term-1)/($interest_rate-1)" | bc)

# Because . . .# The algorithm behind the loop#+ is actually a sum of geometric proportion series.# The sum formula is e0(1-q^n)/(1-q),#+ where e0 is the first element and q=e(n+1)/e(n)#+ and n is the number of elements.# --------------------------------------------------------------------------

# 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 16-48. Base Conversion

#!/bin/bash############################################################################ 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 $# ==> Above line is RCS ID info.############################################################################ Description#

# Changes# 21-03-95 stv fixed error occuring with 0xb as input (0.2)###########################################################################

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

NOARGS=85PN=`basename "$0"` # Program nameVER=`echo '$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 } # ==> Prints usage message.

Msg () { for i # ==> in [list] missing. Why? 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 decimaldec=`echo "ibase=$ibase; $number" | bc` # ==> 'bc' is

calculator utility.

case "$dec" in [0-9]*) ;; # number ok *) continue;; # error: ignoreesac

# 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 ]# ==> Is a "while loop" really necessary here,# ==>+ since all the cases either break out of the loop# ==>+ or terminate the script.# ==> (Above comment by Paulo Marcel Coelho Aragao.)do case "$1" in

--) shift; break;;-h) Usage;; # ==> Help message.-*) Usage;;

*) break;; # First number esac # ==> Error checking for illegal input might be appropriate. shiftdone

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

PrintBases $line donefi

exit

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_STRINGoptionsstatementsoperations

LIMIT_STRING`

...or...

variable=$(bc << LIMIT_STRINGoptionsstatementsoperationsLIMIT_STRING)

Example 16-49. Invoking bc using a here document

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

var1=`bc << EOF18.33 * 19.78EOF`echo $var1 # 362.56

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

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

var3=$(bc -l << EOFscale = 9s ( 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...hypotenuse () # Calculate hypotenuse of a right triangle.{ # c = sqrt( a^2 + b^2 )

hyp=$(bc -l << EOFscale = 9sqrt ( $1 * $1 + $2 * $2 )EOF)# Can't directly return floating point values from a Bash function.# But, can echo-and-capture:echo "$hyp"}

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

exit 0

Example 16-50. Calculating PI

#!/bin/bash# cannon.sh: Approximating PI by firing cannonballs.

# Author: Mendel Cooper# License: Public Domain# Version 2.2, reldate 13oct08.

# This is a very simple instance of a "Monte Carlo" simulation:#+ a mathematical model of a real-life event,#+ using pseudorandom numbers to emulate random chance.

# Consider a perfectly square plot of land, 10000 units on a side.# This land has a perfectly circular lake in its center,#+ with a diameter of 10000 units.# The plot is actually mostly water, except for land in the four corners.# (Think of it as a square with an inscribed circle.)## We will fire iron cannonballs from an old-style cannon#+ at the square.# All the shots impact somewhere on the square,#+ either in the lake or on the dry corners.# Since the lake takes up most of the area,#+ most of the shots will SPLASH! into the water.# Just a few shots will THUD! into solid ground#+ in the four corners of the square.## If we take enough random, unaimed shots at the square,#+ Then the ratio of SPLASHES to total shots will approximate#+ the value of PI/4.## The simplified explanation is that the cannon is actually#+ shooting only at the upper right-hand quadrant of the square,#+ i.e., Quadrant I of the Cartesian coordinate plane.##

# Theoretically, the more shots taken, the better the fit.# However, a shell script, as opposed to a compiled language#+ with floating-point math built in, requires some compromises.# This decreases the accuracy of the simulation.

DIMENSION=10000 # Length of each side of the plot. # Also sets ceiling for random integers generated.

MAXSHOTS=1000 # Fire this many shots. # 10000 or more would be better, but would take too long.PMULTIPLIER=4.0 # Scaling factor.

declare -r M_PI=3.141592654 # Actual 9-place value of PI, for comparison purposes.

get_random (){SEED=$(head -n 1 /dev/urandom | od -N 1 | awk '{ print $2 }')RANDOM=$SEED # From "seeding-random.sh" #+ example script.let "rnum = $RANDOM % $DIMENSION" # Range less than 10000.echo $rnum}

distance= # Declare global variable.hypotenuse () # Calculate hypotenuse of a right triangle.{ # From "alt-bc.sh" example.distance=$(bc -l << EOFscale = 0sqrt ( $1 * $1 + $2 * $2 )EOF)# Setting "scale" to zero rounds down result to integer value,#+ a necessary compromise in this script.# It decreases the accuracy of this simulation.}

# ==========================================================# main() {# "Main" code block, mimicking a C-language main() function.

# Initialize variables.shots=0splashes=0thuds=0Pi=0error=0

while [ "$shots" -lt "$MAXSHOTS" ] # Main loop.

do

xCoord=$(get_random) # Get random X and Y coords. yCoord=$(get_random) hypotenuse $xCoord $yCoord # Hypotenuse of #+ right-triangle = distance. ((shots++))

printf "#%4d " $shots printf "Xc = %4d " $xCoord printf "Yc = %4d " $yCoord printf "Distance = %5d " $distance # Distance from #+ center of lake #+ -- the "origin" -- #+ coordinate (0,0).

if [ "$distance" -le "$DIMENSION" ] then echo -n "SPLASH! " ((splashes++)) else echo -n "THUD! " ((thuds++)) fi

Pi=$(echo "scale=9; $PMULTIPLIER*$splashes/$shots" | bc) # Multiply ratio by 4.0. echo -n "PI ~ $Pi" echo

done

echoecho "After $shots shots, PI looks like approximately $Pi"# Tends to run a bit high,#+ possibly due to round-off error and imperfect randomness of $RANDOM.# But still usually within plus-or-minus 5% . . .#+ a pretty fair rough approximation.error=$(echo "scale=9; $Pi - $M_PI" | bc)pct_error=$(echo "scale=2; 100.0 * $error / $M_PI" | bc)echo -n "Deviation from mathematical value of PI = $error"echo " ($pct_error% error)"echo

# End of "main" code block.# }# ==========================================================

exit 0

# One might well wonder whether a shell script is appropriate for#+ an application as complex and computation-intensive as a simulation.## There are at least two justifications.# 1) As a proof of concept: to show it can be done.# 2) To prototype and test the algorithms before rewriting#+ it in a compiled high-level language.

See also Example A-37.

dc

The dc (desk calculator) utility is stack-oriented and uses RPN (Reverse Polish Notation). Like bc, it has much of the power of a programming language.

Similar to the procedure with bc, echo a command-string to dc.

echo "[Printing a string ... ]P" | dc# The P command prints the string between the preceding brackets.

# And now for some simple arithmetic.echo "7 8 * p" | dc # 56# Pushes 7, then 8 onto the stack,#+ multiplies ("*" operator), then prints the result ("p" operator).

Most persons avoid dc, because of its non-intuitive input and rather cryptic operators. Yet, it has its uses.

Example 16-51. Converting a decimal number to hexadecimal

#!/bin/bash# hexconvert.sh: Convert a decimal number to hexadecimal.

E_NOARGS=85 # Command-line arg missing.BASE=16 # Hexadecimal.

if [ -z "$1" ]then # Need a command-line argument. echo "Usage: $0 number" exit $E_NOARGSfi # Exercise: add argument validity checking.

hexcvt (){if [ -z "$1" ]then echo 0 return # "Return" 0 if no arg passed to function.

fi

echo ""$1" "$BASE" o p" | dc# o sets radix (numerical base) of output.# p prints the top of stack.# For other options: 'man dc' ...return}

hexcvt "$1"

exit

Studying the info page for dc is a painful path to understanding its intricacies. There seems to be a small, select group of dc wizards who delight in showing off their mastery of this powerful, but arcane utility.

bash$ echo "16i[q]sa[ln0=aln100%Pln100/snlbx]sbA0D68736142snlbxq" | dcBash

dc <<< 10k5v1+2/p # 1.6180339887# ^^^ Feed operations to dc using a Here String.# ^^^ Pushes 10 and sets that as the precision (10k).# ^^ Pushes 5 and takes its square root# (5v, v = square root).# ^^ Pushes 1 and adds it to the running total (1+).# ^^ Pushes 2 and divides the running total by that (2/).# ^ Pops and prints the result (p)# The result is 1.6180339887 ...# ... which happens to be the Pythagorean Golden Ratio, to 10 places.

Example 16-52. Factoring

#!/bin/bash# factr.sh: Factor a number

MIN=2 # Will not work for number smaller than this.E_NOARGS=85E_TOOSMALL=86

if [ -z $1 ]then echo "Usage: $0 number" exit $E_NOARGSfi

if [ "$1" -lt "$MIN" ]then echo "Number to factor must be $MIN or greater."

exit $E_TOOSMALLfi

# Exercise: Add type checking (to reject non-integer arg).

echo "Factors of $1:"# -------------------------------------------------------echo "$1[p]s2[lip/dli%0=1dvsr]s12sid2%0=13sidvsr[dli%0=\1lrli2+dsi!>.]ds.xd1<2" | dc# -------------------------------------------------------# Above code written by Michel Charpentier <charpov@cs.unh.edu># (as a one-liner, here broken into two lines for display purposes).# Used in ABS Guide with permission (thanks!).

exit

# $ sh factr.sh 270138 # 2 # 3 # 11 # 4093

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 16-53. 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=85 # Wrong number of arguments.

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

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

# Now, pipe the parameters to awk. echo -n "Hypotenuse of $1 and $2 = " echo $1 $2 | awk "$AWKSCRIPT"# ^^^^^^^^^^^^# An echo-and-pipe is an easy way of passing shell parameters to awk.

exit

# Exercise: Rewrite this script using 'bc' rather than awk.# Which method is more intuitive?

 Shell   scripting to   find   prime   number?

!/bin/shecho "Enter the number"read numbertemp=`expr $number - 1`for i in `seq 2 $temp`do mod=`expr $number % $i` if [ $mod = 0 ] then echo "Given Number is not a prime" exit fidoneecho "Given number...

 Shell   script   to   find   area of a circle?

echo -n "Enter the radius of a circle : "read r # use formula to get itarea=$(echo "scale=2;3.14 * ($r * $r)" | bc) # use formula to get itd=$(echo "scale=2;2 * $r"|bc)circumference=$(echo...

 Write a   Shell   script   to   find   out the user is valid or not?

!/bin/sh echo "Please enter the username you want to check: " read USER grep $USER /etc/passwd > /tmp/lusertest sleep 5 if [ -s /tmp/lusertest ] then echo "User exists" else echo "User does not...

 Where do you   find   scripts ?

Drew's Script-O-Rama has a wide range of screenplays and movie scripts. http://www.script-o-rama.com

 Find   prime   prime   factorization of 100?

the prime factorization is 2 x 2 x 5 x 5!

Shell script to find a prime no?In: Uncategorized [Edit categories]Answer:

i=2 rem=1 echo -e "Enter a number: \c" read num if [ $num -lt 2 ]; then echo -e "$num is not prime\n" exit 0 fi while [ $i -le `expr $num / 2` -a $rem -ne 0 ]; do rem=`expr $num % $i` i=`expr $i + 1` done if [ $rem -ne 0 ]; then echo -e "$num is prime\n" else echo -e "$num is not prime\n" fi

Write a shell script to check whether given year is a leap year or not?

# store year yy=0 isleap="false" 

echo -n "Enter year (yyyy) : " read yy 

# find out if it is a leap year or not 

if [ $((yy % 4)) -ne 0 ] ; then : # not a leap year : means do nothing and use old value of isleap elif [ $((yy % 400)) -eq 0 ] ; then # yes, it's a leap year isleap="true" elif [ $((yy % 100)) -eq 0 ] ; then : # not a leap year do nothing and use old value of isleap else # it is a leap year isleap="true" fi if [ "$isleap" == "true" ]; then echo "$yy is leap year" else echo "$yy is NOT leap year" fi 

Write a shell program to generate the first hundred numbers in the Fibonacci series?

echo "Enter How many numbers:" read 100 

num1=0 num2=1 

echo "Fibonacci series:" 

echo $num1 echo $num2 

count=2 

while [ $count -le $num ] do num3=`expr $num1 + $num2` echo $num3 num1=$num2 num2=$num3 count=`expr $count + 1` done 

Shell Programs# Write a shell script to print the area of circleClear echo “Enter the Radius of a Circle : - ”read radiusecho ‘expr 22 \* $radius \* $rad / 7’echo “Area of Circle:echo “ ”OutputEnter the Radius of Circle: -3Area of Circle:28