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 10000
PRIME=0
E_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 # 0
else
return $E_NOTPRIME # null
fi
}
echo
for n in $(seq $CEILING)
do
if is_prime $n
then
printf %5d $n
fi # ^ Five positions per number suffices.
done # For a higher $CEILING, adjust upward, as necessary.
echo
exit
Bash can't handle floating point calculations, and it lacks operators for certain important mathematical functions. Fortunately, bc gallops to the rescue.
Not just a versatile, arbitrary precision calculation utility, bc offers many of the facilities of a programming language. It has a syntax vaguely resembling C.
Since it is a fairly well-behaved UNIX utility, and may therefore be used in a pipe, bc comes in handy in scripts.
Here is a simple template for using bc to calculate a script variable. This uses command substitution.
variable=$(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
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; $interest_r/100.0" | bc) # Convert to decimal.
# ^^^^^^^^^^^^^^^^^ Divide by 100.
# "scale" determines how many decimal places.
interest_rate=$(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
# $Id$
# ==> 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=85
PN=`basename "$0"` # Program name
VER=`echo '$Revision$' | cut -d' ' -f2` # ==> VER=1.2
Usage () {
echo "$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 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 ]
# ==> 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.
shift
done
if [ $# -gt 0 ]
then
PrintBases "$@"
else # Read from stdin.
while read line
do
PrintBases $line
done
fi
exit
An alternate method of invoking bc involves using a here document embedded within a command substitution block. This is especially appropriate when a script needs to pass a list of options and commands to bc.
variable=`bc << LIMIT_STRING options statements operations LIMIT_STRING ` ...or... variable=$(bc << LIMIT_STRING options statements operations LIMIT_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 << 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 $var3 # .991664810
# Now, try it in a function...
hypotenuse () # Calculate hypotenuse of a right triangle.
{ # c = sqrt( a^2 + b^2 )
hyp=$(bc -l << EOF
scale = 9
sqrt ( $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 << EOF
scale = 0
sqrt ( $1 * $1 + $2 * $2 )
EOF
)
# Setting "scale" to zero rounds down result to integer value,
#+ a necessary compromise in this script.
# It decreases the accuracy of this simulation.
}
# ==========================================================
# main() {
# "Main" code block, mimicking a C-language main() function.
# Initialize variables.
shots=0
splashes=0
thuds=0
Pi=0
error=0
while [ "$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
echo
echo "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, “Standard Deviation”.
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_NOARGS
fi # 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=85 E_TOOSMALL=86 if [ -z $1 ] then echo "Usage: $0 number" exit $E_NOARGS fi if [ "$1" -lt "$MIN" ] then echo "Number to factor must be $MIN or greater." exit $E_TOOSMALL fi # 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
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_BADARGS
fi
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?