# 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 < 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```