added math operations using bash dc , an older unix language

ebook/en/content/1001-bash-Math-with-dc.md

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+Math using dc
+dc is one of the oldest language on Unix.
+
+It is using the reverse polish notation, which means that you are first stacking numbers, then operations. For example 1+1 is written as 1 1+.
+
+To print an element from the top of the stack use command p
+
+echo '2 3 + p' | dc
+5
+
+or
+
+dc <<< '2 3 + p'
+5
+You can print the top element many times
+
+dc <<< '1 1 + p 2 + p'
+2
+4
+For negative numbers use _ prefix
+
+dc <<< '_1 p'
+-1
+You can also use capital letters from A to F for numbers between 10 and 15 and . as a decimal point
+
+dc <<< 'A.4 p'
+10.4
+dc is using abitrary precision which means that the precision is limited only by the available memory. By default the precision is set to 0 decimals
+
+dc <<< '4 3 / p'
+1
+We can increase the precision using command k. 2k will use
+
+dc <<< '2k 4 3 / p'
+1.33
+
+dc <<< '4k 4 3 / p'
+1.3333
+You can also use it over multiple lines
+
+dc << EOF
+1 1 +
+3 *
+p
+EOF
+6
+bc is a preprocessor for dc.
+
+Math using bc
+bc is an arbitrary precision calculator language. It could be used interactively or be executed from command line.
+
+For example, it can print out the result of an expression:
+
+echo '2 + 3' | bc
+5
+
+echo '12 / 5' | bc
+2
+For floating-post arithmetic, you can import standard library bc -l:
+
+echo '12 / 5' | bc -l
+2.40000000000000000000
+It can be used for comparing expressions:
+
+echo '8 > 5' | bc
+1
+
+echo '10 == 11' | bc
+0
+
+echo '10 == 10 && 8 > 3' | bc
+1
+Math using bash capabilities
+Arithmetic computation can be also done without involving any other programs like this:
+
+Multiplication:
+
+echo $((5 * 2))
+10
+Division:
+
+echo $((5 / 2))
+2
+Modulo:
+
+echo $((5 % 2))
+1
+Exponentiation:
+
+echo $((5 ** 2))
+25
+Math using expr
+expr or Evaluate expressions evaluates an expression and writes the result on standard output
+
+Basic arithmetics
+
+expr 2 + 3
+5
+When multiplying, you need to escape the * sign
+
+expr 2 \* 3
+6
+You can also use variables
+
+a=2
+expr $a + 3
+5
+Keep in mind that it only supports integers, so expression like this
+
+expr 3.0 / 2
+will throw an error expr: not a decimal number: '3.0'.
+
+It supports regular expression to match patterns
+
+expr 'Hello World' : 'Hell\(.*\)rld'
+o Wo
+Or find the index of the first char in the search string
+
+This will throw expr: syntax error on Mac OS X, because it uses BSD expr which does not have the index command, while expr on Linux is generally GNU expr
+
+expr index hello l
+3
+
+expr index 'hello' 'lo'
+3