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dc

A command-line, arbitrary-precision "reverse Polish notation" (RPN) calculator.

dc is based on the concept of a stack, which is central to the operations of modern digital computer. A computer stack is not unlike a stack of kitchen plates, the last to come on stack, is the first to go out (this is also known as LIFO="last-in, first-out"). This contrasts with a queue (another important concept) where the first in is the first out (FIFO).

You can perform operations only on the number(s) which is on the top of the stack. The two basic operations are: push and pop (put on the top of stack, and retrieve from the top of stack). Unary operations pop one value off the stack ("unary" means "requiring one operand"). Binary operations pop two values off the stack ("binary" means "requiring two operands"). Tertiary operations pop three values off the stack ("tertiary" means "requiring three operands"). In all cases, the result is always pushed back onto the top of stack.

RPN calculators (regular, hand-held) are very popular among technically oriented people and in academia. The RPN notation never requires parentheses.

History. The parentheses-free logic was developed by Polish mathematician Jan Lukasiewicz (1878-1956) before the WWII. Originally, the operator preceded the values. For computer applications, it's been modified so that the operator goes after the values, hence "reversed" in the name "reversed Polish notation".

To exercise some operations on stack, try this:
dc [start the arbitrary precision reverse Polish notation calculator]
1 [push "1" on the stack]
2 [push another number on the stack]
3 [push yet another number on the stack]
4 [push yet another number on the stack]
f [print the entire stack; you should see 1 2 3 4]
p [print the number on the top of the stack without affecting the stack; you should see 4]
+ [perform addition (binary operation), therefore pop two last values off the stack (4,3), and push the result (7) on the stack]
p [print the number on the top of the stack, i.e. the results of the last addition (7).].
p [print again the number on the top of the stack to see that the stack wasn't affected by printing (7)]
* [perform multiplication (binary operation), therefore pop two last values, and push the result (14)]
p [print the result of the multiplication (14)]
P [pop the last number off the stack (14)]
p [print the number on the top of the stack]
2000 [push a large integer on the stack]
k [set the precision to the value which is on the top of the stack, i.e. 2000]
1 [push another number on the stack]
f [print the content of the entire stack]
701 [push another number on the stack]
/ [divide last two numbers on the stack, i.e. "1/701" with 2000 decimal places of precision]
p [print the result of the last division]
q [quit the arbitrary precision reverse Polish notation calculator]

Please note that when using the reverse Polish notation (RPN) you never need parentheses. Try man dc to read about other capabilities of dc.

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