# Program to emulate calculations performed on the HP-35 calculator

Automatic Testing  This task is available for automatic testing using the name hp-35. You can run the demo using demo hp-35 and you can test your work using try hp-35 <filename.    Background

The HP-35 was the first scientific hand-held calculator, released in 1972 and an immediate success with engineers and scientists. Amongst other features, it used an unusual way of entering numbers, called RPN. RPN (reverse Polish notation, named for Polish mathematician Jan Lukasiewicz) allows complex calculations to be entered without the use of parentheses. The key difference is that operators are entered after the operands, rather than between them The HP-35 implemented RPN using a stack of 4 registers, referred to as X, Y , Z, and T. The value in the X register is the one shown on the calculator's LED display; the other registers are used for temporary values during calculations. New values are entered into the X register, with existing values "pushed" up the register stack: the old value of X goes into Y, the old value of Y goes into Z, the old value of Z goes into T, and the old value of T is lost. Single-operand functions (such as square root) use and replace the value in the X register; other registers are unchanged. Functions that operate on 2 values (such as the arithmetic operators) use the values in Y and X, with the result going back into X. Values in the Z and T registers are "dropped" down the stack, with Z overwriting the old Y and T overwriting the old Z. The value of T is preserved, providing a simple way to do calculations with repeated values. This scheme allows calculations to be entered without using parentheses. For example, you could compute the compound expression (5 + 4)/(3 - 2) like this: 5 ENTER 4 + 3 ENTER 2 - ÷   Hints

You'll need to define the class HPStack to represent the calculator's operand stack, with operations such as push (push all values up 1 level and store a value into X), pop (drop all values down 1 evel and return the old X value), and peek (return the current X value). The simplest approach is to use an array to store the register values, with the methods manipulating the array elements. The calculator should read and process tokens representing numbers and operator keys, with the current value of the X register displayed after processing each line. It should exit when all lines of input have been processed.

A suitable main function will contain code such as this:
HPStack stack;         string line;           while (getline(cin, line)) {             stringstream expression             (line             );         string token;             while (expression token) {                 if (isdigit(token[0])) {                     stack.push(atof(token.data()));                 } else if (token == "+") { // other arithmetic ops similar                     double x = stack.pop();                     double y = stack.pop();                     stack.push(y + x);                 }             }             cout << stack.peek();         }

Level 1: Basic Implement the arithmetic operations so that the calculator can compute basic expressions:
54 + 3 2 - / // should be 9 3456 + + + // should be 18 1.23 4.5 67 / * // should be 0.0826119

Level 2: Scientific

Implement π (pi) and the functions chs (change the sign of X), 1/x (recip), log (decimal logarithm), ln (natural logarithm), ex (exp), √x (sqrt), sin, cos, tan (and their inverses arcsin, arccos, and arctan), and xy (pow). The function names should be accepted in either upper or lower case. Use the functions in the cmath library to do the actual work! The predefined constant M_PI contains the value of pi.
PI 2 / SIN // should be 1 (or very close) 100 100 * sqrt // should be 100 1E-5 LOG CHS // should be 5 5 EXP LN // should be 5 3 recip 8 pow // should be 2 2 1 arctan cos pow // should be 0.5
Level 3: Memory

Implement STO (store X into memory) and RCL (recall from memory into X, ushing other values up), CLR (set all registers to 0), and CLx (drop the X value).
100 sto 2 * rcl / // should be 2 1 2 clx 3 + // should be 4 1 2 3 4 clr + + + // should be 0

Level 4: Stack Control
Implement x􂁶y (swap X and Y), R↓ (roll the stack down, with each register moved into the register below it and X moved into T), and ENTER↑ (push all values up the stack, preserving X and losing T). (Note that this interpretation of ENTER is not identical to that on the original calculator, where it is also used to separate consecutive numbers).

2 8 swap / // should be 4 1 2 3 4 // should be 4 roll roll // now 2 roll roll // back to 4 2 enter enter enter // 2 + + + + // 10