Calculator computing arithmetic expressions.

• Calculator uses Reverse Polish Notation for evaluation of math expressions.
• Defines some builtin functions:
  • trigonometric (sin, cos, tan),
  • inverse trigonometric (asin, acos, atan, atan2),
  • hyperbolic (sinh, cosh, tanh),
  • log and exp,
  • abs, sgn and sqrt,
  • conversions: degrees to radians (d2r), radians to degrees (r2d),
  • min and max,
  • neg (unary minus).
• Predefined constants: PI and E.
• Calculator allows user to define own custom functions and constants.

As mentioned before, calculator evaluates expressions using RPN and shunting-yard algorithm. No additional syntax check is performed, which makes expression syntax quite liberal. Here are some examples of valid expressions:

> 2+2*2
6.0

> 2^2^3
256.0

> sin(PI)
1.2246467991473532E-16

> cos 0*2
2.0

> atan2(2+2, 3+3)
0.5880026035475675

> log exp -1
-1

> 7-(2*PI + cos 12.3456)
-0.25891429587906956

As can be seen, brackets are not needed for unary functions. All operators except power (^) are evaluated left to right. Power operator as well as functions are evaluated right to left. This allows function composition without explicit using brackets.

Moreover, functions have higher priority than operators. Following table shows operator precedence and associativity.

( ) ,

Special commands start with colon (:). Here is the list of all defined commands:

• :c, :del and :ce - clear and clear all,
• :func, :const and :s - user defined functions and constants,
• :p and :pd - print list of functions and constants.

Clearing results

• :c - clear. Result of every expression evaluation is stored in variable ans. Command :c erases last result and sets ans to 0.
• :del {name} - deletes constant or function with name {name}. Default builtin functions and constants (e.e. sin or PI) cannot be removed.
• :ce - clear all. Clears last result (see :c) and deletes all user defined functions and constants.

Defining functions and constants

Custom functions and constants are nothing more than expressions. Arguments for function are denoted in its body as {0}, {1}..., {N}. Constants are functions without arguments, which makes them constant expressions.

Function or constant name cannot be equal to any of the default function or constant. If custom (non-default) function or constant with the same name already exists, new function or constant overwrites it.

• :func {name} {expression} - define a function with name {name}. Examples of function definitions:
  • :func square {0}*{0} - defines an unary function named square that multiplies the argument by itself,
  • :func dist max({0},{1}) - min({0},{1}) - defines binary function calculating absolute distance between two numbers.
• :const {name} {expression} - define a constant with name {name}. Examples of constant definitions:
  • :const ONE 1 - constant with value 1,
  • :const PI_2 PI/2 - constant with value PI / 2.
• :s {name} - save last result (i.e. ans) to a new constant named {name}.

Printing functions and constants

• :p - print all custom functions and constants.
• :pd - print all default, predefined functions and constants (e.g. sin, abs, PI).