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Math-RPN-1.08 >
Math::RPN

Module Version: 1.08
RPN - Perl extension for Reverse Polish Math Expression Evaluation

use Math::RPN; $value=rpn(expr...); @array=rpn(expr...); expr... is one or more scalars or lists of scalars which contain RPN expressions. An RPN expression is a series of numbers and/or operators separated by commas. (commas are only required within scalars).

The rpn function will take a scalar or list of sclars which contain an RPN expression as a set of comma delimited values and operators, and return the result or stack, depending on context. If the function is called in an array context, it will return the entire remaining stack. If it is called in a scalar context, it will return the top item of the stack. In a scalar context, if more than one value remains on the stack, a warning will be sent to STDERR.

In the event of an error, an error message will be sent to STDERR, and rpn will return undef.

The expression can contain any combination of values and operators. Any token which is not an operator is assumed to be a value to be pushed onto the stack.

An explanation of Reverse Polish Notation is beyond the scope of this document, but it I will describe it briefly as a stack-based way of writing mathematical expressions. This has the advantage of eliminating the need for parenthesis and simplifying parsing for computers vs. normal algebraic notation at a slight cost in the ability of humans to easily comprehend the expressions.

This evaluator works by cycling through the expression from left to right. As each token is encountered, it is checked against the list of operators. If it matches, then a check is performed for stack underflow. If the stack has not underflowed, the operation is performed by removing the required number of operands from the top of the stack. The result is then pushed on to the stack. Operations for which order is significant (-,/,%,etc.) are processed such that the top item on the stack is treated as the right operand, and the next item down is treated as the left operand. Thus, "5,3,-" would yield 2, not -2. If the token does not match any of the known operators, the token is blindly pushed onto the stack. As a result, one can produce unexpected results. For example, the expression "5,3,grandma,+,*" would produce 15 because 5*(3+0) is how it would end up evaluated. That is, 5 would be pushed onto the stack, then 3, then "grandma". Next, + is evaluated, so 3+"grandma" is evaluated. PERL evaluates "grandma" to be numerically 0, so 3 is pushed back onto the stack. Next, the * multiplies the top two items of the stack [5][3], producing 15, which is pushed back onto the stack.

The operators below are expressed in terms of a simple stack grammar. Each item enclosed in brackets ([]) represents a single stack element. The -> represents the transformation that the operator performs. That is, everything to the left of -> is what must be present on the stack before the operator, and everything to the right is what ends up on the stack after the operator. For example, [a][b]->[a+b] means that before the + operator, there must be two elements on the stack, and that afterwards, the sum of the two elements will be left on the stack. Anything on the stack below the first item specified on the left side of the -> is not affected and the stack below that point remains as the stack below the indicated results on the right side. In other words, if the stack is [5][3][2][5][6] and we evaluate a + operator, the transform [a][b]->[a+b] means that 5 and 6 would be pulled off the top of the stack and replaced with [11], and the resultant stack would be [5][3][2][11].

Additionally, there are constructs like (condition ? result : otherwise) which indicate that if condition is true, result will be placed on the stack. If condition is false, otherwise will be placed on the stack. Thus, (a!=0 ? [b] : [c]) means that if a is not equal to 0, the [b] will be placed on the stack. If a is equal to 0, then [c] will be placed on the stack.

A glossary of other symbols is provided below for reference.

The following operators are supported in the RPN evaluator:

Operator Operation +,ADD [a][b]->[a+b] ++,INCR [a]->[a+1] -,SUB [a][b]->[a-b] --,DECR [a]->[a-1] *,MUL [a][b]->[a*b] /,DIV [a][b]->[a/b] %,MOD [a][b]->[a%b] POW [a][b]->[a^b] SQRT [a]->[sqrt(a)] SIN [a]->[sin(a)] COS [a]->[cos(a)] TAN [a]->[tan(a)] LOG [a]->[log(a)] EXP [a]->[e^a] ABS [a]->[abs(a)] INT [a]->[int(a)] &,AND [a][b]->[a&b] |,OR [a][b]->[a|b] !,NOT [a]->(a==0 ? [1] : [0]) ~ [a]->(a xor -1) (Inverts all the bits in a) <,LT [a][b]->(a<b ? [1] : [0]) <=,LE [a][b]->(a<=b ? [1] : [0]) =,==,EQ [a][b]->(a==b ? [1] : [0]) >,GT [a][b]->(a>b ? [1] : [0]) >=,GE [a][b]->(a>=b ? [1] : [0]) !=,NE [a][b]=>(a!=b ? [1] : [0]) IF [a][b][c]-> (a!=0 ? [b] : [c]) DUP [a]->[a][a] EXCH [a][b]->[b][a] POP [a][b]->[a] MIN [a][b]->([a]<[b] ? [a] : [b]) MAX [a][b]->([a]>[b] ? [a] : [b]) TIME Pushes current time (seconds since midnight UTC 1970) RAND Pushes a random number 0<x<1 onto the stack. LRAND [a]->[x=rand(0<x<a)]

Bitwise Boolean operations (&,|,!,~) are performed against the integerized (truncated) versions of the values on the stack. That is, [a][b]->[a&b] is performed internally as `push(@stack, (int(pop(@stack))&int(pop(@stack))))`

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In addition, the IF operator supports special constructs for the "then" and "else" clauses on the stack. The construct allows an RPN expression to be enclosed in curly braces ({expr}), which will cause the entire expression to be pushed on to the stack unevaluated. If this expression is to be pushed onto the stack as a result of an IF, it is evaluated at that time. This allows more flexibility in IF statements and provides some performance benefits because any computations in the unused clause are not performed.

An example would look like so:

1,{,5,3,+,10,*,},{,1,2,3,+,+,},IF

This example would result in the stack containing 80 at the end of the evaluation. First, the IF would be true because 1, so {,5,3,+,10,*,} would be evaluated and the result placed on the stack.

The boolean operator xor is incorporated into the code, but is not tested. It is believed at this time that the underlying xor functionality in PERL may be broken, so the operator is considered strictly experimental. Use it at your own risk. The xor operator is not otherwise documented.

The following are a few examples of RPN expressions for common tasks and to help demonstrate the syntax used in the RPN evaluator...

100,9,*,5,/,32,+ Convert 100 degrees C to 212 degrees F (100*9/5+32) 5,3,LT,100,500,IF Yields 500 (5!<3=0,100,500,IF==500, the "else" clause)

The following symbols and are used in the description of the RPN operators. The explanation here is intended as a brief reference. For more information, consult a text on mathematics, boolean algebra, or trigonometry, as appropriate.

SYMBOL CATEGORY Meaning ^ (MATH) Power of (x^y is X to the power of Y, x^2 is X Squared, etc.) % (MATH) Modulus, or Division Remainder & (BOOLEAN) Boolean Bitwise AND | (BOOLEAN) Boolean Bitwise OR ! (BOOLEAN) Invert a boolean value (true->false, false->true) sqrt (MATH) Square Root (sqrt(9) is 3) sin (TRIG) SINE of the given angle (in radians) cos (TRIG) COSINE of the given angle (in radians) tan (TRIG) TANGENT of the given angle (in radians) log (MATH) The logarithm of the given number. (such that e^log(x) is x [e is an irrational mathematical constant used for all sorts of things]) exp (MATH) The opposite of log. exp(x) returns e^x. exp(log(x)) returns x. abs (MATH) The "absolute" value of the given number. abs(-5) is 5. abs(5) is 5. Basically, x=(x<0? x*-1 : x). int (MATH) Truncate the given number to its integer portion, discarding any fractional part. (This does not round, 4.9 would become 4) If rounding is desired, n,.5,+,INT can be used.

Owen DeLong, owen@delong.com

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