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evaluate.cpp
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evaluate.cpp
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/**
* @file evaluate.cpp
*/
/*
* This program source code file is part of KiCad, a free EDA CAD application.
*
* Copyright (C) 1992-2017 Jean-Pierre Charras <jp.charras at wanadoo.fr>
* Copyright (C) 1992-2017 KiCad Developers, see change_log.txt for contributors.
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* as published by the Free Software Foundation; either version 2
* of the License, or (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, you may find one here:
* http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
* or you may search the http://www.gnu.org website for the version 2 license,
* or you may write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
*/
/* How to evaluate an arithmetic expression like those used in Aperture Macro Definition in Gerber?
*
* See http://stackoverflow.com/questions/28256/equation-expression-parser-with-precedence
*
* The shunting yard algorithm is the right tool for this.
* Wikipedia is really confusing about this, but basically the algorithm works like this:
*
* Say, you want to evaluate 1 + 2 * 3 + 4. Intuitively, you "know" you have to do the 2 * 3 first,
* but how do you get this result?
* The key is to realize that when you're scanning the string from left to right, you will evaluate
* an operator when the operator that follows it has a lower (or equal to) precedence.
*
* In the context of the example, here's what you want to do:
*
* Look at: 1 + 2, don't do anything.
* Now look at 1 + 2 * 3, still don't do anything.
* Now look at 1 + 2 * 3 + 4, now you know that 2 * 3 has to to be evaluated because
* the next operator has lower precedence.
*
* How do you implement this?
*
* You want to have two stacks, one for numbers, and another for operators.
* You push numbers onto the stack all the time.
* You compare each new operator with the one at the top of the stack,
* if the one on top of the stack has higher priority, you pop it off the operator stack,
* pop the operands off the number stack, apply the operator and push the result onto the number stack.
*
* Now you repeat the comparison with the top of stack operator.
*
* Coming back to the example, it works like this:
*
* N = [ ] Ops = [ ]
*
* Read 1. N = [1], Ops = [ ]
* Read +. N = [1], Ops = [+]
* Read 2. N = [1 2], Ops = [+]
* Read *. N = [1 2], Ops = [+ *]
* Read 3. N = [1 2 3], Ops = [+ *]
* Read +. N = [1 2 3], Ops = [+ *]
* Pop 3, 2 and execute 2*3, and push result onto N. N = [1 6], Ops = [+]
* is left associative, so you want to pop 1, 6 off as well and execute the +. N = [7], Ops = [].
* Finally push the [+] onto the operator stack. N = [7], Ops = [+].
* Read 4. N = [7 4]. Ops = [+].
*
* You're run out off input, so you want to empty the stacks now.
* Upon which you will get the result 11.
*/
#include <am_param.h>
/**
* Evaluate an basic arithmetic expression (infix notation) with precedence
* The expression is a sequence of numbers (double) and arith operators:
* operators are + - x / ( and )
* the expression is stored in a std::vector
* each item is a AM_PARAM_EVAL (each item is an operator or a double)
* @param aExp = the arithmetic expression to evaluate
* @return the value
*/
/*
The instructions ( subset of parm_item_type)
----------------
NOP : The no operation. the AM_PARAM_EVAL item stores a value.
ADD
SUB
MUL
DIV
OPEN_PAR : Opening parenthesis: modify the precedence of operators inside ( and )
CLOSE_PAR : Closing parenthesis: modify the precedence of operators by closing the local block.
POPVALUE : used to initialize a sequence
*/
double Evaluate( AM_PARAM_EVAL_STACK& aExp )
{
class OP_CODE // A small class to store a operator and its priority
{
public:
parm_item_type m_Optype;
int m_Priority;
OP_CODE( AM_PARAM_EVAL& aAmPrmEval )
: m_Optype( aAmPrmEval.GetOperator() ),
m_Priority( aAmPrmEval.GetPriority() )
{}
OP_CODE( parm_item_type aOptype )
: m_Optype( aOptype ), m_Priority( 0 )
{}
};
double result = 0.0;
std::vector<double> values; // the current list of values
std::vector<OP_CODE> optype; // the list of arith operators
double curr_value = 0.0;
int extra_priority = 0;
for( unsigned ii = 0; ii < aExp.size(); ii++ )
{
AM_PARAM_EVAL& prm = aExp[ii];
if( prm.IsOperator() )
{
if( prm.GetOperator() == OPEN_PAR )
{
extra_priority += AM_PARAM_EVAL::GetPriority( OPEN_PAR );
}
else if( prm.GetOperator() == CLOSE_PAR )
{
extra_priority -= AM_PARAM_EVAL::GetPriority( CLOSE_PAR );
}
else
{
optype.emplace_back( prm );
optype.back().m_Priority += extra_priority;
}
}
else // we have a value:
{
values.push_back( prm.GetValue() );
if( optype.size() < 2 )
continue;
OP_CODE& previous_optype = optype[optype.size() - 2];
if( optype.back().m_Priority > previous_optype.m_Priority )
{
double op1 = 0.0;
double op2 = values.back();
values.pop_back();
if( values.size() )
{
op1 = values.back();
values.pop_back();
}
switch( optype.back().m_Optype )
{
case ADD:
values.push_back( op1+op2 );
break;
case SUB:
values.push_back( op1-op2 );
break;
case MUL:
values.push_back( op1*op2 );
break;
case DIV:
values.push_back( op1/op2 );
break;
default:
break;
}
optype.pop_back();
}
}
}
// Now all operators have the same priority, or those having the higher priority
// are before others, calculate the final result by combining initial values and/or
// replaced values.
if( values.size() > optype.size() )
// If there are n values, the number of operator is n-1 or n if the first
// item of the expression to evaluate is + or - (like -$1/2)
// If the number of operator is n-1 the first value is just copied to result
optype.insert( optype.begin(), OP_CODE( POPVALUE ) );
wxASSERT( values.size() == optype.size() );
for( unsigned idx = 0; idx < values.size(); idx++ )
{
curr_value = values[idx];
switch( optype[idx].m_Optype )
{
case POPVALUE:
result = curr_value;
break;
case ADD:
result += curr_value;
break;
case SUB:
result -= curr_value;
break;
case MUL:
result *= curr_value;
break;
case DIV:
result /= curr_value;
break;
default:
break;
}
}
return result;
}