evaluate.cpp

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/*
 * 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>
 
 /*
 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;
}