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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-24 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin stack_machine.cpp}
Example Differentiating a Stack Machine Interpreter
###################################################
{xrst_literal
// BEGIN C++
// END C++
}
{xrst_end stack_machine.cpp}
*/
// BEGIN C++
# include <cstring>
# include <cstddef>
# include <cstdlib>
# include <cctype>
# include <cassert>
# include <stack>
# include <cppad/cppad.hpp>
namespace {
// Begin empty namespace ------------------------------------------------
bool is_number( const std::string &s )
{ char ch = s[0];
bool number = (std::strchr("0123456789.", ch) != 0);
return number;
}
bool is_binary( const std::string &s )
{ char ch = s[0];
bool binary = (strchr("+-*/.", ch) != 0);
return binary;
}
bool is_variable( const std::string &s )
{ char ch = s[0];
bool variable = ('a' <= ch) && (ch <= 'z');
return variable;
}
void StackMachine(
std::stack< std::string > &token_stack ,
CppAD::vector< CppAD::AD<double> > &variable )
{ using std::string;
using std::stack;
using CppAD::AD;
stack< AD<double> > value_stack;
string token;
AD<double> value_one;
AD<double> value_two;
while( ! token_stack.empty() )
{ string s = token_stack.top();
token_stack.pop();
if( is_number(s) )
{ value_one = std::atof( s.c_str() );
value_stack.push( value_one );
}
else if( is_variable(s) )
{ value_one = variable[ size_t(s[0]) - size_t('a') ];
value_stack.push( value_one );
}
else if( is_binary(s) )
{ assert( value_stack.size() >= 2 );
value_one = value_stack.top();
value_stack.pop();
value_two = value_stack.top();
value_stack.pop();
switch( s[0] )
{
case '+':
value_stack.push(value_one + value_two);
break;
case '-':
value_stack.push(value_one - value_two);
break;
case '*':
value_stack.push(value_one * value_two);
break;
case '/':
value_stack.push(value_one / value_two);
break;
default:
assert(0);
}
}
else if( s[0] == '=' )
{ assert( value_stack.size() >= 1 );
assert( token_stack.size() >= 1 );
//
s = token_stack.top();
token_stack.pop();
//
assert( is_variable( s ) );
value_one = value_stack.top();
value_stack.pop();
//
variable[ size_t(s[0]) - size_t('a') ] = value_one;
}
else assert(0);
}
return;
}
// End empty namespace -------------------------------------------------------
}
bool StackMachine(void)
{ bool ok = true;
using std::string;
using std::stack;
using CppAD::AD;
using CppAD::NearEqual;
double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
using CppAD::vector;
// The users program in that stack machine language
const char *program[] = {
"1.0", "a", "+", "=", "b", // b = a + 1
"2.0", "b", "*", "=", "c", // c = b * 2
"3.0", "c", "-", "=", "d", // d = c - 3
"4.0", "d", "/", "=", "e" // e = d / 4
};
size_t n_program = sizeof( program ) / sizeof( program[0] );
// put the program in the token stack
stack< string > token_stack;
size_t i = n_program;
while(i--)
token_stack.push( program[i] );
// domain space vector
size_t n = 1;
vector< AD<double> > X(n);
X[0] = 0.;
// declare independent variables and start tape recording
CppAD::Independent(X);
// x[0] corresponds to a in the stack machine
vector< AD<double> > variable(26);
variable[0] = X[0];
// calculate the resutls of the program
StackMachine( token_stack , variable);
// range space vector
size_t m = 4;
vector< AD<double> > Y(m);
Y[0] = variable[1]; // b = a + 1
Y[1] = variable[2]; // c = (a + 1) * 2
Y[2] = variable[3]; // d = (a + 1) * 2 - 3
Y[3] = variable[4]; // e = ( (a + 1) * 2 - 3 ) / 4
// create f : X -> Y and stop tape recording
CppAD::ADFun<double> f(X, Y);
// use forward mode to evaluate function at different argument value
size_t p = 0;
vector<double> x(n);
vector<double> y(m);
x[0] = 1.;
y = f.Forward(p, x);
// check function values
ok &= (y[0] == x[0] + 1.);
ok &= (y[1] == (x[0] + 1.) * 2.);
ok &= (y[2] == (x[0] + 1.) * 2. - 3.);
ok &= (y[3] == ( (x[0] + 1.) * 2. - 3.) / 4.);
// Use forward mode (because x is shorter than y) to calculate Jacobian
p = 1;
vector<double> dx(n);
vector<double> dy(m);
dx[0] = 1.;
dy = f.Forward(p, dx);
ok &= NearEqual(dy[0], 1., eps99, eps99);
ok &= NearEqual(dy[1], 2., eps99, eps99);
ok &= NearEqual(dy[2], 2., eps99, eps99);
ok &= NearEqual(dy[3], .5, eps99, eps99);
// Use Jacobian routine (which automatically decides which mode to use)
dy = f.Jacobian(x);
ok &= NearEqual(dy[0], 1., eps99, eps99);
ok &= NearEqual(dy[1], 2., eps99, eps99);
ok &= NearEqual(dy[2], 2., eps99, eps99);
ok &= NearEqual(dy[3], .5, eps99, eps99);
return ok;
}
// END C++
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