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eval.js
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eval.js
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// simplify the expression tree with rules against of CR and BR also algebra
//
// the analyze is based on symbolic interpretation of the input expression
// program. If BR invovled, the output should be a CR and user can use it
// to translate into an efficient algorithm which computes f(x) over a list of
// periodically increasing numbers
var util = require("util");
var ast = require("./ast.js");
function mergePosition(lhs,rhs) {
let start = Math.min(lhs.start,rhs.start);
let end = Math.max(lhs.end ,rhs.end );
return new ast.Position(lhs.source,start,end);
}
function unexpected(node) {
let msg = util.format("unexpected expression node here %s",node.constructor.name);
let stk = new Error().stack;
throw util.format("%s\n%s",msg,stk);
}
// There're 2 internal IR node that is used to do CR algebra algorithm. These 2 IR node
// will implements the corresponding CR algebra rules and AST node will be converted
// into the following 2 IR nodes for evaluation. After the evaluation, we should only
// see 1) constant or 2) CR. The CR node is essentially recursively nested
class CR {
constructor( first , rest , pos ) {
this.position = pos;
this.first = first;
this.rest = rest;
}
// operator evaluation
add(rhs) {
if( rhs instanceof Constant ) {
return new CR( this.first.add(rhs) , this.rest ,
mergePosition(this.position ,rhs.position));
} else if( rhs instanceof CR ) {
return new CR( this.first.add(rhs.first) , this.rest.add(rhs.rest) ,
mergePosition(this.position ,rhs.position));
} else {
unexpected(rhs);
}
}
sub(rhs) {
if( rhs instanceof Constant ) {
return this.add(rhs.negate());
} else if( rhs instanceof CR ) {
// CR - CR
return new CR( this.first.sub(rhs.first) , this.rest.sub(rhs.rest) ,
mergePosition(this.position ,rhs.position));
} else {
unexpected(rhs);
}
}
mul(rhs) {
if( rhs instanceof Constant ) {
return new CR( this.first.mul(rhs) , this.rest.mul(rhs) ,
mergePosition(this.position,rhs.position));
} else if( rhs instanceof CR ) {
let firstComp = this.first.mul(rhs.first);
let rc1 = this.mul(rhs.rest);
let rc2 = rhs.rest.mul(this.rest);
let rc3 = this.rest.mul(rhs);
return new CR( firstComp , rc1.add(rc2).add(rc3) , mergePosition(this.position,rhs.position));
} else {
unexpected(rhs);
}
}
negate() {
return this.mul( new Constant(-1,this.position) );
}
toString() {
let buf = [];
this._toString(buf);
return "(" + buf.join(",+,") + ")";
}
isCR () { return true; }
isConstant() { return false; }
_toString(buf) {
this.first._toString(buf);
this.rest._toString (buf);
}
// helper function to flatten the CR into a list of integers
_flatten(output) {
this.first._flatten(output);
this.rest._flatten (output);
}
flatten() {
let output = [];
this._flatten(output);
return output;
}
};
class Constant {
constructor( value, pos ) {
this.position = pos;
this.value = value;
};
// operator evaluation
add(rhs) {
if( rhs instanceof Constant ) {
return new Constant( this.value + rhs.value , mergePosition(this.position,rhs.position) );
} else if( rhs instanceof CR ) {
return new CR( this.add(rhs.first) , rhs.rest ,
mergePosition(this.position,rhs.position) );
} else {
unexpected(rhs);
}
}
sub(rhs) {
if( rhs instanceof Constant ) {
return this.add( rhs.negate() );
} else if( rhs instanceof CR ) {
return new CR( this.sub(rhs.first), rhs.rest ,
mergePosition(this.position,rhs.position) );
} else {
unexpected(rhs);
}
}
mul(rhs) {
if( rhs instanceof Constant ) {
return new Constant( this.value * rhs.value , mergePosition(this.position,rhs.position) );
} else if( rhs instanceof CR ) {
return new CR( this.mul(rhs.first) , this.mul(rhs.rest) ,
mergePosition(this.position, rhs.position));
} else {
unexpected(rhs);
}
}
negate() {
return new Constant( -this.value, this.position );
}
toString() {
return util.format("%d",this.value);
}
isCR () { return false; }
isConstant() { return true; }
_toString(buf) {
buf.push(this.toString());
}
_flatten(output) { output.push(this.value); }
};
// Builder takes AST as input and produce only CR/recursively nested CR.
class Eval {
constructor() {
this.vmap = {};
this.output = null;
}
_buildBinary(bin) {
let lhs = this._buildExpr(bin.lhs);
let rhs = this._buildExpr(bin.rhs);
switch(bin.op) {
case ast.Operator.opAdd: return lhs.add(rhs);
case ast.Operator.opSub: return lhs.sub(rhs);
case ast.Operator.opMul: return lhs.mul(rhs);
default: return null;
}
}
_buildNegate(neg) {
let opr = this._buildExpr(bin.neg);
return opr.negate();
}
_buildInteger(n) {
return new Constant(n.value,n.position);
}
_buildVariable(n) {
if(n.name in this.vmap) {
return this.vmap[n.name];
}
throw util.format("variable %s doesn't exist",n.name);
}
_buildAddRecurrence(n) {
let first = this._buildExpr(n.start);
let second= this._buildExpr(n.stride);
return new CR( first, second, n.position );
}
_buildExpr( expr ) {
if(expr instanceof ast.Binary) return this._buildBinary(expr);
if(expr instanceof ast.Negate) return this._buildNegate(expr);
if(expr instanceof ast.Integer) return this._buildInteger(expr);
if(expr instanceof ast.Variable) return this._buildVariable(expr);
if(expr instanceof ast.AddRecurrence) return this._buildAddRecurrence(expr);
throw util.format("parser error ?? unexpected expression ast node %s",expr.constructor.name);
}
_buildVar(node) {
this.vmap[node.lhs.name] = this._buildExpr(node.rhs);
}
_buildOutput(node) {
this.output = [];
for( const x of node.tuple ) {
this.output.push( this._buildExpr(x) );
}
}
build(prg) {
for( const x of prg.statement ) {
if(x instanceof ast.Var ) {
this._buildVar(x);
} else if(x instanceof ast.Output) {
this._buildOutput(x);
} else {
throw util.format("parser error ?? unexpected statement ast node %s",x.constructor.name);
}
}
}
};
module.exports = function(node) {
let b = new Eval();
b.build(node);
return b.output;
};