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Po_expand_poly.cpp
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Po_expand_poly.cpp
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/*******************************************************************/
/*** FILE : Po_expand_poly.c ***/
/*** AUTHOR: Sekhar Muddana ***/
/*** PUBLIC ROUTINES: ***/
/*** struct unexp_tnode *Expand_poly() ***/
/*** struct unexp_tnode *Simplify_polY() ***/
/*** struct unexp_tnode *Elim_subtraction() ***/
/*** PRIVATE ROUTINES: ***/
/*** struct unexp_tnode *Simplify_art_word() ***/
/*** int Get_degree() ***/
/*** MODULE DESCRIPTION: ***/
/*** The parse tree obtained after parsing is expanded in ***/
/*** this module using the formulae. ***/
/*******************************************************************/
#include <stdio.h>
#include "Po_expand_poly.h"
#include "Memory_routines.h"
#include "Po_parse_poly.h"
#include "Po_semantics.h"
#include "Ty_routines.h"
static struct unexp_tnode *Simplify_art_word(int T, struct unexp_tnode *Pntr);
static int Get_degree(struct unexp_tnode *Pntr);
static void Assert_scalar_bounds(int i);
/*******************************************************************/
/* MODIFIES: */
/* Unexp_tree -- pointer to the unexpanded parse tree. */
/* REQUIRES: None. */
/* RETURNS: */
/* Pointer to the Expanded tree of the polynomial. */
/* FUNCTION: */
/* Applies the formulae for Commutator, Associator etc to do */
/* the expansion. */
/* NOTE: */
/* The expanded tree contains only the basic operations. */
/* i.e Scalar multiplication,Juxtaposed product, Addition and */
/* Subtraction. */
/*******************************************************************/
struct unexp_tnode *Expand_parse_tree(struct unexp_tnode *Unexp_tree)
{
struct unexp_tnode *temp_tnode_ptr;
struct unexp_tnode *temp1; /* Temporary nodes used during expansion */
struct unexp_tnode *temp2;
struct unexp_tnode *temp3;
struct unexp_tnode *temp4;
struct unexp_tnode *temp5;
struct unexp_tnode *temp6;
struct unexp_tnode *temp7;
struct unexp_tnode *temp;
/*int i;*/
if (Unexp_tree == NULL)
return(NULL);
if (Unexp_tree->op == SMALL_LETTER) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SMALL_LETTER;
temp_tnode_ptr->s_letter = Unexp_tree->s_letter;
temp_tnode_ptr->next = Unexp_tree->next;
return(temp_tnode_ptr);
}
else if (Unexp_tree->op == SCALAR) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR;
temp_tnode_ptr->scalar_num = Unexp_tree->scalar_num;
temp_tnode_ptr->next = Unexp_tree->next;
return(temp_tnode_ptr);
}
else {
switch (Unexp_tree->op) {
case UNARY_PLUS : /* +(polynomial) becomes polynomial */
return(Expand_parse_tree(Unexp_tree->operand1));
break;
case UNARY_MINUS : /* -(poly) becomes -1(poly) */
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = SCALAR;
temp1->scalar_num = -1;
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = Expand_parse_tree(Unexp_tree->operand1);
return(temp_tnode_ptr);
break;
case ADDITION :
case SUBTRACTION :
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = Unexp_tree->op;
temp_tnode_ptr->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp_tnode_ptr->operand2 = Expand_parse_tree(Unexp_tree->operand2);
return(temp_tnode_ptr);
break;
case SCALAR_MULT :
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp_tnode_ptr->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp_tnode_ptr->operand2 = Expand_parse_tree(Unexp_tree->operand2);
return(temp_tnode_ptr);
break;
case EXPONENTIATION : /* x^3 = (xx)x */
if (Unexp_tree->operand2->scalar_num <= 1)
return(Expand_parse_tree(Unexp_tree->operand1));
else {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = JUXT_PROD;
temp_tnode_ptr->operand2=Expand_parse_tree(Unexp_tree->operand1);
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = EXPONENTIATION;
temp1->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp1->operand2 = temp2;
temp2->op = SCALAR;
temp2->scalar_num = Unexp_tree->operand2->scalar_num - 1;
temp_tnode_ptr->operand1 = Expand_parse_tree(temp1);
return(temp_tnode_ptr);
}
break;
case JUXT_PROD :
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = JUXT_PROD;
temp_tnode_ptr->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp_tnode_ptr->operand2 = Expand_parse_tree(Unexp_tree->operand2);
return(temp_tnode_ptr);
break;
case COMMUTATION : /* [x,y] = xy-yx */
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SUBTRACTION;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = temp2->op = JUXT_PROD;
temp1->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp2->operand2 = Expand_parse_tree(Unexp_tree->operand1);
temp1->operand2 = Expand_parse_tree(Unexp_tree->operand2);
temp2->operand1 = Expand_parse_tree(Unexp_tree->operand2);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
return(temp_tnode_ptr);
break;
case JORDAN_PROD : /* x*y = xy+yx */
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = ADDITION;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = temp2->op = JUXT_PROD;
temp1->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp2->operand2 = Expand_parse_tree(Unexp_tree->operand1);
temp1->operand2 = Expand_parse_tree(Unexp_tree->operand2);
temp2->operand1 = Expand_parse_tree(Unexp_tree->operand2);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
return(temp_tnode_ptr);
break;
case ASSOCIATION : /* (x,y,z) = (xy)z-x(yz) */
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SUBTRACTION;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp3 = Unexp_tnode_alloc();
temp4 = Unexp_tnode_alloc();
temp1->op = temp2->op = JUXT_PROD;
temp3->op = temp4->op = JUXT_PROD;
temp1->operand1 = temp3;
temp2->operand2 = temp4;
temp3->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp2->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp3->operand2 = Expand_parse_tree(Unexp_tree->operand2);
temp4->operand1 = Expand_parse_tree(Unexp_tree->operand2);
temp1->operand2 = Expand_parse_tree(Unexp_tree->operand3);
temp4->operand2 = Expand_parse_tree(Unexp_tree->operand3);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
return(temp_tnode_ptr);
break;
case JACOBI : /* J(x,y,z) = (xy)z+(yz)x+(zx)y */
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = ADDITION;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp3 = Unexp_tnode_alloc();
temp4 = Unexp_tnode_alloc();
temp5 = Unexp_tnode_alloc();
temp6 = Unexp_tnode_alloc();
temp7 = Unexp_tnode_alloc();
temp1->op = ADDITION;
temp2->op = temp3->op = temp4->op = JUXT_PROD;
temp5->op = temp6->op = temp7->op = JUXT_PROD;
temp1->operand1 = temp3;
temp1->operand2 = temp4;
temp2->operand1 = temp5;
temp3->operand1 = temp6;
temp4->operand1 = temp7;
temp6->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp4->operand2 = Expand_parse_tree(Unexp_tree->operand1);
temp5->operand2 = Expand_parse_tree(Unexp_tree->operand1);
temp6->operand2 = Expand_parse_tree(Unexp_tree->operand2);
temp7->operand1 = Expand_parse_tree(Unexp_tree->operand2);
temp2->operand2 = Expand_parse_tree(Unexp_tree->operand2);
temp3->operand2 = Expand_parse_tree(Unexp_tree->operand3);
temp7->operand2 = Expand_parse_tree(Unexp_tree->operand3);
temp5->operand1 = Expand_parse_tree(Unexp_tree->operand3);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
return(temp_tnode_ptr);
break;
case JORDAN_ASSOC : /* <x,y,z> = (x*y)*z-x*(y*z) */
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SUBTRACTION;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp3 = Unexp_tnode_alloc();
temp4 = Unexp_tnode_alloc();
temp1->op = temp2->op = JORDAN_PROD;
temp3->op = temp4->op = JORDAN_PROD;
temp1->operand1 = temp3;
temp2->operand2 = temp4;
temp3->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp2->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp3->operand2 = Expand_parse_tree(Unexp_tree->operand2);
temp4->operand1 = Expand_parse_tree(Unexp_tree->operand2);
temp1->operand2 = Expand_parse_tree(Unexp_tree->operand3);
temp4->operand2 = Expand_parse_tree(Unexp_tree->operand3);
temp_tnode_ptr->operand1 = Expand_parse_tree(temp1);
temp_tnode_ptr->operand2 = Expand_parse_tree(temp2);
return(temp_tnode_ptr);
break;
case OPERATOR_PROD : /* {xy`z'u'} = ((yx)z)u */
if (Unexp_tree->operand2 == NULL)
return(Expand_parse_tree(Unexp_tree->operand1));
else {
temp1 = Unexp_tnode_alloc();
temp_tnode_ptr = Unexp_tnode_alloc();
temp1->op = OPERATOR_PROD;
temp1->operand1 = temp_tnode_ptr;
temp1->operand2 = Unexp_tree->operand2->next;
temp_tnode_ptr->op = JUXT_PROD;
if (Unexp_tree->operand2->op == LEFT_MULT) {
temp_tnode_ptr->operand1 = Expand_parse_tree(Unexp_tree->operand2->operand1);
temp_tnode_ptr->operand2 = Expand_parse_tree(Unexp_tree->operand1);
}
else {
temp_tnode_ptr->operand2 = Expand_parse_tree(Unexp_tree->operand2->operand1);
temp_tnode_ptr->operand1 = Expand_parse_tree(Unexp_tree->operand1);
}
return(Expand_parse_tree(temp1));
}
break;
case ARTIFICIAL_WORD : /* W{n;(xy):y:a:c...} */
temp = Unexp_tnode_alloc();
temp->op = ARTIFICIAL_WORD;
temp->operand1 = Expand_parse_tree(Unexp_tree->operand1);
temp->operand2 = Expand_parse_tree(Unexp_tree->operand2);
temp1 = temp->operand2;
temp2 = Unexp_tree->operand2;
while (temp2 != NULL) {
temp1->next = Expand_parse_tree(temp2->next);
temp1 = temp1->next;
temp2 = temp2->next;
}
temp1 = Simplify_art_word(temp->operand1->scalar_num,temp->operand2);
return(Expand_parse_tree(temp1));
break;
default :
printf("operator not defined\n");
}
}
return NULL;
}
/*******************************************************************/
/* MODIFIES: */
/* Unexp_tree -- pointer to the unexpanded parse tree. */
/* REQUIRES: */
/* T -- Association type. */
/* RETURNS: */
/* Pointer to the Expanded tree for the Artificial word. */
/* FUNCTION: */
/* Constructs the tree recursively using the Type and the list */
/* atoms. */
/* NOTE: */
/* This routine is called only during the expansion. */
/* A special algorithm to create a tree given the type and a */
/* list of operators is used. */
/*******************************************************************/
struct unexp_tnode *Simplify_art_word(int T, struct unexp_tnode *Pntr)
{
struct unexp_tnode *temp,*temp1,*temp2,*left_tree,*right_tree;
int deg,j,offset,sum,deg1,deg2,t1,t2;
if (Pntr == NULL)
return(NULL);
deg = Get_degree(Pntr);
if (deg == 0)
return(NULL);
if (Get_catalan(deg) < T)
return(NULL);
if (deg == 1) {
Pntr->next = NULL;
return(Pntr);
}
else if (deg == 2) {
temp = Unexp_tnode_alloc();
temp->op = JUXT_PROD;
temp->operand1 = Pntr;
temp->operand2 = Pntr->next;
temp->operand1->next = NULL;
temp->operand2->next = NULL;
return(temp);
}
else {
j = 1;
offset = 0;
sum = Get_catalan(deg - 1) * Get_catalan(1);
while (sum < T) {
offset += Get_catalan(deg - j) * Get_catalan(j);
j++;
sum += Get_catalan(deg - j) * Get_catalan(j);
}
deg1 = deg - j;
deg2 = j;
t2 = 0;
if ((deg2 == 1) || (deg2 == 2))
t2 = 1;
if ((deg1 == 1) || (deg1 == 2))
t1 = 1;
else {
if (t2 != 1)
t1 = (T - offset) % Get_catalan(deg1);
else
t1 = T - offset;
}
t2 = (T - offset - t1) / Get_catalan(deg1) + 1;
temp1 = Pntr;
j = 1;
while (j < deg1) {
temp1 = temp1->next;
j++;
}
temp2 = temp1->next;
temp1->next = NULL;
left_tree = Simplify_art_word(t1,Pntr);
right_tree = Simplify_art_word(t2,temp2);
temp = Unexp_tnode_alloc();
temp->op = JUXT_PROD;
temp->operand1 = left_tree;
temp->operand2 = right_tree;
return(temp);
}
}
/*******************************************************************/
/* MODIFIES: None. */
/* REQUIRES: */
/* Pointer to a list of letters. (i.e list of tnodes) */
/* RETURNS: */
/* Total number of letters present the list. */
/* FUNCTION: */
/* Traverses the list to find the number of tnodes in the list.*/
/* NOTE: */
/* is called only from the routine Simplify_art_word(). */
/*******************************************************************/
int Get_degree(struct unexp_tnode *Pntr)
{
int i = 0;
struct unexp_tnode *temp;
temp = Pntr;
while (temp != NULL) {
i++;
temp = temp->next;
}
return(i);
}
/*******************************************************************/
/* MODIFIES: */
/* Unsimp_tree -- pointer to the unsimplified polynomial tree. */
/* *Modified_ptr -- Flag to indicate whether there are any */
/* changes to the tree in this call. */
/* REQUIRES: None. */
/* RETURNS: */
/* Pointer to the Simplified tree. */
/* FUNCTION: */
/* Applies the distributive laws to simplify the tree. */
/* NOTE: */
/* 3(2x+3y) = 6x + 9y. */
/* Operators Addition, Subtraction and scalar multiplication */
/* bubble up in the tree. */
/* i.e Juxtaposed product bubbles down. */
/* In the Simplified tree, the operands for the operator */
/* juxtaposed product will be letters, numbers or another */
/* subtree for juxtaposed product. */
/* This routine is called until there is no change in the */
/* tree due to the previous call. */
/*******************************************************************/
struct unexp_tnode *Simplify_parse_tree(struct unexp_tnode *Unsimp_tree, int *Modified_ptr)
{
/*int i;*/
struct unexp_tnode *temp1;
struct unexp_tnode *temp2;
struct unexp_tnode *temp_tnode_ptr;
if (Unsimp_tree == NULL)
return(NULL);
if (Unsimp_tree->op == SMALL_LETTER) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SMALL_LETTER;
temp_tnode_ptr->s_letter = Unsimp_tree->s_letter;
temp_tnode_ptr->next = Unsimp_tree->next;
return(temp_tnode_ptr);
}
else if (Unsimp_tree->op == SCALAR) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR;
temp_tnode_ptr->scalar_num = Unsimp_tree->scalar_num;
temp_tnode_ptr->next = Unsimp_tree->next;
return(temp_tnode_ptr);
}
else {
switch (Unsimp_tree->op) {
case ADDITION :
case SUBTRACTION :
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = Unsimp_tree->op;
temp_tnode_ptr->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp_tnode_ptr->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
return(temp_tnode_ptr);
break;
case JUXT_PROD :
if (((Unsimp_tree->operand1->op == JUXT_PROD) ||
(Unsimp_tree->operand1->op == SMALL_LETTER)) &&
((Unsimp_tree->operand2->op == JUXT_PROD) ||
(Unsimp_tree->operand2->op == SMALL_LETTER))) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = JUXT_PROD;
temp_tnode_ptr->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp_tnode_ptr->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
return(temp_tnode_ptr);
}
/* x(y+z) = xy + xz */
else if (((Unsimp_tree->operand1->op == SMALL_LETTER) ||
(Unsimp_tree->operand1->op == JUXT_PROD)) &&
((Unsimp_tree->operand2->op == ADDITION) ||
(Unsimp_tree->operand2->op == SUBTRACTION))) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op=Unsimp_tree->operand2->op;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = temp2->op = JUXT_PROD;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp2->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2->operand1,Modified_ptr);
temp2->operand2 = Simplify_parse_tree(Unsimp_tree->operand2->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* (x+y)z = xz + yz */
else if (((Unsimp_tree->operand2->op == SMALL_LETTER) ||
(Unsimp_tree->operand2->op == JUXT_PROD)) &&
((Unsimp_tree->operand1->op == ADDITION) ||
(Unsimp_tree->operand1->op == SUBTRACTION))) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op=Unsimp_tree->operand1->op;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = temp2->op = JUXT_PROD;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand1,Modified_ptr);
temp2->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand2,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
temp2->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* (a+b)(c-d) = ac+bc-bc-bd */
else if (((Unsimp_tree->operand1->op == ADDITION) ||
(Unsimp_tree->operand1->op == SUBTRACTION)) &&
((Unsimp_tree->operand2->op == ADDITION) ||
(Unsimp_tree->operand2->op == SUBTRACTION))) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op=Unsimp_tree->operand1->op;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = temp2->op = JUXT_PROD;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand1,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
temp2->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand2,Modified_ptr);
temp2->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* (x.y).3x = 3(x.y).x */
else if (((Unsimp_tree->operand1->op == JUXT_PROD) ||
(Unsimp_tree->operand1->op == SMALL_LETTER)) &&
(Unsimp_tree->operand2->op == SCALAR_MULT)) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = JUXT_PROD;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = Simplify_parse_tree(Unsimp_tree->operand2->operand1,Modified_ptr);
temp_tnode_ptr->operand2 = temp1;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
else if ((Unsimp_tree->operand1->op == SCALAR_MULT) &&
((Unsimp_tree->operand2->op == SMALL_LETTER) ||
(Unsimp_tree->operand2->op == JUXT_PROD))) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = JUXT_PROD;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand2,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand1,Modified_ptr);
temp_tnode_ptr->operand2 = temp1;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* 3(4x) = 12x */
else if ((Unsimp_tree->operand1->op == SCALAR_MULT) &&
(Unsimp_tree->operand2->op == SCALAR_MULT)) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = SCALAR;
Assert_scalar_bounds(Unsimp_tree->operand1->operand1->scalar_num);
Assert_scalar_bounds(Unsimp_tree->operand2->operand1->scalar_num);
temp1->scalar_num = Unsimp_tree->operand1->operand1->scalar_num * Unsimp_tree->operand2->operand1->scalar_num;
temp2 = Unexp_tnode_alloc();
temp2->op = JUXT_PROD;
temp2->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand2,Modified_ptr);
temp2->operand2 = Simplify_parse_tree(Unsimp_tree->operand2->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* 3x.(y+z) = 3x.y + 3x.z */
else if ((Unsimp_tree->operand1->op == SCALAR_MULT) &&
((Unsimp_tree->operand2->op == ADDITION) ||
(Unsimp_tree->operand2->op == SUBTRACTION))) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = JUXT_PROD;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand2,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = Simplify_parse_tree(Unsimp_tree->operand1->operand1,Modified_ptr);
temp_tnode_ptr->operand2 = temp1;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* (y+z).3x = 3y.x + 3z.x */
else if ((Unsimp_tree->operand2->op == SCALAR_MULT) &&
((Unsimp_tree->operand1->op == ADDITION) ||
(Unsimp_tree->operand1->op == SUBTRACTION))) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = JUXT_PROD;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = Simplify_parse_tree(Unsimp_tree->operand2->operand1,Modified_ptr);
temp_tnode_ptr->operand2 = temp1;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
break;
case SCALAR_MULT :
if ((Unsimp_tree->operand2->op == SMALL_LETTER) ||
(Unsimp_tree->operand2->op == JUXT_PROD)) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp_tnode_ptr->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp_tnode_ptr->operand2=Simplify_parse_tree(Unsimp_tree->operand2,Modified_ptr);
return(temp_tnode_ptr);
}
/* 3(3x) = 9x */
else if (Unsimp_tree->operand2->op == SCALAR_MULT) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = SCALAR;
Assert_scalar_bounds(Unsimp_tree->operand1->scalar_num);
Assert_scalar_bounds(Unsimp_tree->operand2->operand1->scalar_num);
temp1->scalar_num = Unsimp_tree->operand1->scalar_num * Unsimp_tree->operand2->operand1->scalar_num;
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2=Simplify_parse_tree(Unsimp_tree->operand2->operand2,Modified_ptr);
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* 3(x+y) = 3x + 3y */
else if ((Unsimp_tree->operand2->op == ADDITION) ||
(Unsimp_tree->operand2->op == SUBTRACTION)) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = Unsimp_tree->operand2->op;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = temp2->op = SCALAR_MULT;
temp1->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp2->operand1 = Simplify_parse_tree(Unsimp_tree->operand1,Modified_ptr);
temp1->operand2 = Simplify_parse_tree(Unsimp_tree->operand2->operand1,Modified_ptr);
temp2->operand2 = Simplify_parse_tree(Unsimp_tree->operand2->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
break;
}
}
return NULL;
}
/*******************************************************************/
/* MODIFIES: */
/* Unsimp_tree -- pointer to the unsimplified polynomial tree. */
/* *Modified_ptr -- Flag to indicate whether there are any */
/* changes to the tree in this call. */
/* REQUIRES: None. */
/* RETURNS: */
/* Pointer to the simplified tree without subtraction. */
/* FUNCTION: */
/* Eliminates the operator SUBTRACTION from the tree. */
/* NOTE: */
/* This routine is called until there is no change in the */
/* tree due to the previous call. */
/*******************************************************************/
struct unexp_tnode *Elim_subtraction(struct unexp_tnode *Unsimp_tree, int *Modified_ptr)
{
struct unexp_tnode *temp_tnode_ptr;
struct unexp_tnode *temp1;
struct unexp_tnode *temp2;
/*int i;*/
if (Unsimp_tree == NULL)
return(NULL);
if (Unsimp_tree->op == SMALL_LETTER) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SMALL_LETTER;
temp_tnode_ptr->s_letter = Unsimp_tree->s_letter;
temp_tnode_ptr->next = Unsimp_tree->next;
return(temp_tnode_ptr);
}
else if (Unsimp_tree->op == SCALAR) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR;
temp_tnode_ptr->scalar_num = Unsimp_tree->scalar_num;
temp_tnode_ptr->next = Unsimp_tree->next;
return(temp_tnode_ptr);
}
else {
switch (Unsimp_tree->op) {
case ADDITION :
case JUXT_PROD :
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = Unsimp_tree->op;
temp_tnode_ptr->operand1 = Elim_subtraction(Unsimp_tree->operand1,Modified_ptr);
temp_tnode_ptr->operand2 = Elim_subtraction(Unsimp_tree->operand2,Modified_ptr);
return(temp_tnode_ptr);
break;
case SUBTRACTION :
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = ADDITION;
temp_tnode_ptr->operand1 = Elim_subtraction(Unsimp_tree->operand1,Modified_ptr);
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = SCALAR_MULT;
temp1->operand1 = temp2;
temp2->op = SCALAR;
temp2->scalar_num = -1;
temp1->operand2 = Elim_subtraction(Unsimp_tree->operand2,Modified_ptr);
temp_tnode_ptr->operand2=temp1;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
break;
case SCALAR_MULT :
if ((Unsimp_tree->operand2->op == SMALL_LETTER) ||
(Unsimp_tree->operand2->op == JUXT_PROD)) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp_tnode_ptr->operand1 = Elim_subtraction(Unsimp_tree->operand1,Modified_ptr);
temp_tnode_ptr->operand2=Elim_subtraction(Unsimp_tree->operand2,Modified_ptr);
return(temp_tnode_ptr);
}
/* 3(3x) = 9x */
else if (Unsimp_tree->operand2->op == SCALAR_MULT) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = SCALAR_MULT;
temp1 = Unexp_tnode_alloc();
temp1->op = SCALAR;
Assert_scalar_bounds(Unsimp_tree->operand1->scalar_num);
Assert_scalar_bounds(Unsimp_tree->operand2->operand1->scalar_num);
temp1->scalar_num = Unsimp_tree->operand1->scalar_num * Unsimp_tree->operand2->operand1->scalar_num;
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2=Elim_subtraction(Unsimp_tree->operand2->operand2,Modified_ptr);
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
/* 3(x+y) = 3x + 3y */
else if ((Unsimp_tree->operand2->op == ADDITION) ||
(Unsimp_tree->operand2->op == SUBTRACTION)) {
temp_tnode_ptr = Unexp_tnode_alloc();
temp_tnode_ptr->op = Unsimp_tree->operand2->op;
temp1 = Unexp_tnode_alloc();
temp2 = Unexp_tnode_alloc();
temp1->op = temp2->op = SCALAR_MULT;
temp1->operand1 = Elim_subtraction(Unsimp_tree->operand1,Modified_ptr);
temp2->operand1 = Elim_subtraction(Unsimp_tree->operand1,Modified_ptr);
temp1->operand2 = Elim_subtraction(Unsimp_tree->operand2->operand1,Modified_ptr);
temp2->operand2 = Elim_subtraction(Unsimp_tree->operand2->operand2,Modified_ptr);
temp_tnode_ptr->operand1 = temp1;
temp_tnode_ptr->operand2 = temp2;
*Modified_ptr = TRUE;
return(temp_tnode_ptr);
}
break;
}
}
return NULL;
}
void Assert_scalar_bounds(int i)
{
if ((i>SCALAR_U_BOUND) || (i<SCALAR_L_BOUND))
printf("Scalar out of bounds. May cause overflow.\n");
}