New polynomial module (not quite CCAN format).

junkcode/iasoule32@gmail.com-polynomial/polynomial_adt.h

@@ -0,0 +1,430 @@
+/* Polynomial ADT 
+** A polynomial module with
+** ability to add,sub,mul derivate/integrate, compose ... polynomials 
+** ..expansion in progress ...
+ * Copyright (c) 2009 I. Soule
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+**          iasoule32@gmail.com
+*/
+
+#ifndef __POLYNOMIAL_ADT
+#define __POLYNOMIAL_ADT
+
+#include <assert.h>
+#include <stdlib.h>
+#include <stdbool.h> //C99 compliance
+#include <math.h>
+
+#define max(a, b) (a) > (b) ? (a) : (b)
+#define sgn(a)    (a) < 0 ? '+' : '-' //for quadratic factored form
+
+typedef struct node {
+    int exp;
+    float coeff;
+    struct node *next;
+}Node;
+
+typedef struct polynomial_adt {
+    Node *head;
+    int terms, hp; //hp highest power
+}PolyAdt;
+
+void display_poly(const PolyAdt *a);
+/**
+* create_adt - create a polynomial on the heap
+* @hp: the highest power in the polynomial
+*/
+PolyAdt *create_adt(int hp) 
+{
+    PolyAdt *pAdt = malloc(sizeof(PolyAdt));
+    assert(pAdt != NULL);
+    
+    pAdt->head = NULL;
+    pAdt->terms = 0;
+    pAdt->hp = hp;
+
+    return pAdt;
+}
+/**
+* create_node - creates a Node (exponent, constant and next pointer) on the heap 
+* @constant: the contant in the term 
+* @exp:      the exponent on the term
+* @next:     the next pointer to another term in the polynomial
+* 
+* This should not be called by client code (hence marked static)
+* used to assist insert_term()
+*/ 
+static Node *create_node(float constant, int exp, Node *next)
+{
+    Node *nNode = malloc(sizeof(Node));
+    assert(nNode != NULL);
+    
+    nNode->exp = exp;
+    nNode->coeff = constant;
+    nNode->next = next;
+    return nNode;
+}
+
+/**
+* insert_term - inserts a term into the polynomial
+* @pAdt: the polynomial 
+* @c:    constant value on the term
+* @e:    the exponent on the term 
+*/
+void insert_term(PolyAdt *pAdt, float c, int e)
+{
+    assert(pAdt != NULL); //assume client code didnt call create_adt()
+    Node *n = malloc(sizeof(Node));
+       
+    if(pAdt->head == NULL)
+        pAdt->head = create_node(c, e, pAdt->head);
+    else
+        for(n = pAdt->head; n->next != NULL; n = n->next); //go to the end of list
+            n->next = create_node(c, e, NULL);
+    
+    pAdt->terms++;
+}
+
+/**
+* polyImage - returns an image (direct) copy of the polynomial
+* @orig: the polynomial to be duplicated
+*/
+PolyAdt *polyImage(const PolyAdt *orig)
+{
+    PolyAdt *img = create_adt(orig->hp);
+    Node *origHead = orig->head;
+    
+    for(; origHead; origHead = origHead->next)
+             insert_term(img, origHead->coeff, origHead->exp);
+    return img;
+}
+
+
+/**
+* add - adds two polynomials together, and returns their sum (as a polynomial)
+* @a: the 1st polynomial 
+* @b: the 2nd polynomial
+*/
+PolyAdt *add(const PolyAdt *a, const PolyAdt *b)
+{
+    PolyAdt *sum;
+    Node *n, *np;
+    _Bool state = true;
+    
+    assert(a != NULL && b != NULL);
+    
+    int hpow = max(a->hp, b->hp);
+    sum = create_adt(hpow); //create space for it
+    
+    /* using state machine to compare the poly with the most terms to 
+    ** the poly with fewer, round robin type of effect comparison of
+    ** exponents => 3 Cases: Equal, Less, Greater
+    */
+        n = a->head; np = b->head;
+        while(state) {
+            /* compare the exponents */
+            if(n->exp == np->exp){
+                insert_term(sum, n->coeff + np->coeff, n->exp);
+                n = n->next;
+                np = np->next;
+            }
+            
+            else if(n->exp < np->exp){
+                insert_term(sum, np->coeff, np->exp);
+                np = np->next; //move to next term of b
+            }
+            
+            else { //greater than
+                insert_term(sum, n->coeff, n->exp);
+                n = n->next;
+            }
+            /* check whether at the end of one list or the other */
+            if(np == NULL && state == true){ //copy rest of a to sum
+                for(; n != NULL; n = n->next)
+                    insert_term(sum, n->coeff, n->exp);
+                state = false;
+            }
+            
+           if(n == NULL && state == true){
+                for(; np != NULL; np = np->next)
+                    insert_term(sum, np->coeff, np->exp);
+                state = false;
+            }       
+     }        
+    return sum;               
+}            
+
+/**
+* sub - subtracts two polynomials, and returns their difference (as a polynomial)
+* @a: the 1st polynomial 
+* @b: the 2nd polynomial
+* Aids in code reuse by negating the terms (b) and then calls the add() function
+*/
+PolyAdt *subtract(const PolyAdt *a, const PolyAdt *b)
+{
+	assert(a != NULL && b != NULL);
+
+    PolyAdt *tmp = create_adt(b->hp);
+    Node *bptr;
+    
+    for(bptr = b->head; bptr != NULL; bptr = bptr->next)
+        insert_term(tmp,-bptr->coeff,bptr->exp);  //negating b's coeffs
+    return add(a,tmp);
+}
+
+/**
+* multiply - multiply two polynomials, and returns their product (as a polynomial)
+* @a: the 1st polynomial 
+* @b: the 2nd polynomial
+*/
+PolyAdt *multiply(const PolyAdt *a, const PolyAdt *b)
+{
+	assert(a != NULL && b != NULL);
+
+    //the polys are inserted in order for now
+    PolyAdt *prod = create_adt(a->head->exp + b->head->exp);
+    Node *n = a->head, *np = b->head;
+    Node *t = b->head; 
+    
+    if(a->terms < b->terms){
+        n = b->head;
+        np = t = a->head;
+    }
+    
+    for(; n != NULL; n = n->next){
+        np = t; //reset to the beginning
+        for(; np != NULL; np = np->next){ //always the least term in this loop
+                insert_term(prod, n->coeff * np->coeff, n->exp + np->exp);
+        }
+    }
+
+    return prod;       
+}
+
+/**
+* derivative - computes the derivative of a polynomial and returns the result
+* @a: the polynomial to take the derivative upon
+*/
+PolyAdt *derivative(const PolyAdt *a)
+{
+	assert(a != NULL);
+	
+	PolyAdt *deriv = create_adt(a->head->exp - 1);
+	Node *n = a->head;
+
+	for(; n != NULL; n = n->next){
+		if(n->exp == 0) break;
+		insert_term(deriv, n->coeff * n->exp, n->exp-1);
+	}
+	return deriv;
+}
+/**
+* integrate - computes the integral of a polynomial and returns the result
+* @a: the polynomial to take the integral of
+* 
+* Will compute an indefinite integral over a
+*/
+PolyAdt *integrate(const PolyAdt *a)
+{
+	assert(a != NULL);
+	
+	PolyAdt *integrand = create_adt(a->head->exp + 1);
+	Node *n;
+
+	for(n = a->head; n != NULL; n = n->next) //very simple term by term
+        insert_term(integrand, (float)n->coeff/(n->exp+1.0F), n->exp + 1);
+    
+	return integrand;
+}
+/**
+* quadratic_roots - finds the roots of the polynomial ax^2+bx+c, a != 0 && b != 0
+* @a: the polynomial
+* @real: a pointer to float of the real(R) part of a
+* @cplx: a pointer to float of the imaginary(I) part of a
+*
+* Usage:
+* Two options can be done by the client 
+* 1. Either pass NULL to real and cplx
+*    this will display the roots by printf
+*    quadratic_roots(myPolynomial, NULL, NULL);
+*
+* 2. Pass in pointers** to type float of the real and complex
+*    if the discriminant is >0 cplx = -ve root of X
+*    quadratic_roots(myPolynomial, &realPart, &complexPart);
+*/
+void quadratic_roots(const PolyAdt *a, float *real, float *cplx)
+{
+	assert(a != NULL);
+	
+	float dscrmnt, _a, b, c;
+	float u, v;
+    
+    Node *n = a->head;
+    _a = n->coeff; b = n->next->coeff; c = n->next->next->coeff;
+    
+	dscrmnt = (b*b) - 4*_a*c;
+    u = -b/(2*_a); v = sqrt((double)fabs(dscrmnt))/(2*_a);
+    
+	if(real && !cplx || !real && cplx)
+		assert(true);
+
+	if(real == NULL && cplx == NULL){
+		if(a->hp != 2 && a->terms < 3){
+		  printf("Invalid Quadratic*, A and B must be non-zero");
+			return;
+        }
+        
+		if(dscrmnt != 0)
+			printf("X = %.2f +/- %.2f%c\n",u,v,dscrmnt < 0 ? 'I':' ');
+		else{
+			printf("(X %c %.2f)(X %c %.2f)\n",sgn(u),fabs(u),sgn(u),fabs(u));
+			printf("X1,2 = %.2f\n",u);
+		}
+	}
+	//save values in pointers
+	else {
+		if(dscrmnt < 0){ //x = u +/- vI Re(x) = u, Im(x) = +v
+			*real = u; 
+			*cplx = v; //understand +/- is not representable
+		}
+		else if(dscrmnt == 0){
+			*real = u; 
+			*cplx = 0.00F;
+		}
+		else{
+			*real = u + v;
+			*cplx = u - v;
+		}
+	}
+}
+
+/**
+* exponentiate - computes polynomial exponentiation (P(x))^n, n E Z*
+* @a: the polynomial
+* @n: the exponent
+* Works fast for small n (n < 8) currently runs ~ O(n^2 lg n)
+*/
+PolyAdt *exponentiate(const PolyAdt *a, int n)
+{
+	assert(a != NULL);
+
+	PolyAdt *expn = create_adt(a->hp *  n);
+	PolyAdt *aptr = polyImage(a);
+    int hl = n / 2;
+    
+    //check default cases before calculation
+    if(n == 0){
+        insert_term(expn, 1, 0);
+        return expn;
+    }
+    else if(n == 1){
+        return aptr;
+    }
+        
+	for(; hl ; hl--)
+        aptr = multiply(aptr, aptr);
+
+    if(n % 2) //odd exponent do a^(n-1) * a = a^n
+        expn = multiply(aptr, a);
+    else
+        expn = aptr;
+    return expn;
+}
+/**
+* compose - computes the composition of two polynomials P(Q(x)) and returns the composition
+* @p: polynomial P(x) which will x will be equal to Q(x)
+* @q: polynomial Q(x) which is the argument to P(x)
+*/
+PolyAdt *compose(const PolyAdt *p, const PolyAdt *q)
+{
+    assert(p && q);
+    
+	PolyAdt *comp = create_adt(p->head->exp * q->head->exp);
+	PolyAdt *exp;
+	
+    Node *pp = p->head;
+    Node *qq = q->head;
+    
+    int swap = 0;
+    
+    if(p->terms < q->terms){
+        pp = q->head;
+        qq = p->head;
+        swap = 1;
+    }
+    
+    /* going through, exponentiate each term with the exponent of p */
+        for(; pp != NULL; pp = pp->next){
+                exp = exponentiate(swap ? p: q, pp->exp);
+                insert_term(comp, pp->coeff * exp->head->coeff, exp->head->exp);
+        }
+    
+    return comp;
+}
+/** 
+* destroy_poly - completely frees the polynomial from the heap and resets all values
+* @poly: the polynomial to release memory back to the heap
+* Usage:
+* destroy_poly(myPoly); //puts polynomial on free list
+*/
+void destroy_poly(PolyAdt *poly)
+{
+    Node *ps = poly->head;
+    Node *tmp = NULL;
+    while(ps != NULL){
+        tmp = ps;
+        free(tmp);
+        ps = ps->next;
+    }
+    poly->hp = poly->terms = 0;
+    poly->head = NULL;
+}
+/**
+* display_poly - displays the polynomial to the console in nice format
+* @a: the polynomial to display 
+*/
+void display_poly(const PolyAdt *a)
+{
+    assert(a != NULL);
+    Node *n;
+    
+    for(n = a->head; n != NULL; n = n->next){
+        
+       n->coeff < 0 ? putchar('-') : putchar('+'); 
+        if(n->exp == 0)
+            printf(" %.2f ",fabs(n->coeff));
+        else if(n->coeff == 1)
+            printf(" X^%d ",n->exp);
+        else if(n->exp == 1)
+            printf(" %.2fX ",fabs(n->coeff));
+        else if(n->coeff == 0)
+            continue;
+        else
+            printf(" %.2fX^%d ",fabs(n->coeff),n->exp);
+        }
+    printf("\n\n");
+}
+
+#endif

junkcode/iasoule32@gmail.com-polynomial/polynomial_adt_test.c

@@ -0,0 +1,132 @@
+/* 
+** polynomial_adt_test.c
+** Test (minimalistic) for the polynomial module
+ * More of a display of functionality
+ * Copyright (c) 2009 I. Soule
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ *    notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ *    notice, this list of conditions and the following disclaimer in the
+ *    documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
+ * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+ * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
+ * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+ * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
+ * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
+ * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
+ * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
+ * SUCH DAMAGE.
+ *
+**          iasoule32@gmail.com
+*/
+
+#include <stdio.h>
+#include "polynomial_adt.h"
+
+int main()
+{
+    PolyAdt *p = create_adt(5), *q = create_adt(4);
+    PolyAdt *sum, *diff, *prod;
+    
+    insert_term(p,1,5);
+    insert_term(p,3,4);
+    insert_term(p,1,3);
+    insert_term(p,9,2);
+    insert_term(p,8,1);
+    
+    insert_term(q,2,4);
+    insert_term(q,8,3);
+    insert_term(q,7,2);
+    insert_term(q,6,1);
+    
+    
+    printf("Displaying Polynomials ...\n");
+    display_poly(p);
+    display_poly(q);
+    
+    sum = add(p,q);
+    printf("P(x) + Q(x) = ");
+    display_poly(sum);
+    
+    diff = subtract(p,q);
+    printf("P(x) - Q(x) = ");
+    display_poly(diff);
+    
+    prod = multiply(p,q);
+    printf("P(x)*Q(x) = ");
+    display_poly(prod);
+    
+    PolyAdt *quad = create_adt(2);
+    insert_term(quad, 10, 2);
+    insert_term(quad, 30, 1);
+    insert_term(quad, 2, 0);
+    
+    quadratic_roots(quad, NULL, NULL); //print out the roots
+    
+    float real, cplx;
+    quadratic_roots(quad, &real, &cplx);
+    
+    printf("X1 = %f, X2 = %f\n\n", real, cplx);
+    
+    PolyAdt *deriv, *integral;
+    
+    deriv = derivative(p);
+    printf("The derivitive of p = ");
+    display_poly(deriv);
+    integral = integrate(q);
+    
+    printf("The integral of q = ");
+    display_poly(integral);
+    
+    printf("\n Computing P(x)^3\n");
+    
+    PolyAdt *expo;
+    expo = exponentiate(p, 3);
+    display_poly(expo);
+    printf("\n");
+    
+    printf("Computing Integral[Q(x)^2]\n");
+    expo = exponentiate(q, 2);
+    integral = integrate(expo);
+    display_poly(integral);
+    
+    
+    printf(" Differentiating and Integrating P\n");
+    display_poly(integrate(derivative(p))); 
+    
+    PolyAdt *L, *M;
+    
+    L = create_adt(3), M = create_adt(2);
+    
+    insert_term(L, 4, 3);
+    insert_term(L, 10, 2);
+    insert_term(L, 15, 1);
+    
+    insert_term(M, 4, 2);
+    printf("L = ");
+    display_poly(L);
+    printf("M = ");
+    display_poly(M);
+    
+    
+    printf("Computing composition L(M(X))\n");
+    display_poly(compose(L, M));
+    
+    printf("Freed memory back to heap for allocated polys'");
+    destroy_poly(sum);
+    destroy_poly(diff);
+    destroy_poly(prod);
+    destroy_poly(L); destroy_poly(M);
+    destroy_poly(q); destroy_poly(p);
+    
+    return 0;
+}