eigenmath/divisors.cpp

#include "stdafx.h"

//-----------------------------------------------------------------------------
//
//	Generate all divisors of a term
//
//	Input:		Term on stack (factor * factor * ...)
//
//	Output:		Divisors on stack
//
//-----------------------------------------------------------------------------

#include "defs.h"

static void gen(int, int);
static void __factor_add(void);
static int __cmp(const void *, const void *);

void
divisors(void)
{
	int i, h, n;
	save();
	h = tos - 1;
	divisors_onstack();
	n = tos - h;
	qsort(stack + h, n, sizeof (U *), __cmp);
	p1 = alloc_tensor(n);
	p1->u.tensor->ndim = 1;
	p1->u.tensor->dim[0] = n;
	for (i = 0; i < n; i++)
		p1->u.tensor->elem[i] = stack[i];
	tos = h;
	push(p1);
	restore();
}

void
divisors_onstack(void)
{
	int h, i, k, n;

	save();

	p1 = pop();

	h = tos;

	// push all of the term's factors

	if (isnum(p1)) {
		push(p1);
		factor_small_number();
	} else if (car(p1) == symbol(ADD)) {
		push(p1);
		__factor_add();
//printf(">>>\n");
//for (i = h; i < tos; i++)
//print(stdout, stack[i]);
//printf("<<<\n");
	} else if (car(p1) == symbol(MULTIPLY)) {
		p1 = cdr(p1);
		if (isnum(car(p1))) {
			push(car(p1));
			factor_small_number();
			p1 = cdr(p1);
		}
		while (iscons(p1)) {
			p2 = car(p1);
			if (car(p2) == symbol(POWER)) {
				push(cadr(p2));
				push(caddr(p2));
			} else {
				push(p2);
				push(one);
			}
			p1 = cdr(p1);
		}
	} else if (car(p1) == symbol(POWER)) {
		push(cadr(p1));
		push(caddr(p1));
	} else {
		push(p1);
		push(one);
	}

	k = tos;

	// contruct divisors by recursive descent

	push(one);

	gen(h, k);

	// move

	n = tos - k;

	for (i = 0; i < n; i++)
		stack[h + i] = stack[k + i];

	tos = h + n;

	restore();
}

//-----------------------------------------------------------------------------
//
//	Generate divisors
//
//	Input:		Base-exponent pairs on stack
//
//			h	first pair
//
//			k	just past last pair
//
//	Output:		Divisors on stack
//
//	For example, factor list 2 2 3 1 results in 6 divisors,
//
//		1
//		3
//		2
//		6
//		4
//		12
//
//-----------------------------------------------------------------------------

#define ACCUM p1
#define BASE p2
#define EXPO p3

static void
gen(int h, int k)
{
	int expo, i;

	save();

	ACCUM = pop();

	if (h == k) {
		push(ACCUM);
		restore();
		return;
	}

	BASE = stack[h + 0];
	EXPO = stack[h + 1];

	push(EXPO);
	expo = pop_integer();

	for (i = 0; i <= abs(expo); i++) {
		push(ACCUM);
		push(BASE);
		push_integer(sign(expo) * i);
		power();
		multiply();
		gen(h + 2, k);
	}

	restore();
}

//-----------------------------------------------------------------------------
//
//	Factor ADD expression
//
//	Input:		Expression on stack
//
//	Output:		Factors on stack
//
//	Each factor consists of two expressions, the factor itself followed
//	by the exponent.
//
//-----------------------------------------------------------------------------

static void
__factor_add(void)
{
	save();

	p1 = pop();

	// get gcd of all terms

	p3 = cdr(p1);
	push(car(p3));
	p3 = cdr(p3);
	while (iscons(p3)) {
		push(car(p3));
		gcd();
		p3 = cdr(p3);
	}

	// check gcd

	p2 = pop();
	if (isplusone(p2)) {
		push(p1);
		push(one);
		restore();
		return;
	}

	// push factored gcd

	if (isnum(p2)) {
		push(p2);
		factor_small_number();
	} else if (car(p2) == symbol(MULTIPLY)) {
		p3 = cdr(p2);
		if (isnum(car(p3))) {
			push(car(p3));
			factor_small_number();
		} else {
			push(car(p3));
			push(one);
		}
		p3 = cdr(p3);
		while (iscons(p3)) {
			push(car(p3));
			push(one);
			p3 = cdr(p3);
		}
	} else {
		push(p2);
		push(one);
	}

	// divide each term by gcd

	push(p2);
	inverse();
	p2 = pop();

	push(zero);
	p3 = cdr(p1);
	while (iscons(p3)) {
		push(p2);
		push(car(p3));
		multiply();
		add();
		p3 = cdr(p3);
	}

	push(one);

	restore();
}

static int
__cmp(const void *p1, const void *p2)
{
	return cmp_expr(*((U **) p1), *((U **) p2));
}

static char *s[] = {

	"divisors(12)",
	"(1,2,3,4,6,12)",

	"divisors(-12)",
	"(1,2,3,4,6,12)",

	"divisors(a)",
	"(1,a)",

	"divisors(-a)",
	"(1,a)",

	"divisors(+3*x+3)",
	"(1,3,1+x,3+3*x)",

	"divisors(+3*x-3)",
	"(1,3,-3+3*x,-1+x)",

	"divisors(-3*x+3)",
	"(1,3,1-x,3-3*x)",

	"divisors(-3*x-3)",
	"(1,3,1+x,3+3*x)",
};

void
test_divisors(void)
{
	test(__FILE__, s, sizeof s / sizeof (char *));
}