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optimize.c
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#include "gc.h"
/*
* Optimizations:
*
* - constant folding for simple arithmetic
* - canonicalization (flatten nesting)
* - some algebraic simplifications
* (which get quite ugly to code)
*
* It has come at a point where almost
* the bulk of the complete program is in
* algebraic simplifications.
*
* Maybe it would be possible to come up with
* a domain-language that simplifies the coding
* of the algebraic simplifications...
* I've been thinking about that for about 2 years
* now and I'm slowly starting to have ideas for
* syntax for such a language
*
* Although in Norvig's PAIP book it is claimed
* that rule-driven approaches always have limits,
* so perhaps it does still make sense to have
* some slightly "dirty" code like this...
*
* The good news is that it is massively unit-tested
* and coverage-checked using included debugging scripts.
*
* So it's reasonably legit. And it's been through lots
* manual testing and been "tested" by presumably hundreds
* of customers of the GUI build around the globe...
*/
#include "tree.h"
#include "tokens.h"
#include <stdio.h>
#include <string.h> /* memcpy */
#ifdef DEBUG_OPT
#define return(X) { /* fprintf(stderr, "[DEBUG] leaving optimizer at line %d\n", \
__LINE__); \
fprintf(stderr, "[DEBUG] fe1: %f, fe2: %f\n", fe_init, float_eval(et, 2.0)); */ \
if (fabs(fe_init - float_eval(et, 2.0)) > 1.0) { \
fprintf(stderr, "\n\n\n**************************************\n"\
" [DEBUG] probably bad code at line %d of optimize.c\n" \
"**************************************\n\n\n", __LINE__); \
exit(1); \
} \
return(X); \
}
#endif
extern int tok2int(token_t *t);
extern int sametree(exp_tree_t *a, exp_tree_t *b);
char buf[1024];
exp_tree_t new, *new_ptr;
exp_tree_t new2, *new2_ptr;
exp_tree_t num, *num_ptr;
exp_tree_t *cancel;
void make_tree_number(exp_tree_t *t, int n)
{
char buffer[128];
sprintf(buffer, "%d", n);
t->tok = make_fake_tok(buffer);
t->head_type = NUMBER;
t->child_count = 0;
}
exp_tree_t* new_tree_number(int n)
{
exp_tree_t t = new_exp_tree(NUMBER, NULL);
make_tree_number(&t, n);
return alloc_exptree(t);
}
/* check for an arithmetic operation tree */
int arith_type(int ty)
{
return ty == ADD
|| ty == SUB
|| ty == MULT
|| ty == DIV;
}
/*
* Performs the conversion:
* e^(a + b + c + ...) => e^a * e^b * e^c * ...
*/
int unwind_expos(exp_tree_t *et)
{
int i, q;
int res = 0;
exp_tree_t *derp, *below;
for (i = 0; i < et->child_count; ++i)
res |= unwind_expos(et->child[i]);
if (et->head_type == EXP
&& et->child_count == 2
&& et->child[1]->head_type == ADD
&& et->child[1]->child_count >= 2) {
if (et->child[0]->head_type == VARIABLE) {
strncpy(buf, et->child[0]->tok->start, et->child[0]->tok->len);
buf[et->child[0]->tok->len] = 0;
if (!strcmp(buf, "e")) {
/* yes */
/* derp = e^ */
derp = copy_tree(et);
derp->child_count = 1;
new = new_exp_tree(MULT, NULL);
new_ptr = alloc_exptree(new);
below = et->child[1];
for (q = 0; q < below->child_count; ++q) {
new2_ptr = copy_tree(derp);
add_child(new2_ptr, below->child[q]);
add_child(new_ptr, new2_ptr);
}
/* transpose */
memcpy(et, new_ptr, sizeof(exp_tree_t));
return 1;
}
}
}
return res;
}
int optimize(exp_tree_t *et)
{
int i = 0;
int q, w, e, r, t, y;
int did = 0;
int chk, chk2, chk3;
int a, b;
int val;
exp_tree_t *below;
exp_tree_t *herp;
exp_tree_t *derp;
exp_tree_t *right_child;
double fe_init;
extern token_t* make_fake_tok(char *s);
extern double float_eval(exp_tree_t *, double val);
#ifdef DEBUG_OPT
fe_init = float_eval(et, 2.0);
#endif
for (i = 0; i < et->child_count; i++) {
did |= optimize(et->child[i]);
}
/* e.g. (DIV 6 3) -> (NUMBER 2) */
if (et->head_type == DIV
&& et->child_count == 2
&& et->child[0]->head_type == NUMBER
&& et->child[1]->head_type == NUMBER) {
a = tok2int(et->child[0]->tok);
b = tok2int(et->child[1]->tok);
if (b != 0 && a % b == 0) {
et->child_count = 0;
et->head_type = NUMBER;
sprintf(buf, "%d", a / b);
et->tok = (token_t *)make_fake_tok(buf);
return(1);
}
}
/*
* Fold trivial arithmetic constants
*/
if (et->head_type == MULT
|| et->head_type == ADD
|| et->head_type == SUB
|| et->head_type == NEGATIVE) {
chk = 1;
for (i = 0; i < et->child_count; ++i)
if (et->child[i]->head_type != NUMBER) {
chk = 0;
break;
}
if (chk) {
did = 1;
val = tok2int(et->child[0]->tok);
for (i = 1; i < et->child_count; ++i) {
switch(et->head_type) {
case MULT:
val *= tok2int(et->child[i]->tok);
break;
case ADD:
val += tok2int(et->child[i]->tok);
break;
case SUB:
val -= tok2int(et->child[i]->tok);
break;
}
}
if (et->head_type == NEGATIVE)
val *= -1;
et->head_type = NUMBER;
sprintf(buf, "%d", val);
et->tok = (token_t *)make_fake_tok(buf);
et->child_count = 0;
} else {
/*
* Simplify mixed number/non-number
* to one number and the rest
*/
chk = 0;
chk2 = 0;
for (i = 0; i < et->child_count; ++i) {
if (et->child[i]->head_type == NUMBER)
chk++;
if (et->child[i]->head_type != NUMBER)
chk2 = 1;
}
if ((chk > 1 || (chk == 1 && et->child[0]->head_type != NUMBER))
&& chk2
&& (et->head_type == ADD || et->head_type == MULT)) {
new = new_exp_tree(et->head_type, et->tok);
val = et->head_type == ADD ? 0 : 1;
for (i = 0; i < et->child_count; ++i) {
if (et->child[i]->head_type == NUMBER) {
switch(et->head_type) {
case MULT:
val *= tok2int(et->child[i]->tok);
break;
case ADD:
val += tok2int(et->child[i]->tok);
break;
}
}
}
sprintf(buf, "%d", val);
num = new_exp_tree(NUMBER, make_fake_tok(buf));
new_ptr = alloc_exptree(new);
add_child(new_ptr, alloc_exptree(num));
for (i = 0; i < et->child_count; ++i)
if (et->child[i]->head_type != NUMBER)
add_child(new_ptr, copy_tree(et->child[i]));
/* overwrite tree data */
memcpy(et, new_ptr, sizeof(exp_tree_t));
return(1);
}
}
}
/*
* Simplify nested binary trees,
* e.g. (SUB (SUB (NUMBER:3) (NUMBER:2)) (NUMBER:1))
* becomes (SUB (NUMBER:3) (NUMBER:2) (NUMBER:1))
*/
if (et->child_count == 2
&& et->child[0]->head_type == et->head_type
&& (et->head_type == ADD ||et->head_type == SUB ||et->head_type == MULT)) {
below = et->child[0];
right_child = et->child[1];
et->child_count = 0;
for (i = 0; i < below->child_count; i++)
add_child(et, below->child[i]);
add_child(et, right_child);
return(1);
}
/* (MUL (MUL xxx) yyy zzz) => (MUL xxx yyy zzz) */
if (et->child_count >= 2
&& et->child[0]->head_type == et->head_type
&& et->child[0]->child_count
&& (et->head_type == MULT || et->head_type == ADD)) {
/*
* 2014-06-01
*
* There was a pretty stupid bug here
* where it was always making MULT nodes
* even if the original was an ADD
*
* The GUI somehow managed to avoid it
*/
new = new_exp_tree(et->head_type, NULL);
new_ptr = alloc_exptree(new);
below = et->child[0];
for (q = 0; q < below->child_count; ++q)
add_child(new_ptr, below->child[q]);
for (q = 1; q < et->child_count; ++q)
add_child(new_ptr, et->child[q]);
memcpy(et, new_ptr, sizeof(exp_tree_t));
return(1);
}
/* (MUL xxx (MUL yyy)) => (MUL xxx yyy) */
if (et->child_count >= 2
&& et->child[et->child_count - 1]->head_type
== et->head_type
&& (et->head_type == MULT || et->head_type == ADD)) {
below = et->child[et->child_count - 1];
if (below->child_count) {
--(et->child_count);
for (i = 0; i < below->child_count; i++)
add_child(et, below->child[i]);
return(1);
}
}
/* (A * 123 * C) / 456 => (123/456) * A * C */
if (et->child_count == 2
&& et->head_type == DIV
&& et->child[0]->head_type == MULT
&& et->child[1]->head_type == NUMBER) {
below = et->child[0];
for (i = 0; i < below->child_count; ++i) {
if (below->child[i]->head_type == NUMBER) {
new = new_exp_tree(DIV, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, copy_tree(below->child[i]));
add_child(new_ptr, copy_tree(et->child[1]));
below->child[i] = new_ptr;
et->child_count--;
return(1);
}
}
}
/* (A * B * C) / C => A * B */
if (et->child_count == 2
&& et->head_type == DIV
&& et->child[0]->head_type == MULT) {
below = et->child[0];
for (i = 0; i < below->child_count; ++i) {
if (sametree(below->child[i], et->child[1])) {
et->child_count--;
make_tree_number(below->child[i], 1);
return(1);
}
}
}
/*
* (A * B * C) / (X * Y * B * Z)
* = (A * C) / (X * Y * Z)
*/
if (et->child_count == 2
&& et->head_type == DIV
&& et->child[0]->head_type == MULT
&& et->child[1]->head_type == MULT) {
for (q = 0; q < et->child[0]->child_count; ++q) {
cancel = et->child[0]->child[q];
for (e = 0; e < et->child[1]->child_count; ++e) {
below = et->child[1]->child[e];
if (sametree(below, cancel)) {
make_tree_number(below, 1);
make_tree_number(cancel, 1);
return(1);
}
}
}
}
/*
* (2/(2 * foo * bar)) => 1/ (foo * bar)
*/
if (et->child_count == 2
&& et->head_type == DIV
&& et->child[0]->head_type != MULT
&& et->child[1]->head_type == MULT) {
cancel = et->child[0];
for (e = 0; e < et->child[1]->child_count; ++e) {
below = et->child[1]->child[e];
if (sametree(below, cancel)) {
make_tree_number(below, 1);
make_tree_number(cancel, 1);
return(1);
}
}
}
/*
* Helper for cases like 6 * 1/x^2 * x
*/
if (et->head_type == MULT) {
chk = 0;
for (q = 0; q < et->child_count; ++q) {
if (et->child[q]->head_type == DIV
&& et->child[q]->child_count == 2
&& et->child[q]->child[0]->head_type == NUMBER
&& tok2int(et->child[q]->child[0]->tok) == 1
&& et->child[q]->child[1]->head_type == EXP
&& et->child[q]->child[1]->child_count == 2
&& et->child[q]->child[1]->child[1]->head_type == NUMBER) {
cancel = et->child[q]->child[1]->child[0];
for (w = 0; w < et->child_count; ++w) {
if (w != q) {
if (sametree(cancel, et->child[w])
|| (et->child[w]->head_type == EXP
&& et->child[w]->child_count == 2
&& sametree(et->child[w]->child[0], cancel))) {
new_ptr = copy_tree(cancel);
chk = tok2int(et->child[q]->child[1]->child[1]->tok);
et->child[q]->head_type = EXP;
et->child[q]->child_count = 2;
et->child[q]->child[0] = new_ptr;
make_tree_number(et->child[q]->child[1], -chk);
return(1);
}
}
}
}
}
}
/*
* 2014-06-11
*
* x ^ 2 * x ^3 * x^A * x
* messed up here prior to fix
*/
/* A * B * A * XYZ * A => A^3 * B * XYZ */
if (et->child_count >= 2
&& et->head_type == MULT) {
for (q = 0; q < et->child_count; ++q) {
chk = 0;
for (w = 0; w < et->child_count; ++w) {
if (sametree(et->child[w], et->child[q]))
++chk;
if (et->child[w]->head_type == EXP
&& et->child[w]->child_count == 2
&& sametree(et->child[w]->child[0], et->child[q])) {
if (et->child[w]->child[1]->head_type == NUMBER) {
chk += tok2int(et->child[w]->child[1]->tok);
} else {
goto non_number_power;
}
}
}
if (et->child[q]->head_type == NUMBER)
chk = 0;
if (chk > 1 || chk < 0) {
chk2 = 0;
cancel = copy_tree(et->child[q]);
for (q = 0; q < et->child_count; ++q) {
if (sametree(cancel, et->child[q])
|| (et->child[q]->head_type == EXP
&& et->child[q]->child_count == 2
&& sametree(et->child[q]->child[0], cancel))) {
if(!chk2) {
chk2 = 1;
new = new_exp_tree(EXP, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, cancel);
add_child(new_ptr, new_tree_number(chk));
et->child[q] = new_ptr;
} else {
make_tree_number(et->child[q], 1);
}
}
}
return(1);
}
}
}
non_number_power: ;
/*
* Remove 1's from products, 0's from additions,
* 0's from subtractions
*/
filter_zeroes:
if ((et->head_type == MULT
|| et->head_type == ADD
|| et->head_type == SUB)
&& et->child_count >= 2) {
chk = 0;
q = et->head_type == MULT;
for (i = 0; i < et->child_count; ++i) {
if (et->child[i]->head_type == NUMBER
&& tok2int(et->child[i]->tok) == q) {
++chk;
}
}
if (chk) {
new = new_exp_tree(et->head_type, NULL);
new_ptr = alloc_exptree(new);
for (i = 0; i < et->child_count; ++i)
if (!(et->child[i]->head_type == NUMBER
&& tok2int(et->child[i]->tok) == q))
add_child(new_ptr, copy_tree(et->child[i]));
/* transpose */
memcpy(et, new_ptr, sizeof(exp_tree_t));
return(1);
}
}
/*
* 2014-04-09
*
* There was a bug here.
* ]=> C + B * A + A
* A * (1 + C + B)
*
* should be fixed now:
* ]=> C + B * A + A
* C + A * (1 + B)
*/
/* A + B * A => A * (1 + B) */
if (et->child_count >= 2
&& et->head_type == ADD) {
chk = 0;
for (i = 0; i < et->child_count; ++i)
if (et->child[i]->head_type == MULT) {
chk = 1;
break;
}
if (chk) {
/* iterate thru terms */
for (q = 0; q < et->child_count; ++q) {
cancel = et->child[q];
/* try to cancel term q from another term */
for (w = 0; w < et->child_count; ++w) {
below = et->child[w];
if (below->head_type == MULT) {
for (e = 0; e < below->child_count; ++e) {
if (sametree(cancel, below->child[e])) {
/* there ! cancel factor from term */
exp_tree_t *new_sum = alloc_exptree(new_exp_tree(ADD, NULL));
make_tree_number(below->child[e], 1);
add_child(new_sum, copy_tree(below));
make_tree_number(below, 0);
/* cancel identical terms => 1 */
cancel = copy_tree(cancel);
for (r = 0; r < et->child_count; ++r)
if (sametree(et->child[r], cancel)) {
make_tree_number(et->child[r], 1);
add_child(new_sum, copy_tree(et->child[r]));
make_tree_number(et->child[r], 0);
}
/* make new product tree */
new = new_exp_tree(MULT, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, cancel);
add_child(new_ptr, copy_tree(new_sum));
add_child(et, new_ptr);
/*
* The above makes lots of useless 0 terms
* as a side effect, so get rid of them.
* Oterhwise, the GUI has weird-looking steps.
*/
goto filter_zeroes;
}
}
}
}
}
}
}
/* (DIV foo), (ADD foo), etc. -> foo */
if (et->child_count == 1
&& arith_type(et->head_type)) {
below = et->child[0];
memcpy(et, below, sizeof(exp_tree_t));
return(1);
}
/* (A * B * C) + (X * Y * B) = B * [(A*C) + (X*Y)] */
if (et->child_count >= 2
&& et->head_type == ADD) {
chk = 1;
for (i = 0; i < et->child_count; ++i)
if (et->child[i]->head_type != MULT) {
chk = 0;
break;
}
if (chk) {
/* iterate through terms */
for (q = 0; q < et->child_count; ++q) {
/* iterate through factors of a term */
for (w = 0; w < et->child[q]->child_count; ++w) {
/* check that this factor occurs in all terms */
chk = 1;
cancel = copy_tree(et->child[q]->child[w]);
for (e = 0; e < et->child_count; ++e) {
chk2 = 0;
for (r = 0; r < et->child[e]->child_count; ++r) {
if (sametree(et->child[e]->child[r], cancel)) {
chk2 = 1;
break;
}
}
chk &= chk2;
}
/* don't factor-out numbers */
if (cancel->head_type == NUMBER)
chk = 0;
if (is_special_tree(cancel->head_type))
chk = 0;
if (chk) {
/* factor => 1 */
for (e = 0; e < et->child_count; ++e)
for (r = 0; r < et->child[e]->child_count; ++r)
if (sametree(et->child[e]->child[r], cancel)) {
make_tree_number(et->child[e]->child[r], 1);
/*
* 2014-06-10
*
* another dumb bug fixed:
* only cancel once!!!
*
* ]=> (A * B * C) + (X * Y * B * B) + (B * S)
* B * (A * C + X * Y * B + S)
*
*/
break;
}
/* make new product tree */
new = new_exp_tree(MULT, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, cancel);
add_child(new_ptr, copy_tree(et));
/* transpose */
memcpy(et, new_ptr, sizeof(exp_tree_t));
return(1);
}
}
}
}
}
/* A * B * (C / D) = (A * B * C) / D */
if (et->child_count > 2
&& et->head_type == MULT
&& et->child[et->child_count - 1]->head_type == DIV
&& et->child[et->child_count - 1]->child_count == 2
/*
* 2015-05-04
*
* Prevent a conflict with
* (A * 123 * C) / 456 => (123/456) * A * C
*/
&& !(et->child[et->child_count - 1]->child[0]->head_type == NUMBER
&& et->child[et->child_count - 1]->child[1]->head_type == NUMBER)
) {
below = copy_tree(et->child[et->child_count - 1]);
et->child_count--;
add_child(et,
below->child[0]);
new = new_exp_tree(DIV, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, copy_tree(et));
add_child(new_ptr,
below->child[1]);
memcpy(et, new_ptr, sizeof(exp_tree_t));
return(1);
}
/*
* (A * B * C ^ 2) / C ^ 6
* => A * B * C ^ -4
*/
if (et->child_count == 2
&& et->head_type == DIV
&& et->child[0]->head_type == MULT
&& et->child[1]->head_type == EXP
&& et->child[1]->child_count == 2) {
cancel = copy_tree(et->child[1]->child[0]);
below = et->child[0];
/*
* 2014-06-10
*
* ensure all the ocurrences of C
* in the numerator are of the 2-child EXP kind
* before proceding !!
*/
chk = 1;
for (i = 0; i < below->child_count; ++i) {
if (!indep(below->child[i], cancel)) {
if (! (below->child[i]->child_count == 2
&& below->child[i]->head_type == EXP)) {
chk = 0;
break;
}
}
}
if (chk) {
chk = 0;
for (i = 0; i < below->child_count; ++i) {
if (below->child[i]->child_count == 2
&& below->child[i]->head_type == EXP) {
if (sametree(below->child[i]->child[0], cancel)) {
chk = 1;
new = new_exp_tree(SUB, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, copy_tree(below->child[i]->child[1]));
add_child(new_ptr, copy_tree(et->child[1]->child[1]));
below->child[i]->child[1] = new_ptr;
}
}
}
if (chk) {
et->child_count--;
return(1);
}
}
}
/*
* sin(x) / (sin(x)^2 * cos(x))
* => 1 / (sin(x) * cos(x))
*/
if (et->head_type == DIV
&& et->child_count == 2
&& et->child[1]->head_type == MULT) {
cancel = et->child[0];
below = et->child[1];
for (i = 0; i < below->child_count; ++i) {
if (below->child[i]->head_type == EXP
&& below->child[i]->child_count == 2) {
if (sametree(cancel, below->child[i]->child[0])) {
num = new_exp_tree(SUB, NULL);
num_ptr = alloc_exptree(num);
add_child(num_ptr, new_tree_number(1));
add_child(num_ptr,
copy_tree(below->child[i]->child[1]));
new = new_exp_tree(EXP, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, et->child[0]);
add_child(new_ptr, num_ptr);
make_tree_number(below->child[i], 1);
et->child[0] = new_ptr;
return(1);
}
}
}
}
/*
* x ^ 2 * x ^3 * x^A = x ^ (5 + A)
*/
if (et->head_type == MULT
&& et->child_count >= 2) {
for (i = 0; i < et->child_count; ++i) {
if (et->child[i]->head_type == EXP
&& et->child[i]->child_count == 2
&& et->child[i]->child[0]->head_type == VARIABLE) {
cancel = et->child[i]->child[0];
/* look for other exponentiations in this variable */
chk = 0;
for (q = 0; q < et->child_count; ++q) {
if (et->child[q]->head_type == EXP
&& et->child[q]->child_count == 2
&& et->child[q]->child[0]->head_type == VARIABLE
&& sametree(cancel, et->child[q]->child[0])) {
++chk;
}
}
/* don't do this on e^x */
strncpy(buf, cancel->tok->start, cancel->tok->len);
buf[cancel->tok->len] = 0;
if (!strcmp(buf, "e"))
chk = 0;
/* yes there are several. first sum up the exponents */
if (chk > 1) {
new = new_exp_tree(ADD, NULL);
new_ptr = alloc_exptree(new);
for (q = 0; q < et->child_count; ++q) {
if (et->child[q]->head_type == EXP
&& et->child[q]->child_count == 2
&& et->child[q]->child[0]->head_type == VARIABLE
&& sametree(cancel, et->child[q]->child[0])) {
add_child(new_ptr,
copy_tree(et->child[q]->child[1]));
}
}
/*
* Now stick them in the first exponentiation,
* and delete the others
*/
r = 0;
for (q = 0; q < et->child_count; ++q) {
if (et->child[q]->head_type == EXP
&& et->child[q]->child_count == 2
&& et->child[q]->child[0]->head_type == VARIABLE
&& sametree(cancel, et->child[q]->child[0])) {
if (!r) {
r = 1;
et->child[q]->child[1] = new_ptr;
} else {
make_tree_number(et->child[q], 1);
}
}
}
return(1);
}
}
}
}
/*
* (A * B^n * C) / B = (A * B ^ (n - 1) * C)
*/
/* A * A * A^3 * U/A * FOO * BAR * XYZ * A * U/A */
if (et->head_type == DIV
&& et->child_count == 2
&& et->child[0]->head_type == MULT) {
cancel = et->child[1];
below = et->child[0];
chk = 0;
for (q = 0; q < below->child_count; ++q) {
if (below->child[q]->head_type == EXP
&& below->child[q]->child_count == 2
&& sametree(below->child[q]->child[0], cancel)) {
chk = 1;
new = new_exp_tree(SUB, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, copy_tree(below->child[q]->child[1]));
add_child(new_ptr, new_tree_number(1));
/* transpose */
memcpy(below->child[q]->child[1],
new_ptr, sizeof(exp_tree_t));
/*
* 2014-07-01
* do this only once!!!
*/
break;
}
}
if (chk) {
et->child_count--;
return(1);
}
}
/*
* A^n * (B + C/A)
* = A^n * B + A^(n-1) * C
*/
if (et->head_type == MULT
&& et->child_count == 2
&& et->child[0]->head_type == EXP
&& et->child[0]->child_count == 2) {
cancel = et->child[0]->child[0];
below = et->child[1];
chk = 0;
for (q = 0; q < below->child_count; ++q)
if (below->child[q]->head_type == DIV
&& below->child[q]->child_count == 2
&& sametree(below->child[q]->child[1], cancel)) {
++chk;
derp = below->child[q];
}
if (chk == 1 && below->head_type == ADD) {
herp = copy_tree(et->child[0]);
new2 = new_exp_tree(ADD, NULL);
new2_ptr = alloc_exptree(new2);
for (q = 0; q < below->child_count; ++q) {
if (below->child[q] != derp) {
new = new_exp_tree(MULT, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr, copy_tree(herp));
add_child(new_ptr, copy_tree(below->child[q]));
add_child(new2_ptr, new_ptr);
} else {
num_ptr = copy_tree(herp);
new = new_exp_tree(SUB, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr,
copy_tree(et->child[0]->child[1]));
add_child(new_ptr, new_tree_number(1));
num_ptr->child[1] = new_ptr;
new = new_exp_tree(MULT, NULL);
new_ptr = alloc_exptree(new);
add_child(new_ptr,
copy_tree(below->child[q]->child[0]));
add_child(new_ptr, num_ptr);
add_child(new2_ptr, new_ptr);
}
}
memcpy(et, new2_ptr, sizeof(exp_tree_t));
return(1);
}
}
/*
* A^n * B * (C + D/A)
* = C * A ^ n * B + D * A ^ (n - 1) * B
*/
if (et->head_type == MULT) {
for (i = 0; i < et->child_count; ++i) {
if (et->child[i]->head_type == EXP
&& et->child[i]->child_count == 2) {
cancel = et->child[i];
chk = 0;
for (q = 0; q < et->child_count; ++q) {
if (et->child[q]->head_type == ADD) {
below = et->child[q];
for (w = 0; w < below->child_count; ++w) {
if (below->child[w]->head_type == DIV
&& below->child[w]->child_count == 2
&& sametree(below->child[w]->child[1],
cancel->child[0])) {
++chk;
chk2 = w; /* divison subchild */
chk3 = q; /* addition child */
}
}
}
}
if (chk == 1) {
below = et->child[chk3];
new = new_exp_tree(ADD, NULL);
new_ptr = alloc_exptree(new);
for (q = 0; q < below->child_count; ++q) {
num = new_exp_tree(MULT, NULL);
num_ptr = alloc_exptree(num);
if (q == chk2) {