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numeric.cc
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numeric.cc
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#include <math.h>
#include "cell.h"
Cell *mk_long(Cell *ctx, long l) {
Cell *num = number_new(ctx);
number_type(num) = NUMBER_LONG;
number_long(num) = l;
return num;
}
Cell *mk_double(Cell *ctx, double d) {
Cell *num = number_new(ctx);
number_type(num) = NUMBER_DOUBLE;
number_double(num) = d;
return num;
}
long num_gcd(long bg, long sm)
{
if (bg < 0) bg = -bg;
if (sm < 0) sm = -sm;
if (bg < sm)
{
return num_gcd(sm, bg);
}
if(sm == 0) return bg;
long res = bg % sm;
while (res != 0)
{
bg = sm;
sm = res ;
res = bg % sm;
}
return sm;
}
Cell *mk_fraction(Cell *ctx, long nr, long dr) {
char s = 1;
long gcd = num_gcd(nr, dr);
gc_var1(num);
gc_preserve1(ctx, num);
num = number_new(ctx);
if (dr < 0) s = -1;
number_type(num) = NUMBER_FRACTION;
number_fn_nr(num) = number_new(ctx);
number_type(number_fn_nr(num)) = NUMBER_LONG;
number_long(number_fn_nr(num)) = s * nr / gcd;
number_fn_dr(num) = number_new(ctx);
number_type(number_fn_dr(num)) = NUMBER_LONG;
number_long(number_fn_dr(num)) = s * dr / gcd;
gc_release(ctx);
return num;
}
Cell *mk_complex(Cell *ctx, Cell *rl, Cell *im) {
Cell *num = number_new(ctx);
number_type(num) = NUMBER_COMPLEX;
number_cx_rl(num) = rl;
number_cx_im(num) = im;
return num;
}
Cell *num_etoi(Cell *ctx, Cell *num) {
switch (number_type(num)) {
case NUMBER_LONG:
number_type(num) = NUMBER_DOUBLE;
number_double(num) = number_long(num);
break;
case NUMBER_DOUBLE:
return num;
case NUMBER_FRACTION:
{
number_type(num) = NUMBER_DOUBLE;
Cell *nr = number_fn_nr(num);
Cell *dr = number_fn_dr(num);
number_double(num) = (double)number_long(nr) / (double)number_long(dr);
break;
}
case NUMBER_COMPLEX:
num_etoi(ctx, number_cx_rl(num));
num_etoi(ctx, number_cx_im(num));
break;
}
return num;
}
Cell *num_itoe(Cell *ctx, Cell *num) {
switch (number_type(num)) {
case NUMBER_LONG:
return num;
case NUMBER_DOUBLE:
{
int n = 0;
double decimal = 0.0, inter = 0;
number_type(num) = NUMBER_FRACTION;
decimal = modf(number_double(num), &inter);
if (decimal > 0.0) {
for(;;) {
decimal *= 10;
++n;
if (decimal - (long)decimal < 0.000001) {
break;
}
}
}
long bg = pow(10, n);
long divisor = num_gcd(bg, decimal);
number_fn_dr(num) = number_new(ctx);
number_type(number_fn_dr(num)) = NUMBER_LONG;
number_long(number_fn_dr(num)) = bg / divisor;
number_fn_nr(num) = number_new(ctx);
number_type(number_fn_nr(num)) = NUMBER_LONG;
number_long(number_fn_nr(num)) = decimal / divisor + number_long(number_fn_dr(num)) * inter;
break;
}
case NUMBER_FRACTION:
return num;
case NUMBER_COMPLEX:
number_cx_rl(num) = num_itoe(ctx, number_cx_rl(num));
number_cx_im(num) = num_itoe(ctx, number_cx_im(num));
break;
}
return num;
}
bool num_equal(Cell *a, Cell *b) {
if (!a || !b) return FALSE;
if (number_type(a) != number_type(b)) return FALSE;
switch (number_type(a)) {
case NUMBER_LONG:
return number_long(a) == number_long(b);
case NUMBER_DOUBLE:
{
double sub = number_double(a) - number_double(b);
return sub > -0.000001 && sub < 0.000001;
}
case NUMBER_FRACTION:
return (number_long(number_fn_nr(a)) == number_long(number_fn_nr(b)) && number_long(number_fn_dr(a)) == number_long(number_fn_dr(b)));
case NUMBER_COMPLEX:
return num_equal(number_cx_rl(a), number_cx_rl(b)) && num_equal(number_cx_im(a), number_cx_im(b));
}
return FALSE;
}
double num_real_compare(Cell *a, Cell *b) {
double d1=0, d2=0;
switch (number_type(a)) {
case NUMBER_LONG:
d1 = number_long(a);
break;
case NUMBER_DOUBLE:
d1 = number_double(a);
break;
case NUMBER_FRACTION:
d1 = (double)number_long(number_fn_nr(a)) / (double)number_long(number_fn_dr(a));
break;
}
switch (number_type(b)) {
case NUMBER_LONG:
d2 = number_long(b);
break;
case NUMBER_DOUBLE:
d2 = number_double(b);
break;
case NUMBER_FRACTION:
d2 = number_long(number_fn_nr(b)) / number_long(number_fn_dr(b));
break;
}
return d1 - d2;
}
static Cell *_num_calcu(Cell *ctx, int op, Cell *a, Cell *b) {
gc_var7(num, rl, im, nr1, dr1, v1, v2);
gc_preserve7(ctx, num, rl, im, nr1, dr1, v1, v2);
long nr, dr, gcd;
switch (number_type(a)) {
case NUMBER_LONG:
switch (number_type(b)) {
case NUMBER_LONG:
switch (op) {
case OP_ADD:
num = mk_long(ctx, number_long(a) + number_long(b));
break;
case OP_SUB:
num = mk_long(ctx, number_long(a) - number_long(b));
break;
case OP_MULTI:
num = mk_long(ctx, number_long(a) * number_long(b));
break;
case OP_DIV:
{
gcd = num_gcd(number_long(a), number_long(b));
if (gcd == number_long(b)) {
num = mk_long(ctx, number_long(a) / gcd);
} else {
num = mk_fraction(ctx, number_long(a), number_long(b));
}
break;
}}
break;
case NUMBER_DOUBLE:
num = _num_calcu(ctx, op, v1 = num_etoi(ctx, a), b);
break;
case NUMBER_FRACTION:
{
nr = number_long(number_fn_nr(b));
dr = number_long(number_fn_dr(b));
switch (op) {
case OP_ADD:
nr = nr + number_long(a) * dr;
num = mk_fraction(ctx, nr, dr);
break;
case OP_SUB:
nr = number_long(a) * dr - nr;
num = mk_fraction(ctx, nr, dr);
break;
case OP_MULTI:
{
nr = number_long(a) * nr;
gcd = num_gcd(number_long(a) * number_long(number_fn_nr(b)), dr);
if (gcd == dr)
num = mk_long(ctx, nr / dr);
else
num = mk_fraction(ctx, nr, dr);
break;
}
case OP_DIV:
{
nr = number_long(a) * dr;
dr = number_long(number_fn_nr(b));
gcd = num_gcd(nr, dr);
if (gcd == nr)
num = mk_long(ctx, nr / dr);
else
num = mk_fraction(ctx, nr, dr);
break;
}}
break;
}
case NUMBER_COMPLEX:
switch (op) {
case OP_ADD:
case OP_SUB:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, a, number_cx_rl(b)), number_cx_im(b));
break;
case OP_MULTI:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, a, number_cx_rl(b)), v2 = _num_calcu(ctx, op, a, number_cx_im(b)));
break;
case OP_DIV:
{
nr1 = _num_calcu(ctx, OP_MULTI, a, number_cx_rl(b));
dr1 = _num_calcu(ctx, OP_ADD, v1 = _num_calcu(ctx, OP_MULTI, number_cx_rl(b), number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, number_cx_im(b), number_cx_im(b)));
rl = _num_calcu(ctx, OP_DIV, nr1, dr1);
nr1 = _num_calcu(ctx, OP_MULTI, v1 = mk_long(ctx, -1), v2 = _num_calcu(ctx, OP_MULTI, a, number_cx_im(b)));
im = _num_calcu(ctx, OP_DIV, nr1, dr1);
num = mk_complex(ctx, rl, im);
break;
}}
break;
}
break;
case NUMBER_DOUBLE:
switch (number_type(b)) {
case NUMBER_LONG:
case NUMBER_FRACTION:
num = _num_calcu(ctx, op, a, v1 = num_etoi(ctx, b));
break;
case NUMBER_DOUBLE:
switch (op) {
case OP_ADD:
num = mk_double(ctx, number_double(a) + number_double(b));
break;
case OP_SUB:
num = mk_double(ctx, number_double(a) - number_double(b));
break;
case OP_MULTI:
num = mk_double(ctx, number_double(a) * number_double(b));
break;
case OP_DIV:
num = mk_double(ctx, number_double(a) / number_double(b));
}
break;
case NUMBER_COMPLEX:
switch (op) {
case OP_ADD:
case OP_SUB:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, a, number_cx_rl(b)), number_cx_im(b));
break;
case OP_MULTI:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, a, number_cx_rl(b)), v2 = _num_calcu(ctx, op, a, number_cx_im(b)));
break;
case OP_DIV:
{
double dr = pow(number_double(number_cx_rl(b)), 2) + pow(number_double(number_cx_im(b)), 2);
num = mk_complex(ctx, v1 = mk_double(ctx, number_double(a) * number_double(number_cx_rl(b)) / dr), v2 = mk_double(ctx, -1 * number_double(a) * number_double(number_cx_im(b)) / dr));
break;
}}
break;
}
break;
case NUMBER_FRACTION:
switch (number_type(b)) {
case NUMBER_LONG:
switch (op) {
case OP_ADD:
case OP_MULTI:
num = _num_calcu(ctx, op, b, a);
break;
case OP_SUB:
nr = number_long(number_fn_nr(a));
dr = number_long(number_fn_dr(a));
nr = nr - number_long(b) * dr;
num = mk_fraction(ctx, nr, dr);
break;
case OP_DIV:
nr = number_long(number_fn_nr(a));
dr = number_long(number_fn_nr(a)) * number_long(b);
gcd = num_gcd(nr, dr);
if (gcd == nr)
num = mk_long(ctx, nr / dr);
else
num = mk_fraction(ctx, nr, dr);
break;
}
break;
case NUMBER_DOUBLE:
num = _num_calcu(ctx, op, v1 = num_etoi(ctx, a), b);
break;
case NUMBER_FRACTION:
{
switch (op) {
case OP_ADD:
nr = number_long(number_fn_nr(a)) * number_long(number_fn_dr(b)) + number_long(number_fn_dr(a)) * number_long(number_fn_nr(b));
dr = number_long(number_fn_dr(a)) * number_long(number_fn_dr(b));
break;
case OP_SUB:
nr = number_long(number_fn_nr(a)) * number_long(number_fn_dr(b)) - number_long(number_fn_dr(a)) * number_long(number_fn_nr(b));
dr = number_long(number_fn_dr(a)) * number_long(number_fn_dr(b));
break;
case OP_MULTI:
nr = number_long(number_fn_nr(a)) * number_long(number_fn_nr(b));
dr = number_long(number_fn_dr(a)) * number_long(number_fn_dr(b));
break;
case OP_DIV:
nr = number_long(number_fn_nr(a)) * number_long(number_fn_dr(b));
dr = number_long(number_fn_dr(a)) * number_long(number_fn_nr(b));
break;
}
gcd = num_gcd(nr, dr);
if (gcd == dr)
num = mk_long(ctx, nr / dr);
else
num = mk_fraction(ctx, nr, dr);
break;
}
case NUMBER_COMPLEX:
switch (op) {
case OP_ADD:
case OP_SUB:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, a, number_cx_rl(b)), number_cx_im(b));
break;
case OP_MULTI:
num = mk_complex(ctx, v1 = _num_calcu(ctx, OP_MULTI, a, number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, a, number_cx_im(b)));
break;
case OP_DIV:
{
nr1 = _num_calcu(ctx, OP_MULTI, a, number_cx_rl(b));
dr1 = _num_calcu(ctx, OP_ADD, v1 = _num_calcu(ctx, OP_MULTI, number_cx_rl(b), number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, number_cx_im(b), number_cx_im(b)));
rl = _num_calcu(ctx, OP_DIV, nr1, dr1);
nr1 = _num_calcu(ctx, OP_MULTI, v1 = mk_long(ctx, -1), v2 = _num_calcu(ctx, OP_MULTI, a, number_cx_im(b)));
im = _num_calcu(ctx, OP_DIV, nr1, dr1);
num = mk_complex(ctx, rl, im);
break;
}}
}
break;
case NUMBER_COMPLEX:
switch (number_type(b)) {
case NUMBER_COMPLEX:
switch (op) {
case OP_ADD:
case OP_SUB:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, number_cx_rl(a), number_cx_rl(b)),
v2 = _num_calcu(ctx, op, number_cx_im(a), number_cx_im(b)));
break;
case OP_MULTI:
rl = _num_calcu(ctx, OP_SUB, v1 = _num_calcu(ctx, OP_MULTI, number_cx_rl(a), number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, number_cx_im(a), number_cx_im(b)));
im = _num_calcu(ctx, OP_ADD, v1 = _num_calcu(ctx, OP_MULTI, number_cx_im(a), number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, number_cx_rl(a), number_cx_im(b)));
num = mk_complex(ctx, rl, im);
break;
case OP_DIV:
{
nr1 = _num_calcu(ctx, OP_ADD, v1 = _num_calcu(ctx, OP_MULTI, number_cx_rl(a), number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, number_cx_im(a), number_cx_im(b)));
dr1 = _num_calcu(ctx, OP_ADD, v1 = _num_calcu(ctx, OP_MULTI, number_cx_rl(b), number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, number_cx_im(b), number_cx_im(b)));
rl = _num_calcu(ctx, OP_DIV, nr1, dr1);
nr1 = _num_calcu(ctx, OP_SUB, v1 = _num_calcu(ctx, OP_MULTI, number_cx_im(a), number_cx_rl(b)), v2 = _num_calcu(ctx, OP_MULTI, number_cx_rl(a), number_cx_im(b)));
im = _num_calcu(ctx, OP_DIV, nr1, dr1);
num = mk_complex(ctx, rl, im);
break;
}}
break;
default:
switch (op) {
case OP_ADD:
case OP_MULTI:
num = _num_calcu(ctx, op, b, a);
break;
case OP_SUB:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, number_cx_rl(a), b), number_cx_im(a));
break;
case OP_DIV:
num = mk_complex(ctx, v1 = _num_calcu(ctx, op, number_cx_rl(a), b), v2 = _num_calcu(ctx, op, number_cx_im(a), b));
break;
}
}
break;
}
gc_release(ctx);
return num;
}
Cell *num_calcu(Cell *ctx, int op, Cell *a, Cell *b) {
gc_var2(c1, c2);
gc_preserve2(ctx, c1, c2);
c1 = a;
c2 = b;
if (number_type(a) == NUMBER_DOUBLE ||
(number_type(a) == NUMBER_COMPLEX &&
(number_type(number_cx_rl(a)) == NUMBER_DOUBLE ||
number_type(number_cx_im(a)) == NUMBER_DOUBLE))) {
if (number_type(b) == NUMBER_LONG || number_type(b) == NUMBER_FRACTION ||
(number_type(b) == NUMBER_COMPLEX && number_type(number_cx_rl(b)) != NUMBER_DOUBLE))
c2 = num_etoi(ctx, b);
} else {
if (number_type(b) == NUMBER_DOUBLE ||
(number_type(b) == NUMBER_COMPLEX &&
(number_type(number_cx_rl(b)) == NUMBER_DOUBLE ||
number_type(number_cx_im(b)) == NUMBER_DOUBLE))) {
c1 = num_etoi(ctx, a);
}
}
c1 = _num_calcu(ctx, op, c1, c2);
gc_release(ctx);
return c1;
}