eigenmath/bignum.cpp

937 lines
11 KiB
C++

#include "stdafx.h"
#include "defs.h"
#define MP_MIN_SIZE 2
#define MP_MAX_FREE 1000
double convert_rational_to_double(U *);
double convert_bignum_to_double(unsigned int *);
int ge(unsigned int *, unsigned int *, int);
int mtotal, mfreecount;
static unsigned int *free_stack[MP_MAX_FREE];
unsigned int *
mnew(int n)
{
unsigned int *p;
if (n < MP_MIN_SIZE)
n = MP_MIN_SIZE;
if (n == MP_MIN_SIZE && mfreecount)
p = free_stack[--mfreecount];
else {
p = (unsigned int *) malloc((n + 3) * sizeof (int));
if (p == 0)
stop("malloc failure");
}
p[0] = n;
mtotal += n;
return p + 3;
}
void
mfree(unsigned int *p)
{
p -= 3;
mtotal -= p[0];
if (p[0] == MP_MIN_SIZE && mfreecount < MP_MAX_FREE)
free_stack[mfreecount++] = p;
else
free(p);
}
// convert int to bignum
unsigned int *
mint(int n)
{
unsigned int *p = mnew(1);
if (n < 0)
MSIGN(p) = -1;
else
MSIGN(p) = 1;
MLENGTH(p) = 1;
p[0] = abs(n);
return p;
}
// copy bignum
unsigned int *
mcopy(unsigned int *a)
{
int i;
unsigned int *b;
b = mnew(MLENGTH(a));
MSIGN(b) = MSIGN(a);
MLENGTH(b) = MLENGTH(a);
for (i = 0; i < MLENGTH(a); i++)
b[i] = a[i];
return b;
}
// a >= b ?
int
ge(unsigned int *a, unsigned int *b, int len)
{
int i;
for (i = len - 1; i > 0; i--)
if (a[i] == b[i])
continue;
else
break;
if (a[i] >= b[i])
return 1;
else
return 0;
}
void
add_numbers(void)
{
double a, b;
if (stack[tos - 1]->k == NUM && stack[tos - 2]->k == NUM) {
qadd();
return;
}
save();
p2 = pop();
p1 = pop();
if (p1->k == DOUBLE)
a = p1->u.d;
else
a = convert_rational_to_double(p1);
if (p2->k == DOUBLE)
b = p2->u.d;
else
b = convert_rational_to_double(p2);
push_double(a + b);
restore();
}
void
subtract_numbers(void)
{
double a, b;
if (stack[tos - 1]->k == NUM && stack[tos - 2]->k == NUM) {
qsub();
return;
}
save();
p2 = pop();
p1 = pop();
if (p1->k == DOUBLE)
a = p1->u.d;
else
a = convert_rational_to_double(p1);
if (p2->k == DOUBLE)
b = p2->u.d;
else
b = convert_rational_to_double(p2);
push_double(a - b);
restore();
}
void
multiply_numbers(void)
{
double a, b;
if (stack[tos - 1]->k == NUM && stack[tos - 2]->k == NUM) {
qmul();
return;
}
save();
p2 = pop();
p1 = pop();
if (p1->k == DOUBLE)
a = p1->u.d;
else
a = convert_rational_to_double(p1);
if (p2->k == DOUBLE)
b = p2->u.d;
else
b = convert_rational_to_double(p2);
push_double(a * b);
restore();
}
void
divide_numbers(void)
{
double a, b;
if (stack[tos - 1]->k == NUM && stack[tos - 2]->k == NUM) {
qdiv();
return;
}
save();
p2 = pop();
p1 = pop();
if (iszero(p2))
stop("divide by zero");
if (p1->k == DOUBLE)
a = p1->u.d;
else
a = convert_rational_to_double(p1);
if (p2->k == DOUBLE)
b = p2->u.d;
else
b = convert_rational_to_double(p2);
push_double(a / b);
restore();
}
void
invert_number(void)
{
unsigned int *a, *b;
save();
p1 = pop();
if (iszero(p1))
stop("divide by zero");
if (p1->k == DOUBLE) {
push_double(1 / p1->u.d);
restore();
return;
}
a = mcopy(p1->u.q.a);
b = mcopy(p1->u.q.b);
MSIGN(b) = MSIGN(a);
MSIGN(a) = 1;
p1 = alloc();
p1->k = NUM;
p1->u.q.a = b;
p1->u.q.b = a;
push(p1);
restore();
}
int
compare_rationals(U *a, U *b)
{
int t;
unsigned int *ab, *ba;
ab = mmul(a->u.q.a, b->u.q.b);
ba = mmul(a->u.q.b, b->u.q.a);
t = mcmp(ab, ba);
mfree(ab);
mfree(ba);
return t;
}
int
compare_numbers(U *a, U *b)
{
double x, y;
if (a->k == NUM && b->k == NUM)
return compare_rationals(a, b);
if (a->k == DOUBLE)
x = a->u.d;
else
x = convert_rational_to_double(a);
if (b->k == DOUBLE)
y = b->u.d;
else
y = convert_rational_to_double(b);
if (x < y)
return -1;
if (x > y)
return 1;
return 0;
}
void
negate_number(void)
{
save();
p1 = pop();
if (iszero(p1)) {
push(p1);
restore();
return;
}
switch (p1->k) {
case NUM:
p2 = alloc();
p2->k = NUM;
p2->u.q.a = mcopy(p1->u.q.a);
p2->u.q.b = mcopy(p1->u.q.b);
MSIGN(p2->u.q.a) *= -1;
push(p2);
break;
case DOUBLE:
push_double(-p1->u.d);
break;
default:
stop("bug caught in mp_negate_number");
break;
}
restore();
}
void
bignum_truncate(void)
{
unsigned int *a;
save();
p1 = pop();
a = mdiv(p1->u.q.a, p1->u.q.b);
p1 = alloc();
p1->k = NUM;
p1->u.q.a = a;
p1->u.q.b = mint(1);
push(p1);
restore();
}
void
mp_numerator(void)
{
save();
p1 = pop();
if (p1->k != NUM) {
push(_one);
restore();
return;
}
p2 = alloc();
p2->k = NUM;
p2->u.q.a = mcopy(p1->u.q.a);
p2->u.q.b = mint(1);
push(p2);
restore();
}
void
mp_denominator(void)
{
save();
p1 = pop();
if (p1->k != NUM) {
push(_one);
restore();
return;
}
p2 = alloc();
p2->k = NUM;
p2->u.q.a = mcopy(p1->u.q.b);
p2->u.q.b = mint(1);
push(p2);
restore();
}
void
bignum_power_number(int expo)
{
unsigned int *a, *b, *t;
save();
p1 = pop();
a = mpow(p1->u.q.a, abs(expo));
b = mpow(p1->u.q.b, abs(expo));
if (expo < 0) {
t = a;
a = b;
b = t;
MSIGN(a) = MSIGN(b);
MSIGN(b) = 1;
}
p1 = alloc();
p1->k = NUM;
p1->u.q.a = a;
p1->u.q.b = b;
push(p1);
restore();
}
double
convert_bignum_to_double(unsigned int *p)
{
int i;
double d = 0.0;
for (i = MLENGTH(p) - 1; i >= 0; i--)
d = 4294967296.0 * d + p[i];
if (MSIGN(p) == -1)
d = -d;
return d;
}
double
convert_rational_to_double(U *p)
{
int i, n, na, nb;
double a = 0.0, b = 0.0;
na = MLENGTH(p->u.q.a);
nb = MLENGTH(p->u.q.b);
if (na < nb)
n = na;
else
n = nb;
for (i = 0; i < n; i++) {
a = a / 4294967296.0 + p->u.q.a[i];
b = b / 4294967296.0 + p->u.q.b[i];
}
if (na > nb)
for (i = nb; i < na; i++) {
a = a / 4294967296.0 + p->u.q.a[i];
b = b / 4294967296.0;
}
if (na < nb)
for (i = na; i < nb; i++) {
a = a / 4294967296.0;
b = b / 4294967296.0 + p->u.q.b[i];
}
if (MSIGN(p->u.q.a) == -1)
a = -a;
return a / b;
}
void
push_integer(int n)
{
save();
p1 = alloc();
p1->k = NUM;
p1->u.q.a = mint(n);
p1->u.q.b = mint(1);
push(p1);
restore();
}
void
push_double(double d)
{
save();
p1 = alloc();
p1->k = DOUBLE;
p1->u.d = d;
push(p1);
restore();
}
void
push_rational(int a, int b)
{
save();
p1 = alloc();
p1->k = NUM;
p1->u.q.a = mint(a);
p1->u.q.b = mint(b);
/* FIXME -- normalize */
push(p1);
restore();
}
int
pop_integer(void)
{
int n;
save();
p1 = pop();
switch (p1->k) {
case NUM:
if (isinteger(p1) && MLENGTH(p1->u.q.a) == 1) {
n = p1->u.q.a[0];
if (n & 0x80000000)
n = 0x80000000;
else
n *= MSIGN(p1->u.q.a);
} else
n = 0x80000000;
break;
case DOUBLE:
n = (int) p1->u.d;
if ((double) n != p1->u.d)
n = 0x80000000;
break;
default:
n = 0x80000000;
break;
}
restore();
return n;
}
int
mp_isfraction(U *p)
{
if (p->k == NUM && !MEQUAL(p->u.q.b, 1))
return 1;
else
return 0;
}
void
print_double(U *p, int flag)
{
static char buf[80];
sprintf(buf, "%g", p->u.d);
if (flag == 1 && *buf == '-')
print_str(buf + 1);
else
print_str(buf);
}
void
bignum_scan_integer(char *s)
{
unsigned int *a;
char sign;
save();
sign = *s;
if (sign == '+' || sign == '-')
s++;
a = mscan(s);
p1 = alloc();
p1->k = NUM;
p1->u.q.a = a;
p1->u.q.b = mint(1);
push(p1);
if (sign == '-')
negate();
restore();
}
void
bignum_scan_float(char *s)
{
push_double(atof(s));
}
// print as unsigned
void
print_number(U *p)
{
char *s;
static char buf[100];
switch (p->k) {
case NUM:
s = mstr(p->u.q.a);
if (*s == '+' || *s == '-')
s++;
print_str(s);
if (mp_isfraction(p)) {
print_str("/");
s = mstr(p->u.q.b);
print_str(s);
}
break;
case DOUBLE:
sprintf(buf, "%g", p->u.d);
if (*buf == '+' || *buf == '-')
print_str(buf + 1);
else
print_str(buf);
break;
default:
break;
}
}
int
iszero(U *p)
{
switch (p->k) {
case NUM:
if (MZERO(p->u.q.a))
return 1;
break;
case DOUBLE:
if (p->u.d == 0.0)
return 1;
break;
default:
break;
}
return 0;
}
int
isnegativenumber(U *p)
{
switch (p->k) {
case NUM:
if (MSIGN(p->u.q.a) == -1)
return 1;
break;
case DOUBLE:
if (p->u.d < 0.0)
return 1;
break;
default:
break;
}
return 0;
}
int
isplusone(U *p)
{
switch (p->k) {
case NUM:
if (MEQUAL(p->u.q.a, 1) && MEQUAL(p->u.q.b, 1))
return 1;
break;
case DOUBLE:
if (p->u.d == 1.0)
return 1;
break;
default:
break;
}
return 0;
}
int
isminusone(U *p)
{
switch (p->k) {
case NUM:
if (MEQUAL(p->u.q.a, -1) && MEQUAL(p->u.q.b, 1))
return 1;
break;
case DOUBLE:
if (p->u.d == -1.0)
return 1;
break;
default:
break;
}
return 0;
}
int
isinteger(U *p)
{
if (p->k == NUM && MEQUAL(p->u.q.b, 1))
return 1;
else
return 0;
}
int
isnonnegativeinteger(U *p)
{
if (p->k == NUM && MEQUAL(p->u.q.b, 1) && MSIGN(p->u.q.a) == 1)
return 1;
else
return 0;
}
void
gcd_numbers(void)
{
save();
p2 = pop();
p1 = pop();
// if (!isinteger(p1) || !isinteger(p2))
// stop("integer args expected for gcd");
p3 = alloc();
p3->k = NUM;
p3->u.q.a = mgcd(p1->u.q.a, p2->u.q.a);
p3->u.q.b = mgcd(p1->u.q.b, p2->u.q.b);
MSIGN(p3->u.q.a) = 1;
push(p3);
restore();
}
void
power_numbers(void)
{
double a, b, base, expo, result, theta;
if (stack[tos - 1]->k == NUM && stack[tos - 2]->k == NUM) {
qpow();
return;
}
expo = pop_double();
base = pop_double();
if (base == 0.0 && expo < 0.0) {
stop("divide by zero");
//divide_by_zero_count++;
push(nil);
return;
}
errno = 0;
result = pow(base, expo);
#ifdef MAC
if (errno || isnan(result)) {
#else
if (errno) {
#endif
errno = 0;
result = pow(fabs(base), expo);
theta = M_PI * expo;
a = cos(theta);
b = sin(theta);
if (fabs(a) < 1e-10)
a = 0.0;
if (fabs(b) < 1e-10)
b = 0.0;
push_double(result * a);
push_double(result * b);
push(unit_imaginary);
multiply();
add();
return;
}
push_double(result);
}
double
pop_double(void)
{
double d;
save();
p1 = pop();
switch (p1->k) {
case NUM:
d = convert_rational_to_double(p1);
break;
case DOUBLE:
d = p1->u.d;
break;
default:
d = 0.0;
break;
}
restore();
return d;
}
void
bignum_float(void)
{
double d;
d = convert_rational_to_double(pop());
push_double(d);
}
static unsigned int *__factorial(int);
void
bignum_factorial(int n)
{
save();
p1 = alloc();
p1->k = NUM;
p1->u.q.a = __factorial(n);
p1->u.q.b = mint(1);
push(p1);
restore();
}
static unsigned int *
__factorial(int n)
{
int i;
unsigned int *a, *b, *t;
if (n == 0 || n == 1) {
a = mint(1);
return a;
}
a = mint(2);
b = mint(0);
for (i = 3; i <= n; i++) {
b[0] = (unsigned int) i;
t = mmul(a, b);
mfree(a);
a = t;
}
mfree(b);
return a;
}
static unsigned int mask[32] = {
0x00000001,
0x00000002,
0x00000004,
0x00000008,
0x00000010,
0x00000020,
0x00000040,
0x00000080,
0x00000100,
0x00000200,
0x00000400,
0x00000800,
0x00001000,
0x00002000,
0x00004000,
0x00008000,
0x00010000,
0x00020000,
0x00040000,
0x00080000,
0x00100000,
0x00200000,
0x00400000,
0x00800000,
0x01000000,
0x02000000,
0x04000000,
0x08000000,
0x10000000,
0x20000000,
0x40000000,
0x80000000,
};
void
mp_set_bit(unsigned int *x, unsigned int k)
{
x[k / 32] |= mask[k % 32];
}
void
mp_clr_bit(unsigned int *x, unsigned int k)
{
x[k / 32] &= ~mask[k % 32];
}
int
iseveninteger(U *p)
{
if (isinteger(p) && (p->u.q.a[0] & 1) == 0)
return 1;
else
return 0;
}
void
mshiftright(unsigned int *a)
{
int c, i, n;
n = MLENGTH(a);
c = 0;
for (i = n - 1; i >= 0; i--)
if (a[i] & 1) {
a[i] = (a[i] >> 1) | c;
c = 0x80000000;
} else {
a[i] = (a[i] >> 1) | c;
c = 0;
}
if (n > 1 && a[n - 1] == 0)
MLENGTH(a) = n - 1;
}