void
split_number(const struct number *n, BIGNUM *i, BIGNUM *f)
{
u_long rem;
bn_checkp(BN_copy(i, n->number));
if (n->scale == 0 && f != NULL)
bn_check(BN_zero(f));
else if (n->scale < sizeof(factors)/sizeof(factors[0])) {
rem = BN_div_word(i, factors[n->scale]);
if (f != NULL)
bn_check(BN_set_word(f, rem));
} else {
BIGNUM *a, *p;
BN_CTX *ctx;
a = BN_new();
bn_checkp(a);
p = BN_new();
bn_checkp(p);
ctx = BN_CTX_new();
bn_checkp(ctx);
bn_check(BN_set_word(a, 10));
bn_check(BN_set_word(p, n->scale));
bn_check(BN_exp(a, a, p, ctx));
bn_check(BN_div(i, f, n->number, a, ctx));
BN_CTX_free(ctx);
BN_free(a);
BN_free(p);
}
}
static void
bmod(void)
{
struct number *a, *b, *r;
BN_CTX *ctx;
u_int scale;
a = pop_number();
if (a == NULL)
return;
b = pop_number();
if (b == NULL) {
push_number(a);
return;
}
r = new_number();
scale = max(a->scale, b->scale);
r->scale = scale;
if (BN_is_zero(a->number))
warnx("remainder by zero");
else {
normalize(a, scale);
normalize(b, scale);
ctx = BN_CTX_new();
bn_checkp(ctx);
bn_check(BN_mod(r->number, b->number, a->number, ctx));
BN_CTX_free(ctx);
}
push_number(r);
free_number(a);
free_number(b);
}
static void
bsqrt(void)
{
struct number *n;
struct number *r;
BIGNUM *x, *y;
u_int scale, onecount;
BN_CTX *ctx;
onecount = 0;
n = pop_number();
if (n == NULL) {
return;
}
if (BN_is_zero(n->number)) {
r = new_number();
push_number(r);
} else if (BN_is_negative(n->number))
warnx("square root of negative number");
else {
scale = max(bmachine.scale, n->scale);
normalize(n, 2*scale);
x = BN_dup(n->number);
bn_checkp(x);
bn_check(BN_rshift(x, x, BN_num_bits(x)/2));
y = BN_new();
bn_checkp(y);
ctx = BN_CTX_new();
bn_checkp(ctx);
for (;;) {
bn_checkp(BN_copy(y, x));
bn_check(BN_div(x, NULL, n->number, x, ctx));
bn_check(BN_add(x, x, y));
bn_check(BN_rshift1(x, x));
if (bsqrt_stop(x, y, &onecount))
break;
}
r = bmalloc(sizeof(*r));
r->scale = scale;
r->number = y;
BN_free(x);
BN_CTX_free(ctx);
push_number(r);
}
free_number(n);
}
static void
bdivmod(void)
{
struct number *a, *b, *frac, *quotient, *rdiv, *remainder;
BN_CTX *ctx;
u_int scale;
a = pop_number();
if (a == NULL)
return;
b = pop_number();
if (b == NULL) {
push_number(a);
return;
}
rdiv = new_number();
quotient = new_number();
remainder = new_number();
scale = max(a->scale, b->scale);
rdiv->scale = 0;
remainder->scale = scale;
quotient->scale = bmachine.scale;
scale = max(a->scale, b->scale);
if (BN_is_zero(a->number))
warnx("divide by zero");
else {
normalize(a, scale);
normalize(b, scale);
ctx = BN_CTX_new();
bn_checkp(ctx);
/*
* Unlike other languages' divmod operations, dc is specified
* to return the remainder and the full quotient, rather than
* the remainder and the floored quotient. bn(3) has no
* function to calculate both. So we'll use BN_div to get the
* remainder and floored quotient, then calculate the full
* quotient from those.
*
* quotient = rdiv + remainder / divisor
*/
bn_check(BN_div(rdiv->number, remainder->number,
b->number, a->number, ctx));
frac = div_number(remainder, a, bmachine.scale);
normalize(rdiv, bmachine.scale);
normalize(remainder, scale);
bn_check(BN_add(quotient->number, rdiv->number, frac->number));
free_number(frac);
BN_CTX_free(ctx);
}
push_number(quotient);
push_number(remainder);
free_number(rdiv);
free_number(a);
free_number(b);
}
struct number *
dup_number(const struct number *a)
{
struct number *n;
n = bmalloc(sizeof(*n));
n->scale = a->scale;
n->number = BN_dup(a->number);
bn_checkp(n->number);
return n;
}
/* Multiply n by 10^s */
void
scale_number(BIGNUM *n, int s)
{
unsigned int abs_scale;
if (s == 0)
return;
abs_scale = s > 0 ? s : -s;
if (abs_scale < sizeof(factors)/sizeof(factors[0])) {
if (s > 0)
bn_check(BN_mul_word(n, factors[abs_scale]));
else
BN_div_word(n, factors[abs_scale]);
} else {
BIGNUM *a, *p;
BN_CTX *ctx;
a = BN_new();
bn_checkp(a);
p = BN_new();
bn_checkp(p);
ctx = BN_CTX_new();
bn_checkp(ctx);
bn_check(BN_set_word(a, 10));
bn_check(BN_set_word(p, abs_scale));
bn_check(BN_exp(a, a, p, ctx));
if (s > 0)
bn_check(BN_mul(n, n, a, ctx));
else
bn_check(BN_div(n, NULL, n, a, ctx));
BN_CTX_free(ctx);
BN_free(a);
BN_free(p);
}
}
static bool
bsqrt_stop(const BIGNUM *x, const BIGNUM *y, u_int *onecount)
{
BIGNUM *r;
bool ret;
r = BN_new();
bn_checkp(r);
bn_check(BN_sub(r, x, y));
if (BN_is_one(r))
(*onecount)++;
ret = BN_is_zero(r);
BN_free(r);
return (ret || *onecount > 1);
}
void
bmul_number(struct number *r, struct number *a, struct number *b, u_int scale)
{
BN_CTX *ctx;
/* Create copies of the scales, since r might be equal to a or b */
u_int ascale = a->scale;
u_int bscale = b->scale;
u_int rscale = ascale + bscale;
ctx = BN_CTX_new();
bn_checkp(ctx);
bn_check(BN_mul(r->number, a->number, b->number, ctx));
BN_CTX_free(ctx);
r->scale = rscale;
if (rscale > bmachine.scale && rscale > ascale && rscale > bscale)
normalize(r, max(scale, max(ascale, bscale)));
}
static void
bdivmod(void)
{
struct number *a, *b;
struct number *rdiv, *rmod;
u_int scale;
BN_CTX *ctx;
a = pop_number();
if (a == NULL) {
return;
}
b = pop_number();
if (b == NULL) {
push_number(a);
return;
}
rdiv = new_number();
rmod = new_number();
rdiv->scale = bmachine.scale;
rmod->scale = max(b->scale, a->scale + bmachine.scale);
scale = max(a->scale, b->scale);
if (BN_is_zero(a->number))
warnx("divide by zero");
else {
normalize(a, scale);
normalize(b, scale + bmachine.scale);
ctx = BN_CTX_new();
bn_checkp(ctx);
bn_check(BN_div(rdiv->number, rmod->number,
b->number, a->number, ctx));
BN_CTX_free(ctx);
}
push_number(rdiv);
push_number(rmod);
free_number(a);
free_number(b);
}
void
print_ascii(FILE *f, const struct number *n)
{
BIGNUM *v;
int numbits, i, ch;
v = BN_dup(n->number);
bn_checkp(v);
if (BN_cmp(v, &zero) < 0)
bn_check(BN_sub(v, &zero, v));
numbits = BN_num_bytes(v) * 8;
while (numbits > 0) {
ch = 0;
for (i = 0; i < 8; i++)
ch |= BN_is_bit_set(v, numbits-i-1) << (7 - i);
putc(ch, f);
numbits -= 8;
}
BN_free(v);
}
static void
bdiv(void)
{
struct number *a, *b, *r;
BN_CTX *ctx;
u_int scale;
a = pop_number();
if (a == NULL) {
return;
}
b = pop_number();
if (b == NULL) {
push_number(a);
return;
}
r = new_number();
r->scale = bmachine.scale;
scale = max(a->scale, b->scale);
if (BN_is_zero(a->number))
warnx("divide by zero");
else {
normalize(a, scale);
normalize(b, scale + r->scale);
ctx = BN_CTX_new();
bn_checkp(ctx);
bn_check(BN_div(r->number, NULL, b->number, a->number, ctx));
BN_CTX_free(ctx);
}
push_number(r);
free_number(a);
free_number(b);
}
static void
bexp(void)
{
struct number *a, *p;
struct number *r;
bool neg;
u_int rscale;
p = pop_number();
if (p == NULL)
return;
a = pop_number();
if (a == NULL) {
push_number(p);
return;
}
if (p->scale != 0) {
BIGNUM *i, *f;
i = BN_new();
bn_checkp(i);
f = BN_new();
bn_checkp(f);
split_number(p, i, f);
if (!BN_is_zero(f))
warnx("Runtime warning: non-zero fractional part in exponent");
BN_free(i);
BN_free(f);
}
normalize(p, 0);
neg = false;
if (BN_is_negative(p->number)) {
neg = true;
negate(p);
rscale = bmachine.scale;
} else {
/* Posix bc says min(a.scale * b, max(a.scale, scale) */
u_long b;
u_int m;
b = BN_get_word(p->number);
m = max(a->scale, bmachine.scale);
rscale = a->scale * (u_int)b;
if (rscale > m || (a->scale > 0 && (b == ULONG_MAX ||
b > UINT_MAX)))
rscale = m;
}
if (BN_is_zero(p->number)) {
r = new_number();
bn_check(BN_one(r->number));
normalize(r, rscale);
} else {
u_int ascale, mscale;
ascale = a->scale;
while (!BN_is_bit_set(p->number, 0)) {
ascale *= 2;
bmul_number(a, a, a, ascale);
bn_check(BN_rshift1(p->number, p->number));
}
r = dup_number(a);
bn_check(BN_rshift1(p->number, p->number));
mscale = ascale;
while (!BN_is_zero(p->number)) {
ascale *= 2;
bmul_number(a, a, a, ascale);
if (BN_is_bit_set(p->number, 0)) {
mscale += ascale;
bmul_number(r, r, a, mscale);
}
bn_check(BN_rshift1(p->number, p->number));
}
if (neg) {
BN_CTX *ctx;
BIGNUM *one;
one = BN_new();
bn_checkp(one);
bn_check(BN_one(one));
ctx = BN_CTX_new();
bn_checkp(ctx);
scale_number(one, r->scale + rscale);
if (BN_is_zero(r->number))
warnx("divide by zero");
else
bn_check(BN_div(r->number, NULL, one,
r->number, ctx));
BN_free(one);
BN_CTX_free(ctx);
r->scale = rscale;
} else
normalize(r, rscale);
}
push_number(r);
free_number(a);
free_number(p);
}
static void
bexp(void)
{
struct number *a, *p;
struct number *r;
bool neg;
u_int scale;
p = pop_number();
if (p == NULL) {
return;
}
a = pop_number();
if (a == NULL) {
push_number(p);
return;
}
if (p->scale != 0)
warnx("Runtime warning: non-zero scale in exponent");
normalize(p, 0);
neg = false;
if (BN_cmp(p->number, &zero) < 0) {
neg = true;
negate(p);
scale = bmachine.scale;
} else {
/* Posix bc says min(a.scale * b, max(a.scale, scale) */
u_long b;
u_int m;
b = BN_get_word(p->number);
m = max(a->scale, bmachine.scale);
scale = a->scale * (u_int)b;
if (scale > m || (a->scale > 0 && (b == BN_MASK2 ||
b > UINT_MAX)))
scale = m;
}
if (BN_is_zero(p->number)) {
r = new_number();
bn_check(BN_one(r->number));
normalize(r, scale);
} else {
while (!BN_is_bit_set(p->number, 0)) {
bmul_number(a, a, a);
bn_check(BN_rshift1(p->number, p->number));
}
r = dup_number(a);
normalize(r, scale);
bn_check(BN_rshift1(p->number, p->number));
while (!BN_is_zero(p->number)) {
bmul_number(a, a, a);
if (BN_is_bit_set(p->number, 0))
bmul_number(r, r, a);
bn_check(BN_rshift1(p->number, p->number));
}
if (neg) {
BN_CTX *ctx;
BIGNUM *one;
one = BN_new();
bn_checkp(one);
bn_check(BN_one(one));
ctx = BN_CTX_new();
bn_checkp(ctx);
scale_number(one, r->scale + scale);
normalize(r, scale);
bn_check(BN_div(r->number, NULL, one, r->number, ctx));
BN_free(one);
BN_CTX_free(ctx);
} else
normalize(r, scale);
}
push_number(r);
free_number(a);
free_number(p);
}
