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/* Common routines for _dtoa and strtod */
#include "fconv.h"
#ifdef DEBUG
#include <stdio.h>
#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}
#endif
double
_tens[] = {
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1e20, 1e21, 1e22
#ifdef VAX
, 1e23, 1e24
#endif
};
#ifdef IEEE_Arith
double _bigtens[] = { 1e16, 1e32, 1e64, 1e128, 1e256 };
double _tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, 1e-256 };
#else
#ifdef IBM
double _bigtens[] = { 1e16, 1e32, 1e64 };
double _tinytens[] = { 1e-16, 1e-32, 1e-64 };
#else
double _bigtens[] = { 1e16, 1e32 };
double _tinytens[] = { 1e-16, 1e-32 };
#endif
#endif
static Bigint *freelist[Kmax+1];
Bigint *
_Balloc(int k)
{
int x;
Bigint *rv;
if (rv = freelist[k]) {
freelist[k] = rv->next;
}
else {
x = 1 << k;
rv = (Bigint *)malloc(sizeof(Bigint) + (x-1)*sizeof(long));
rv->k = k;
rv->maxwds = x;
}
rv->sign = rv->wds = 0;
return rv;
}
void
_Bfree(Bigint *v)
{
if (v) {
v->next = freelist[v->k];
freelist[v->k] = v;
}
}
Bigint *
_multadd(Bigint *b, int m, int a) /* multiply by m and add a */
{
int i, wds;
unsigned long *x, y;
#ifdef Pack_32
unsigned long xi, z;
#endif
Bigint *b1;
wds = b->wds;
x = b->x;
i = 0;
do {
#ifdef Pack_32
xi = *x;
y = (xi & 0xffff) * m + a;
z = (xi >> 16) * m + (y >> 16);
a = (int)(z >> 16);
*x++ = (z << 16) + (y & 0xffff);
#else
y = *x * m + a;
a = (int)(y >> 16);
*x++ = y & 0xffff;
#endif
}
while(++i < wds);
if (a) {
if (wds >= b->maxwds) {
b1 = Balloc(b->k+1);
Bcopy(b1, b);
Bfree(b);
b = b1;
}
b->x[wds++] = a;
b->wds = wds;
}
return b;
}
int
_hi0bits(register unsigned long x)
{
register int k = 0;
if (!(x & 0xffff0000)) {
k = 16;
x <<= 16;
}
if (!(x & 0xff000000)) {
k += 8;
x <<= 8;
}
if (!(x & 0xf0000000)) {
k += 4;
x <<= 4;
}
if (!(x & 0xc0000000)) {
k += 2;
x <<= 2;
}
if (!(x & 0x80000000)) {
k++;
if (!(x & 0x40000000))
return 32;
}
return k;
}
static int
lo0bits(unsigned long *y)
{
register int k;
register unsigned long x = *y;
if (x & 7) {
if (x & 1)
return 0;
if (x & 2) {
*y = x >> 1;
return 1;
}
*y = x >> 2;
return 2;
}
k = 0;
if (!(x & 0xffff)) {
k = 16;
x >>= 16;
}
if (!(x & 0xff)) {
k += 8;
x >>= 8;
}
if (!(x & 0xf)) {
k += 4;
x >>= 4;
}
if (!(x & 0x3)) {
k += 2;
x >>= 2;
}
if (!(x & 1)) {
k++;
x >>= 1;
if (!x & 1)
return 32;
}
*y = x;
return k;
}
Bigint *
_i2b(int i)
{
Bigint *b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
Bigint *
_mult(Bigint *a, Bigint *b)
{
Bigint *c;
int k, wa, wb, wc;
unsigned long carry, y, z;
unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
#ifdef Pack_32
unsigned long z2;
#endif
if (a->wds < b->wds) {
c = a;
a = b;
b = c;
}
k = a->k;
wa = a->wds;
wb = b->wds;
wc = wa + wb;
if (wc > a->maxwds)
k++;
c = Balloc(k);
for(x = c->x, xa = x + wc; x < xa; x++)
*x = 0;
xa = a->x;
xae = xa + wa;
xb = b->x;
xbe = xb + wb;
xc0 = c->x;
#ifdef Pack_32
for(; xb < xbe; xb++, xc0++) {
if (y = *xb & 0xffff) {
x = xa;
xc = xc0;
carry = 0;
do {
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
Storeinc(xc, z2, z);
}
while(x < xae);
*xc = carry;
}
if (y = *xb >> 16) {
x = xa;
xc = xc0;
carry = 0;
z2 = *xc;
do {
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
Storeinc(xc, z, z2);
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
carry = z2 >> 16;
}
while(x < xae);
*xc = z2;
}
}
#else
for(; xb < xbe; xc0++) {
if (y = *xb++) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * y + *xc + carry;
carry = z >> 16;
*xc++ = z & 0xffff;
}
while(x < xae);
*xc = carry;
}
}
#endif
for(xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds = wc;
return c;
}
static Bigint *p5s;
Bigint *
_pow5mult(Bigint *b, int k)
{
Bigint *b1, *p5, *p51;
int i;
static int p05[3] = { 5, 25, 125 };
if (i = k & 3)
b = multadd(b, p05[i-1], 0);
if (!(k >>= 2))
return b;
if (!(p5 = p5s)) {
/* first time */
p5 = p5s = i2b(625);
p5->next = 0;
}
for(;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1))
break;
if (!(p51 = p5->next)) {
p51 = p5->next = mult(p5,p5);
p51->next = 0;
}
p5 = p51;
}
return b;
}
Bigint *
_lshift(Bigint *b, int k)
{
int i, k1, n, n1;
Bigint *b1;
unsigned long *x, *x1, *xe, z;
#ifdef Pack_32
n = k >> 5;
#else
n = k >> 4;
#endif
k1 = b->k;
n1 = n + b->wds + 1;
for(i = b->maxwds; n1 > i; i <<= 1)
k1++;
b1 = Balloc(k1);
x1 = b1->x;
for(i = 0; i < n; i++)
*x1++ = 0;
x = b->x;
xe = x + b->wds;
#ifdef Pack_32
if (k &= 0x1f) {
k1 = 32 - k;
z = 0;
do {
*x1++ = *x << k | z;
z = *x++ >> k1;
}
while(x < xe);
if (*x1 = z)
++n1;
}
#else
if (k &= 0xf) {
k1 = 16 - k;
z = 0;
do {
*x1++ = *x << k & 0xffff | z;
z = *x++ >> k1;
}
while(x < xe);
if (*x1 = z)
++n1;
}
#endif
else do
*x1++ = *x++;
while(x < xe);
b1->wds = n1 - 1;
Bfree(b);
return b1;
}
int
_cmp(Bigint *a, Bigint *b)
{
unsigned long *xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
#ifdef DEBUG
if (i > 1 && !a->x[i-1])
Bug("cmp called with a->x[a->wds-1] == 0");
if (j > 1 && !b->x[j-1])
Bug("cmp called with b->x[b->wds-1] == 0");
#endif
if (i -= j)
return i;
xa0 = a->x;
xa = xa0 + j;
xb0 = b->x;
xb = xb0 + j;
for(;;) {
if (*--xa != *--xb)
return *xa < *xb ? -1 : 1;
if (xa <= xa0)
break;
}
return 0;
}
Bigint *
_diff(Bigint *a, Bigint *b)
{
Bigint *c;
int i, wa, wb;
long borrow, y; /* We need signed shifts here. */
unsigned long *xa, *xae, *xb, *xbe, *xc;
#ifdef Pack_32
long z;
#endif
i = cmp(a,b);
if (!i) {
c = Balloc(0);
c->wds = 1;
c->x[0] = 0;
return c;
}
if (i < 0) {
c = a;
a = b;
b = c;
i = 1;
}
else
i = 0;
c = Balloc(a->k);
c->sign = i;
wa = a->wds;
xa = a->x;
xae = xa + wa;
wb = b->wds;
xb = b->x;
xbe = xb + wb;
xc = c->x;
borrow = 0;
#ifdef Pack_32
do {
y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
borrow = z >> 16;
Sign_Extend(borrow, z);
Storeinc(xc, z, y);
}
while(xb < xbe);
while(xa < xae) {
y = (*xa & 0xffff) + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
z = (*xa++ >> 16) + borrow;
borrow = z >> 16;
Sign_Extend(borrow, z);
Storeinc(xc, z, y);
}
#else
do {
y = *xa++ - *xb++ + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
*xc++ = y & 0xffff;
}
while(xb < xbe);
while(xa < xae) {
y = *xa++ + borrow;
borrow = y >> 16;
Sign_Extend(borrow, y);
*xc++ = y & 0xffff;
}
#endif
while(!*--xc)
wa--;
c->wds = wa;
return c;
}
Bigint *
_d2b(double darg, int *e, int *bits)
{
Bigint *b;
int de, i, k;
unsigned long *x, y, z;
Dul d;
#ifdef VAX
unsigned long d0, d1;
d.d = darg;
d0 = word0(d) >> 16 | word0(d) << 16;
d1 = word1(d) >> 16 | word1(d) << 16;
#else
d.d = darg;
#define d0 word0(d)
#define d1 word1(d)
#endif
#ifdef Pack_32
b = Balloc(1);
#else
b = Balloc(2);
#endif
x = b->x;
z = d0 & Frac_mask;
d0 &= 0x7fffffff; /* clear sign bit, which we ignore */
#ifdef Sudden_Underflow
de = (int)(d0 >> Exp_shift);
#ifndef IBM
z |= Exp_msk11;
#endif
#else
if (de = (int)(d0 >> Exp_shift))
z |= Exp_msk1;
#endif
#ifdef Pack_32
if (y = d1) {
if (k = lo0bits(&y)) {
x[0] = y | z << 32 - k;
z >>= k;
}
else
x[0] = y;
i = b->wds = (x[1] = z) ? 2 : 1;
}
else {
#ifdef DEBUG
if (!z)
Bug("Zero passed to d2b");
#endif
k = lo0bits(&z);
x[0] = z;
i = b->wds = 1;
k += 32;
}
#else
if (y = d1) {
if (k = lo0bits(&y))
if (k >= 16) {
x[0] = y | z << 32 - k & 0xffff;
x[1] = z >> k - 16 & 0xffff;
x[2] = z >> k;
i = 2;
}
else {
x[0] = y & 0xffff;
x[1] = y >> 16 | z << 16 - k & 0xffff;
x[2] = z >> k & 0xffff;
x[3] = z >> k+16;
i = 3;
}
else {
x[0] = y & 0xffff;
x[1] = y >> 16;
x[2] = z & 0xffff;
x[3] = z >> 16;
i = 3;
}
}
else {
#ifdef DEBUG
if (!z)
Bug("Zero passed to d2b");
#endif
k = lo0bits(&z);
if (k >= 16) {
x[0] = z;
i = 0;
}
else {
x[0] = z & 0xffff;
x[1] = z >> 16;
i = 1;
}
k += 32;
}
while(!x[i])
--i;
b->wds = i + 1;
#endif
#ifndef Sudden_Underflow
if (de) {
#endif
#ifdef IBM
*e = (de - Bias - (P-1) << 2) + k;
*bits = 4*P + 8 - k - hi0bits(word0(d) & Frac_mask);
#else
*e = de - Bias - (P-1) + k;
*bits = P - k;
#endif
#ifndef Sudden_Underflow
}
else {
*e = de - Bias - (P-1) + 1 + k;
#ifdef Pack_32
*bits = 32*i - hi0bits(x[i-1]);
#else
*bits = (i+2)*16 - hi0bits(x[i]);
#endif
}
#endif
return b;
}
#undef d0
#undef d1