# bignum.c   [plain text]

```/**********************************************************************

bignum.c -

\$Author: shyouhei \$
\$Date: 2008-08-04 14:05:38 +0900 (Mon, 04 Aug 2008) \$
created at: Fri Jun 10 00:48:55 JST 1994

Copyright (C) 1993-2003 Yukihiro Matsumoto

**********************************************************************/

#include "ruby.h"
#include "rubysig.h"

#include <math.h>
#include <float.h>
#include <ctype.h>
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif

VALUE rb_cBignum;

#if defined __MINGW32__
#define USHORT _USHORT
#endif

#define BDIGITS(x) ((BDIGIT*)RBIGNUM(x)->digits)
#define BITSPERDIG (SIZEOF_BDIGITS*CHAR_BIT)
#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
#define DIGSPERLONG ((unsigned int)(SIZEOF_LONG/SIZEOF_BDIGITS))
#if HAVE_LONG_LONG
# define DIGSPERLL ((unsigned int)(SIZEOF_LONG_LONG/SIZEOF_BDIGITS))
#endif
#define BIGUP(x) ((BDIGIT_DBL)(x) << BITSPERDIG)
#define BIGDN(x) RSHIFT(x,BITSPERDIG)
#define BIGLO(x) ((BDIGIT)((x) & (BIGRAD-1)))
#define BDIGMAX ((BDIGIT)-1)

#define BIGZEROP(x) (RBIGNUM(x)->len == 0 || \
(BDIGITS(x)[0] == 0 && \
(RBIGNUM(x)->len == 1 || bigzero_p(x))))

static int bigzero_p(VALUE);
static int
bigzero_p(x)
VALUE x;
{
long i;
for (i = 0; i < RBIGNUM(x)->len; ++i) {
if (BDIGITS(x)[i]) return 0;
}
return 1;
}

static VALUE
bignew_1(klass, len, sign)
VALUE klass;
long len;
int sign;
{
NEWOBJ(big, struct RBignum);
OBJSETUP(big, klass, T_BIGNUM);
big->sign = sign?1:0;
big->len = len;
big->digits = ALLOC_N(BDIGIT, len);

return (VALUE)big;
}

#define bignew(len,sign) bignew_1(rb_cBignum,len,sign)

VALUE
rb_big_clone(x)
VALUE x;
{
VALUE z = bignew_1(CLASS_OF(x), RBIGNUM(x)->len, RBIGNUM(x)->sign);

MEMCPY(BDIGITS(z), BDIGITS(x), BDIGIT, RBIGNUM(x)->len);
return z;
}

/* modify a bignum by 2's complement */
static void
get2comp(x)
VALUE x;
{
long i = RBIGNUM(x)->len;
BDIGIT *ds = BDIGITS(x);
BDIGIT_DBL num;

if (!i) return;
while (i--) ds[i] = ~ds[i];
i = 0; num = 1;
do {
num += ds[i];
ds[i++] = BIGLO(num);
num = BIGDN(num);
} while (i < RBIGNUM(x)->len);
if (num != 0) {
REALLOC_N(RBIGNUM(x)->digits, BDIGIT, ++RBIGNUM(x)->len);
ds = BDIGITS(x);
ds[RBIGNUM(x)->len-1] = RBIGNUM(x)->sign ? ~0 : 1;
}
}

void
rb_big_2comp(x)			/* get 2's complement */
VALUE x;
{
get2comp(x);
}

static VALUE
bigtrunc(x)
VALUE x;
{
long len = RBIGNUM(x)->len;
BDIGIT *ds = BDIGITS(x);

if (len == 0) return x;
while (--len && !ds[len]);
RBIGNUM(x)->len = ++len;
return x;
}

static VALUE
bigfixize(x)
VALUE x;
{
long len = RBIGNUM(x)->len;
BDIGIT *ds = BDIGITS(x);

if (len*SIZEOF_BDIGITS <= sizeof(VALUE)) {
long num = 0;
while (len--) {
num = BIGUP(num) + ds[len];
}
if (num >= 0) {
if (RBIGNUM(x)->sign) {
if (POSFIXABLE(num)) return LONG2FIX(num);
}
else {
if (NEGFIXABLE(-(long)num)) return LONG2FIX(-(long)num);
}
}
}
return x;
}

static VALUE
bignorm(x)
VALUE x;
{
if (!FIXNUM_P(x) && TYPE(x) == T_BIGNUM) {
x = bigfixize(bigtrunc(x));
}
return x;
}

VALUE
rb_big_norm(x)
VALUE x;
{
return bignorm(x);
}

VALUE
rb_uint2big(n)
unsigned long n;
{
BDIGIT_DBL num = n;
long i = 0;
BDIGIT *digits;
VALUE big;

big = bignew(DIGSPERLONG, 1);
digits = BDIGITS(big);
while (i < DIGSPERLONG) {
digits[i++] = BIGLO(num);
num = BIGDN(num);
}

i = DIGSPERLONG;
while (--i && !digits[i]) ;
RBIGNUM(big)->len = i+1;
return big;
}

VALUE
rb_int2big(n)
long n;
{
long neg = 0;
VALUE big;

if (n < 0) {
n = -n;
neg = 1;
}
big = rb_uint2big(n);
if (neg) {
RBIGNUM(big)->sign = 0;
}
return big;
}

VALUE
rb_uint2inum(n)
unsigned long n;
{
if (POSFIXABLE(n)) return LONG2FIX(n);
return rb_uint2big(n);
}

VALUE
rb_int2inum(n)
long n;
{
if (FIXABLE(n)) return LONG2FIX(n);
return rb_int2big(n);
}

#ifdef HAVE_LONG_LONG

void
rb_quad_pack(buf, val)
char *buf;
VALUE val;
{
LONG_LONG q;

val = rb_to_int(val);
if (FIXNUM_P(val)) {
q = FIX2LONG(val);
}
else {
long len = RBIGNUM(val)->len;
BDIGIT *ds;

if (len > SIZEOF_LONG_LONG/SIZEOF_BDIGITS)
rb_raise(rb_eRangeError, "bignum too big to convert into `quad int'");
ds = BDIGITS(val);
q = 0;
while (len--) {
q = BIGUP(q);
q += ds[len];
}
if (!RBIGNUM(val)->sign) q = -q;
}
memcpy(buf, (char*)&q, SIZEOF_LONG_LONG);
}

VALUE
rb_quad_unpack(buf, sign)
const char *buf;
int sign;
{
unsigned LONG_LONG q;
long neg = 0;
long i;
BDIGIT *digits;
VALUE big;

memcpy(&q, buf, SIZEOF_LONG_LONG);
if (sign) {
if (FIXABLE((LONG_LONG)q)) return LONG2FIX((LONG_LONG)q);
if ((LONG_LONG)q < 0) {
q = -(LONG_LONG)q;
neg = 1;
}
}
else {
if (POSFIXABLE(q)) return LONG2FIX(q);
}

i = 0;
big = bignew(DIGSPERLL, 1);
digits = BDIGITS(big);
while (i < DIGSPERLL) {
digits[i++] = BIGLO(q);
q = BIGDN(q);
}

i = DIGSPERLL;
while (i-- && !digits[i]) ;
RBIGNUM(big)->len = i+1;

if (neg) {
RBIGNUM(big)->sign = 0;
}
return bignorm(big);
}

#else

#define QUAD_SIZE 8

void
rb_quad_pack(buf, val)
char *buf;
VALUE val;
{
long len;

memset(buf, 0, QUAD_SIZE);
val = rb_to_int(val);
if (FIXNUM_P(val)) {
val = rb_int2big(FIX2LONG(val));
}
len = RBIGNUM(val)->len * SIZEOF_BDIGITS;
if (len > QUAD_SIZE) {
rb_raise(rb_eRangeError, "bignum too big to convert into `quad int'");
}
memcpy(buf, (char*)BDIGITS(val), len);
if (!RBIGNUM(val)->sign) {
len = QUAD_SIZE;
while (len--) {
*buf = ~*buf;
buf++;
}
}
}

#define BNEG(b) (RSHIFT(((BDIGIT*)b)[QUAD_SIZE/SIZEOF_BDIGITS-1],BITSPERDIG-1) != 0)

VALUE
rb_quad_unpack(buf, sign)
const char *buf;
int sign;
{
VALUE big = bignew(QUAD_SIZE/SIZEOF_BDIGITS, 1);

memcpy((char*)BDIGITS(big), buf, QUAD_SIZE);
if (sign && BNEG(buf)) {
long len = QUAD_SIZE;
char *tmp = (char*)BDIGITS(big);

RBIGNUM(big)->sign = 0;
while (len--) {
*tmp = ~*tmp;
tmp++;
}
}

return bignorm(big);
}

#endif

VALUE
rb_cstr_to_inum(str, base, badcheck)
const char *str;
int base;
int badcheck;
{
const char *s = str;
char *end;
char sign = 1, nondigit = 0;
int c;
BDIGIT_DBL num;
long len, blen = 1;
long i;
VALUE z;
BDIGIT *zds;

#define conv_digit(c) \
(!ISASCII(c) ? -1 : \
isdigit(c) ? ((c) - '0') : \
islower(c) ? ((c) - 'a' + 10) : \
isupper(c) ? ((c) - 'A' + 10) : \
-1)

if (!str) {
if (badcheck) goto bad;
return INT2FIX(0);
}
if (badcheck) {
while (ISSPACE(*str)) str++;
}
else {
while (ISSPACE(*str) || *str == '_') str++;
}

if (str[0] == '+') {
str++;
}
else if (str[0] == '-') {
str++;
sign = 0;
}
if (str[0] == '+' || str[0] == '-') {
if (badcheck) goto bad;
return INT2FIX(0);
}
if (base <= 0) {
if (str[0] == '0') {
switch (str[1]) {
case 'x': case 'X':
base = 16;
break;
case 'b': case 'B':
base = 2;
break;
case 'o': case 'O':
base = 8;
break;
case 'd': case 'D':
base = 10;
break;
default:
base = 8;
}
}
else if (base < -1) {
base = -base;
}
else {
base = 10;
}
}
switch (base) {
case 2:
len = 1;
if (str[0] == '0' && (str[1] == 'b'||str[1] == 'B')) {
str += 2;
}
break;
case 3:
len = 2;
break;
case 8:
if (str[0] == '0' && (str[1] == 'o'||str[1] == 'O')) {
str += 2;
}
case 4: case 5: case 6: case 7:
len = 3;
break;
case 10:
if (str[0] == '0' && (str[1] == 'd'||str[1] == 'D')) {
str += 2;
}
case 9: case 11: case 12: case 13: case 14: case 15:
len = 4;
break;
case 16:
len = 4;
if (str[0] == '0' && (str[1] == 'x'||str[1] == 'X')) {
str += 2;
}
break;
default:
if (base < 2 || 36 < base) {
rb_raise(rb_eArgError, "illegal radix %d", base);
}
if (base <= 32) {
len = 5;
}
else {
len = 6;
}
break;
}
if (*str == '0') {		/* squeeze preceeding 0s */
int us = 0;
while ((c = *++str) == '0' || c == '_') {
if (c == '_') {
if (++us >= 2)
break;
} else
us = 0;
}
if (!(c = *str) || ISSPACE(c)) --str;
}
c = *str;
c = conv_digit(c);
if (c < 0 || c >= base) {
if (badcheck) goto bad;
return INT2FIX(0);
}
len *= strlen(str)*sizeof(char);

if (len <= (sizeof(VALUE)*CHAR_BIT)) {
unsigned long val = strtoul((char*)str, &end, base);

if (*end == '_') goto bigparse;
if (badcheck) {
if (end == str) goto bad; /* no number */
while (*end && ISSPACE(*end)) end++;
if (*end) goto bad;	      /* trailing garbage */
}

if (POSFIXABLE(val)) {
if (sign) return LONG2FIX(val);
else {
long result = -(long)val;
return LONG2FIX(result);
}
}
else {
VALUE big = rb_uint2big(val);
RBIGNUM(big)->sign = sign;
return bignorm(big);
}
}
bigparse:
len = (len/BITSPERDIG)+1;
if (badcheck && *str == '_') goto bad;

z = bignew(len, sign);
zds = BDIGITS(z);
for (i=len;i--;) zds[i]=0;
while ((c = *str++) != 0) {
if (c == '_') {
if (nondigit) {
if (badcheck) goto bad;
break;
}
nondigit = c;
continue;
}
else if ((c = conv_digit(c)) < 0) {
break;
}
if (c >= base) break;
nondigit = 0;
i = 0;
num = c;
for (;;) {
while (i<blen) {
num += (BDIGIT_DBL)zds[i]*base;
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
if (num) {
blen++;
continue;
}
break;
}
}
if (badcheck) {
str--;
if (s+1 < str && str[-1] == '_') goto bad;
while (*str && ISSPACE(*str)) str++;
if (*str) {
bad:
rb_invalid_str(s, "Integer");
}
}

return bignorm(z);
}

VALUE
rb_str_to_inum(str, base, badcheck)
VALUE str;
int base;
int badcheck;
{
char *s;
long len;

StringValue(str);
if (badcheck) {
s = StringValueCStr(str);
}
else {
s = RSTRING(str)->ptr;
}
if (s) {
len = RSTRING(str)->len;
if (s[len]) {		/* no sentinel somehow */
char *p = ALLOCA_N(char, len+1);

MEMCPY(p, s, char, len);
p[len] = '\0';
s = p;
}
}
return rb_cstr_to_inum(s, base, badcheck);
}

#if HAVE_LONG_LONG

VALUE
rb_ull2big(n)
unsigned LONG_LONG n;
{
BDIGIT_DBL num = n;
long i = 0;
BDIGIT *digits;
VALUE big;

big = bignew(DIGSPERLL, 1);
digits = BDIGITS(big);
while (i < DIGSPERLL) {
digits[i++] = BIGLO(num);
num = BIGDN(num);
}

i = DIGSPERLL;
while (i-- && !digits[i]) ;
RBIGNUM(big)->len = i+1;
return big;
}

VALUE
rb_ll2big(n)
LONG_LONG n;
{
long neg = 0;
VALUE big;

if (n < 0) {
n = -n;
neg = 1;
}
big = rb_ull2big(n);
if (neg) {
RBIGNUM(big)->sign = 0;
}
return big;
}

VALUE
rb_ull2inum(n)
unsigned LONG_LONG n;
{
if (POSFIXABLE(n)) return LONG2FIX(n);
return rb_ull2big(n);
}

VALUE
rb_ll2inum(n)
LONG_LONG n;
{
if (FIXABLE(n)) return LONG2FIX(n);
return rb_ll2big(n);
}

#endif  /* HAVE_LONG_LONG */

VALUE
rb_cstr2inum(str, base)
const char *str;
int base;
{
return rb_cstr_to_inum(str, base, base==0);
}

VALUE
rb_str2inum(str, base)
VALUE str;
int base;
{
return rb_str_to_inum(str, base, base==0);
}

const char ruby_digitmap[] = "0123456789abcdefghijklmnopqrstuvwxyz";
VALUE
rb_big2str0(x, base, trim)
VALUE x;
int base;
int trim;
{
volatile VALUE t;
BDIGIT *ds;
long i, j, hbase;
VALUE ss;
char *s;

if (FIXNUM_P(x)) {
return rb_fix2str(x, base);
}
i = RBIGNUM(x)->len;
if (BIGZEROP(x)) {
return rb_str_new2("0");
}
if (i >= LONG_MAX/SIZEOF_BDIGITS/CHAR_BIT) {
rb_raise(rb_eRangeError, "bignum too big to convert into `string'");
}
j = SIZEOF_BDIGITS*CHAR_BIT*i;
switch (base) {
case 2: break;
case 3:
j = j * 53L / 84 + 1;
break;
case 4: case 5: case 6: case 7:
j = (j + 1) / 2;
break;
case 8: case 9:
j = (j + 2) / 3;
break;
case 10: case 11: case 12: case 13: case 14: case 15:
j = j * 28L / 93 + 1;
break;
case 16: case 17: case 18: case 19: case 20: case 21:
case 22: case 23: case 24: case 25: case 26: case 27:
case 28: case 29: case 30: case 31:
j = (j + 3) / 4;
break;
case 32: case 33: case 34: case 35: case 36:
j = (j + 4) / 5;
break;
default:
rb_raise(rb_eArgError, "illegal radix %d", base);
break;
}
j++;			/* space for sign */

hbase = base * base;
#if SIZEOF_BDIGITS > 2
hbase *= hbase;
#endif

t = rb_big_clone(x);
ds = BDIGITS(t);
ss = rb_str_new(0, j+1);
s = RSTRING(ss)->ptr;

s[0] = RBIGNUM(x)->sign ? '+' : '-';
TRAP_BEG;
while (i && j > 1) {
long k = i;
BDIGIT_DBL num = 0;

while (k--) {
num = BIGUP(num) + ds[k];
ds[k] = (BDIGIT)(num / hbase);
num %= hbase;
}
if (trim && ds[i-1] == 0) i--;
k = SIZEOF_BDIGITS;
while (k--) {
s[--j] = ruby_digitmap[num % base];
num /= base;
if (!trim && j <= 1) break;
if (trim && i == 0 && num == 0) break;
}
}
if (trim) {while (s[j] == '0') j++;}
i = RSTRING(ss)->len - j;
if (RBIGNUM(x)->sign) {
memmove(s, s+j, i);
RSTRING(ss)->len = i-1;
}
else {
memmove(s+1, s+j, i);
RSTRING(ss)->len = i;
}
s[RSTRING(ss)->len] = '\0';
TRAP_END;

return ss;
}

VALUE
rb_big2str(VALUE x, int base)
{
return rb_big2str0(x, base, Qtrue);
}

/*
*  call-seq:
*     big.to_s(base=10)   =>  string
*
*  Returns a string containing the representation of <i>big</i> radix
*  <i>base</i> (2 through 36).
*
*     12345654321.to_s         #=> "12345654321"
*     12345654321.to_s(2)      #=> "1011011111110110111011110000110001"
*     12345654321.to_s(8)      #=> "133766736061"
*     12345654321.to_s(16)     #=> "2dfdbbc31"
*     78546939656932.to_s(36)  #=> "rubyrules"
*/

static VALUE
rb_big_to_s(argc, argv, x)
int argc;
VALUE *argv;
VALUE x;
{
VALUE b;
int base;

rb_scan_args(argc, argv, "01", &b);
if (argc == 0) base = 10;
else base = NUM2INT(b);
return rb_big2str(x, base);
}

static unsigned long
big2ulong(x, type)
VALUE x;
char *type;
{
long len = RBIGNUM(x)->len;
BDIGIT_DBL num;
BDIGIT *ds;

if (len > SIZEOF_LONG/SIZEOF_BDIGITS)
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
ds = BDIGITS(x);
num = 0;
while (len--) {
num = BIGUP(num);
num += ds[len];
}
return num;
}

unsigned long
rb_big2ulong_pack(x)
VALUE x;
{
unsigned long num = big2ulong(x, "unsigned long");
if (!RBIGNUM(x)->sign) {
return -num;
}
return num;
}

unsigned long
rb_big2ulong(x)
VALUE x;
{
unsigned long num = big2ulong(x, "unsigned long");

if (!RBIGNUM(x)->sign) {
if ((long)num < 0) {
rb_raise(rb_eRangeError, "bignum out of range of unsigned long");
}
return -num;
}
return num;
}

long
rb_big2long(x)
VALUE x;
{
unsigned long num = big2ulong(x, "long");

if ((long)num < 0 && (RBIGNUM(x)->sign || (long)num != LONG_MIN)) {
rb_raise(rb_eRangeError, "bignum too big to convert into `long'");
}
if (!RBIGNUM(x)->sign) return -(long)num;
return num;
}

#if HAVE_LONG_LONG

static unsigned LONG_LONG
big2ull(x, type)
VALUE x;
char *type;
{
long len = RBIGNUM(x)->len;
BDIGIT_DBL num;
BDIGIT *ds;

if (len > SIZEOF_LONG_LONG/SIZEOF_BDIGITS)
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
ds = BDIGITS(x);
num = 0;
while (len--) {
num = BIGUP(num);
num += ds[len];
}
return num;
}

unsigned LONG_LONG
rb_big2ull(x)
VALUE x;
{
unsigned LONG_LONG num = big2ull(x, "unsigned long long");

if (!RBIGNUM(x)->sign) return -num;
return num;
}

LONG_LONG
rb_big2ll(x)
VALUE x;
{
unsigned LONG_LONG num = big2ull(x, "long long");

if ((LONG_LONG)num < 0 && (RBIGNUM(x)->sign
|| (LONG_LONG)num != LLONG_MIN)) {
rb_raise(rb_eRangeError, "bignum too big to convert into `long long'");
}
if (!RBIGNUM(x)->sign) return -(LONG_LONG)num;
return num;
}

#endif  /* HAVE_LONG_LONG */

static VALUE
dbl2big(d)
double d;
{
long i = 0;
BDIGIT c;
BDIGIT *digits;
VALUE z;
double u = (d < 0)?-d:d;

if (isinf(d)) {
rb_raise(rb_eFloatDomainError, d < 0 ? "-Infinity" : "Infinity");
}
if (isnan(d)) {
rb_raise(rb_eFloatDomainError, "NaN");
}

while (!POSFIXABLE(u) || 0 != (long)u) {
u /= (double)(BIGRAD);
i++;
}
z = bignew(i, d>=0);
digits = BDIGITS(z);
while (i--) {
u *= BIGRAD;
c = (BDIGIT)u;
u -= c;
digits[i] = c;
}

return z;
}

VALUE
rb_dbl2big(d)
double d;
{
return bignorm(dbl2big(d));
}

static double
big2dbl(x)
VALUE x;
{
double d = 0.0;
long i = RBIGNUM(x)->len;
BDIGIT *ds = BDIGITS(x);

while (i--) {
d = ds[i] + BIGRAD*d;
}
if (!RBIGNUM(x)->sign) d = -d;
return d;
}

double
rb_big2dbl(x)
VALUE x;
{
double d = big2dbl(x);

if (isinf(d)) {
rb_warn("Bignum out of Float range");
d = HUGE_VAL;
}
return d;
}

/*
*  call-seq:
*     big.to_f -> float
*
*  Converts <i>big</i> to a <code>Float</code>. If <i>big</i> doesn't
*  fit in a <code>Float</code>, the result is infinity.
*
*/

static VALUE
rb_big_to_f(x)
VALUE x;
{
return rb_float_new(rb_big2dbl(x));
}

/*
*  call-seq:
*     big <=> numeric   => -1, 0, +1
*
*  Comparison---Returns -1, 0, or +1 depending on whether <i>big</i> is
*  less than, equal to, or greater than <i>numeric</i>. This is the
*  basis for the tests in <code>Comparable</code>.
*
*/

static VALUE
rb_big_cmp(x, y)
VALUE x, y;
{
long xlen = RBIGNUM(x)->len;

switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;

case T_BIGNUM:
break;

case T_FLOAT:
return rb_dbl_cmp(rb_big2dbl(x), RFLOAT(y)->value);

default:
return rb_num_coerce_cmp(x, y);
}

if (RBIGNUM(x)->sign > RBIGNUM(y)->sign) return INT2FIX(1);
if (RBIGNUM(x)->sign < RBIGNUM(y)->sign) return INT2FIX(-1);
if (xlen < RBIGNUM(y)->len)
return (RBIGNUM(x)->sign) ? INT2FIX(-1) : INT2FIX(1);
if (xlen > RBIGNUM(y)->len)
return (RBIGNUM(x)->sign) ? INT2FIX(1) : INT2FIX(-1);

while(xlen-- && (BDIGITS(x)[xlen]==BDIGITS(y)[xlen]));
if (-1 == xlen) return INT2FIX(0);
return (BDIGITS(x)[xlen] > BDIGITS(y)[xlen]) ?
(RBIGNUM(x)->sign ? INT2FIX(1) : INT2FIX(-1)) :
(RBIGNUM(x)->sign ? INT2FIX(-1) : INT2FIX(1));
}

/*
*  call-seq:
*     big == obj  => true or false
*
*  Returns <code>true</code> only if <i>obj</i> has the same value
*  as <i>big</i>. Contrast this with <code>Bignum#eql?</code>, which
*  requires <i>obj</i> to be a <code>Bignum</code>.
*
*     68719476736 == 68719476736.0   #=> true
*/

static VALUE
rb_big_eq(x, y)
VALUE x, y;
{
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
{
volatile double a, b;

a = RFLOAT(y)->value;
if (isnan(a)) return Qfalse;
b = rb_big2dbl(x);
return (a == b)?Qtrue:Qfalse;
}
default:
return rb_equal(y, x);
}
if (RBIGNUM(x)->sign != RBIGNUM(y)->sign) return Qfalse;
if (RBIGNUM(x)->len != RBIGNUM(y)->len) return Qfalse;
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM(y)->len) != 0) return Qfalse;
return Qtrue;
}

/*
*  call-seq:
*     big.eql?(obj)   => true or false
*
*  Returns <code>true</code> only if <i>obj</i> is a
*  <code>Bignum</code> with the same value as <i>big</i>. Contrast this
*  with <code>Bignum#==</code>, which performs type conversions.
*
*     68719476736.eql?(68719476736.0)   #=> false
*/

static VALUE
rb_big_eql(x, y)
VALUE x, y;
{
if (TYPE(y) != T_BIGNUM) return Qfalse;
if (RBIGNUM(x)->sign != RBIGNUM(y)->sign) return Qfalse;
if (RBIGNUM(x)->len != RBIGNUM(y)->len) return Qfalse;
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM(y)->len) != 0) return Qfalse;
return Qtrue;
}

/*
* call-seq:
*    -big   =>  other_big
*
* Unary minus (returns a new Bignum whose value is 0-big)
*/

static VALUE
rb_big_uminus(x)
VALUE x;
{
VALUE z = rb_big_clone(x);

RBIGNUM(z)->sign = !RBIGNUM(x)->sign;

return bignorm(z);
}

/*
* call-seq:
*     ~big  =>  integer
*
* Inverts the bits in big. As Bignums are conceptually infinite
* length, the result acts as if it had an infinite number of one
* bits to the left. In hex representations, this is displayed
* as two periods to the left of the digits.
*
*   sprintf("%X", ~0x1122334455)    #=> "..FEEDDCCBBAA"
*/

static VALUE
rb_big_neg(x)
VALUE x;
{
VALUE z = rb_big_clone(x);
long i;
BDIGIT *ds;

if (!RBIGNUM(x)->sign) get2comp(z);
ds = BDIGITS(z);
i = RBIGNUM(x)->len;
if (!i) return INT2FIX(~0);
while (i--) ds[i] = ~ds[i];
RBIGNUM(z)->sign = !RBIGNUM(z)->sign;
if (RBIGNUM(x)->sign) get2comp(z);

return bignorm(z);
}

static VALUE
bigsub(x, y)
VALUE x, y;
{
VALUE z = 0;
BDIGIT *zds;
BDIGIT_DBL_SIGNED num;
long i = RBIGNUM(x)->len;

/* if x is larger than y, swap */
if (RBIGNUM(x)->len < RBIGNUM(y)->len) {
z = x; x = y; y = z;	/* swap x y */
}
else if (RBIGNUM(x)->len == RBIGNUM(y)->len) {
while (i > 0) {
i--;
if (BDIGITS(x)[i] > BDIGITS(y)[i]) {
break;
}
if (BDIGITS(x)[i] < BDIGITS(y)[i]) {
z = x; x = y; y = z;	/* swap x y */
break;
}
}
}

z = bignew(RBIGNUM(x)->len, z==0);
zds = BDIGITS(z);

for (i = 0, num = 0; i < RBIGNUM(y)->len; i++) {
num += (BDIGIT_DBL_SIGNED)BDIGITS(x)[i] - BDIGITS(y)[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
while (num && i < RBIGNUM(x)->len) {
num += BDIGITS(x)[i];
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
while (i < RBIGNUM(x)->len) {
zds[i] = BDIGITS(x)[i];
i++;
}

return z;
}

static VALUE
bigadd(x, y, sign)
VALUE x, y;
int sign;
{
VALUE z;
BDIGIT_DBL num;
long i, len;

sign = (sign == RBIGNUM(y)->sign);
if (RBIGNUM(x)->sign != sign) {
if (sign) return bigsub(y, x);
return bigsub(x, y);
}

if (RBIGNUM(x)->len > RBIGNUM(y)->len) {
len = RBIGNUM(x)->len + 1;
z = x; x = y; y = z;
}
else {
len = RBIGNUM(y)->len + 1;
}
z = bignew(len, sign);

len = RBIGNUM(x)->len;
for (i = 0, num = 0; i < len; i++) {
num += (BDIGIT_DBL)BDIGITS(x)[i] + BDIGITS(y)[i];
BDIGITS(z)[i] = BIGLO(num);
num = BIGDN(num);
}
len = RBIGNUM(y)->len;
while (num && i < len) {
num += BDIGITS(y)[i];
BDIGITS(z)[i++] = BIGLO(num);
num = BIGDN(num);
}
while (i < len) {
BDIGITS(z)[i] = BDIGITS(y)[i];
i++;
}
BDIGITS(z)[i] = (BDIGIT)num;

return z;
}

/*
*  call-seq:
*     big + other  => Numeric
*
*  Adds big and other, returning the result.
*/

VALUE
rb_big_plus(x, y)
VALUE x, y;
{
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
/* fall through */
case T_BIGNUM:
return bignorm(bigadd(x, y, 1));

case T_FLOAT:
return rb_float_new(rb_big2dbl(x) + RFLOAT(y)->value);

default:
return rb_num_coerce_bin(x, y);
}
}

/*
*  call-seq:
*     big - other  => Numeric
*
*  Subtracts other from big, returning the result.
*/

VALUE
rb_big_minus(x, y)
VALUE x, y;
{
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
/* fall through */
case T_BIGNUM:
return bignorm(bigadd(x, y, 0));

case T_FLOAT:
return rb_float_new(rb_big2dbl(x) - RFLOAT(y)->value);

default:
return rb_num_coerce_bin(x, y);
}
}

VALUE
rb_big_mul0(x, y)
VALUE x, y;
{
long i, j;
BDIGIT_DBL n = 0;
VALUE z;
BDIGIT *zds;

if (FIXNUM_P(x)) x = rb_int2big(FIX2LONG(x));
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;

case T_BIGNUM:
break;

case T_FLOAT:
return rb_float_new(rb_big2dbl(x) * RFLOAT(y)->value);

default:
return rb_num_coerce_bin(x, y);
}

j = RBIGNUM(x)->len + RBIGNUM(y)->len + 1;
z = bignew(j, RBIGNUM(x)->sign==RBIGNUM(y)->sign);
zds = BDIGITS(z);
while (j--) zds[j] = 0;
for (i = 0; i < RBIGNUM(x)->len; i++) {
BDIGIT_DBL dd = BDIGITS(x)[i];
if (dd == 0) continue;
n = 0;
for (j = 0; j < RBIGNUM(y)->len; j++) {
BDIGIT_DBL ee = n + (BDIGIT_DBL)dd * BDIGITS(y)[j];
n = zds[i + j] + ee;
if (ee) zds[i + j] = BIGLO(n);
n = BIGDN(n);
}
if (n) {
zds[i + j] = n;
}
}

return z;
}

/*
*  call-seq:
*     big * other  => Numeric
*
*  Multiplies big and other, returning the result.
*/

VALUE
rb_big_mul(x, y)
VALUE x, y;
{
return bignorm(rb_big_mul0(x, y));
}

static void
bigdivrem(x, y, divp, modp)
VALUE x, y;
VALUE *divp, *modp;
{
long nx = RBIGNUM(x)->len, ny = RBIGNUM(y)->len;
long i, j;
VALUE yy, z;
BDIGIT *xds, *yds, *zds, *tds;
BDIGIT_DBL t2;
BDIGIT_DBL_SIGNED num;
BDIGIT dd, q;

if (BIGZEROP(y)) rb_num_zerodiv();
yds = BDIGITS(y);
if (nx < ny || (nx == ny && BDIGITS(x)[nx - 1] < BDIGITS(y)[ny - 1])) {
if (divp) *divp = rb_int2big(0);
if (modp) *modp = x;
return;
}
xds = BDIGITS(x);
if (ny == 1) {
dd = yds[0];
z = rb_big_clone(x);
zds = BDIGITS(z);
t2 = 0; i = nx;
while (i--) {
t2 = BIGUP(t2) + zds[i];
zds[i] = (BDIGIT)(t2 / dd);
t2 %= dd;
}
RBIGNUM(z)->sign = RBIGNUM(x)->sign==RBIGNUM(y)->sign;
if (modp) {
*modp = rb_uint2big((unsigned long)t2);
RBIGNUM(*modp)->sign = RBIGNUM(x)->sign;
}
if (divp) *divp = z;
return;
}
z = bignew(nx==ny?nx+2:nx+1, RBIGNUM(x)->sign==RBIGNUM(y)->sign);
zds = BDIGITS(z);
if (nx==ny) zds[nx+1] = 0;
while (!yds[ny-1]) ny--;

dd = 0;
q = yds[ny-1];
while ((q & (1U<<(BITSPERDIG-1))) == 0) {
q <<= 1;
dd++;
}
if (dd) {
yy = rb_big_clone(y);
tds = BDIGITS(yy);
j = 0;
t2 = 0;
while (j<ny) {
t2 += (BDIGIT_DBL)yds[j]<<dd;
tds[j++] = BIGLO(t2);
t2 = BIGDN(t2);
}
yds = tds;
j = 0;
t2 = 0;
while (j<nx) {
t2 += (BDIGIT_DBL)xds[j]<<dd;
zds[j++] = BIGLO(t2);
t2 = BIGDN(t2);
}
zds[j] = (BDIGIT)t2;
}
else {
zds[nx] = 0;
j = nx;
while (j--) zds[j] = xds[j];
}

j = nx==ny?nx+1:nx;
do {
if (zds[j] ==  yds[ny-1]) q = BIGRAD-1;
else q = (BDIGIT)((BIGUP(zds[j]) + zds[j-1])/yds[ny-1]);
if (q) {
i = 0; num = 0; t2 = 0;
do {			/* multiply and subtract */
BDIGIT_DBL ee;
t2 += (BDIGIT_DBL)yds[i] * q;
ee = num - BIGLO(t2);
num = (BDIGIT_DBL)zds[j - ny + i] + ee;
if (ee) zds[j - ny + i] = BIGLO(num);
num = BIGDN(num);
t2 = BIGDN(t2);
} while (++i < ny);
num += zds[j - ny + i] - t2;/* borrow from high digit; don't update */
while (num) {		/* "add back" required */
i = 0; num = 0; q--;
do {
BDIGIT_DBL ee = num + yds[i];
num = (BDIGIT_DBL)zds[j - ny + i] + ee;
if (ee) zds[j - ny + i] = BIGLO(num);
num = BIGDN(num);
} while (++i < ny);
num--;
}
}
zds[j] = q;
} while (--j >= ny);
if (divp) {			/* move quotient down in z */
*divp = rb_big_clone(z);
zds = BDIGITS(*divp);
j = (nx==ny ? nx+2 : nx+1) - ny;
for (i = 0;i < j;i++) zds[i] = zds[i+ny];
RBIGNUM(*divp)->len = i;
}
if (modp) {			/* normalize remainder */
*modp = rb_big_clone(z);
zds = BDIGITS(*modp);
while (--ny && !zds[ny]); ++ny;
if (dd) {
t2 = 0; i = ny;
while(i--) {
t2 = (t2 | zds[i]) >> dd;
q = zds[i];
zds[i] = BIGLO(t2);
t2 = BIGUP(q);
}
}
RBIGNUM(*modp)->len = ny;
RBIGNUM(*modp)->sign = RBIGNUM(x)->sign;
}
}

static void
bigdivmod(x, y, divp, modp)
VALUE x, y;
VALUE *divp, *modp;
{
VALUE mod;

bigdivrem(x, y, divp, &mod);
if (RBIGNUM(x)->sign != RBIGNUM(y)->sign && !BIGZEROP(mod)) {
if (divp) *divp = bigadd(*divp, rb_int2big(1), 0);
if (modp) *modp = bigadd(mod, y, 1);
}
else {
if (divp) *divp = *divp;
if (modp) *modp = mod;
}
}

/*
*  call-seq:
*     big / other     => Numeric
*     big.div(other)  => Numeric
*
*  Divides big by other, returning the result.
*/

static VALUE
rb_big_div(x, y)
VALUE x, y;
{
VALUE z;

switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;

case T_BIGNUM:
break;

default:
return rb_num_coerce_bin(x, y);
}
bigdivmod(x, y, &z, 0);

return bignorm(z);
}

/*
*  call-seq:
*     big % other         => Numeric
*     big.modulo(other)   => Numeric
*
*  Returns big modulo other. See Numeric.divmod for more
*  information.
*/

static VALUE
rb_big_modulo(x, y)
VALUE x, y;
{
VALUE z;

switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;

case T_BIGNUM:
break;

default:
return rb_num_coerce_bin(x, y);
}
bigdivmod(x, y, 0, &z);

return bignorm(z);
}

/*
*  call-seq:
*     big.remainder(numeric)    => number
*
*  Returns the remainder after dividing <i>big</i> by <i>numeric</i>.
*
*     -1234567890987654321.remainder(13731)      #=> -6966
*     -1234567890987654321.remainder(13731.24)   #=> -9906.22531493148
*/
static VALUE
rb_big_remainder(x, y)
VALUE x, y;
{
VALUE z;

switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;

case T_BIGNUM:
break;

default:
return rb_num_coerce_bin(x, y);
}
bigdivrem(x, y, 0, &z);

return bignorm(z);
}

static int
bdigbitsize(BDIGIT x)
{
int size = 1;
int nb = BITSPERDIG / 2;
BDIGIT bits = (~0 << nb);

if (!x) return 0;
while (x > 1) {
if (x & bits) {
size += nb;
x >>= nb;
}
x &= ~bits;
nb /= 2;
bits >>= nb;
}

return size;
}

static VALUE big_lshift _((VALUE, unsigned long));
static VALUE big_rshift _((VALUE, unsigned long));

static VALUE big_shift(x, n)
VALUE x;
int n;
{
if (n < 0)
return big_lshift(x, (unsigned int)n);
else if (n > 0)
return big_rshift(x, (unsigned int)n);
return x;
}

/*
*  call-seq:
*     big.divmod(numeric)   => array
*
*  See <code>Numeric#divmod</code>.
*
*/
VALUE
rb_big_divmod(x, y)
VALUE x, y;
{
VALUE div, mod;

switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;

case T_BIGNUM:
break;

default:
return rb_num_coerce_bin(x, y);
}
bigdivmod(x, y, &div, &mod);

return rb_assoc_new(bignorm(div), bignorm(mod));
}

/*
*  call-seq:
*     big.quo(numeric) -> float
*     big.fdiv(numeric) -> float
*
*  Returns the floating point result of dividing <i>big</i> by
*  <i>numeric</i>.
*
*     -1234567890987654321.quo(13731)      #=> -89910996357705.5
*     -1234567890987654321.quo(13731.24)   #=> -89909424858035.7
*
*/

static VALUE
rb_big_quo(x, y)
VALUE x, y;
{
double dx = big2dbl(x);
double dy;

if (isinf(dx)) {
#define DBL_BIGDIG ((DBL_MANT_DIG + BITSPERDIG) / BITSPERDIG)
VALUE z;
int ex, ey;

ex = (RBIGNUM(bigtrunc(x))->len - 1) * BITSPERDIG;
ex += bdigbitsize(BDIGITS(x)[RBIGNUM(x)->len - 1]);
ex -= 2 * DBL_BIGDIG * BITSPERDIG;
if (ex) x = big_shift(x, ex);

switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
case T_BIGNUM: {
ey = (RBIGNUM(bigtrunc(y))->len - 1) * BITSPERDIG;
ey += bdigbitsize(BDIGITS(y)[RBIGNUM(y)->len - 1]);
ey -= DBL_BIGDIG * BITSPERDIG;
if (ey) y = big_shift(y, ey);
bignum:
bigdivrem(x, y, &z, 0);
return rb_float_new(ldexp(big2dbl(z), ex - ey));
}
case T_FLOAT:
y = dbl2big(ldexp(frexp(RFLOAT(y)->value, &ey), DBL_MANT_DIG));
ey -= DBL_MANT_DIG;
goto bignum;
}
}
switch (TYPE(y)) {
case T_FIXNUM:
dy = (double)FIX2LONG(y);
break;

case T_BIGNUM:
dy = rb_big2dbl(y);
break;

case T_FLOAT:
dy = RFLOAT(y)->value;
break;

default:
return rb_num_coerce_bin(x, y);
}
return rb_float_new(dx / dy);
}

static VALUE
bigsqr(x)
VALUE x;
{
long len = RBIGNUM(x)->len, k = len / 2, i;
VALUE a, b, a2, z;
BDIGIT_DBL num;

if (len < 4000 / BITSPERDIG) {
return rb_big_mul0(x, x);
}

a = bignew(len - k, 1);
MEMCPY(BDIGITS(a), BDIGITS(x) + k, BDIGIT, len - k);
b = bignew(k, 1);
MEMCPY(BDIGITS(b), BDIGITS(x), BDIGIT, k);

a2 = bigtrunc(bigsqr(a));
z = bigsqr(b);
REALLOC_N(RBIGNUM(z)->digits, BDIGIT, (len = 2 * k + RBIGNUM(a2)->len) + 1);
while (RBIGNUM(z)->len < 2 * k) BDIGITS(z)[RBIGNUM(z)->len++] = 0;
MEMCPY(BDIGITS(z) + 2 * k, BDIGITS(a2), BDIGIT, RBIGNUM(a2)->len);
RBIGNUM(z)->len = len;
a2 = bigtrunc(rb_big_mul0(a, b));
len = RBIGNUM(a2)->len;
TRAP_BEG;
for (i = 0, num = 0; i < len; i++) {
num += (BDIGIT_DBL)BDIGITS(z)[i + k] + ((BDIGIT_DBL)BDIGITS(a2)[i] << 1);
BDIGITS(z)[i + k] = BIGLO(num);
num = BIGDN(num);
}
TRAP_END;
if (num) {
len = RBIGNUM(z)->len;
for (i += k; i < len && num; ++i) {
num += (BDIGIT_DBL)BDIGITS(z)[i];
BDIGITS(z)[i] = BIGLO(num);
num = BIGDN(num);
}
if (num) {
BDIGITS(z)[RBIGNUM(z)->len++] = BIGLO(num);
}
}
return bigtrunc(z);
}

/*
*  call-seq:
*     big ** exponent   #=> numeric
*
*  Raises _big_ to the _exponent_ power (which may be an integer, float,
*  or anything that will coerce to a number). The result may be
*  a Fixnum, Bignum, or Float
*
*    123456789 ** 2      #=> 15241578750190521
*    123456789 ** 1.2    #=> 5126464716.09932
*    123456789 ** -2     #=> 6.5610001194102e-17
*/

VALUE
rb_big_pow(x, y)
VALUE x, y;
{
double d;
long yy;

if (y == INT2FIX(0)) return INT2FIX(1);
switch (TYPE(y)) {
case T_FLOAT:
d = RFLOAT(y)->value;
break;

case T_BIGNUM:
rb_warn("in a**b, b may be too big");
d = rb_big2dbl(y);
break;

case T_FIXNUM:
yy = FIX2LONG(y);
if (yy > 0) {
VALUE z = 0;
long mask;
const long BIGLEN_LIMIT = 1024*1024 / SIZEOF_BDIGITS;

if ((RBIGNUM(x)->len > BIGLEN_LIMIT) ||
(RBIGNUM(x)->len > BIGLEN_LIMIT / yy)) {
rb_warn("in a**b, b may be too big");
d = (double)yy;
break;
}
for (mask = FIXNUM_MAX + 1; mask; mask >>= 1) {
if (z) z = bigtrunc(bigsqr(z));
if (yy & mask) {
z = z ? bigtrunc(rb_big_mul0(z, x)) : x;
}
}
return bignorm(z);
}
d = (double)yy;
break;

default:
return rb_num_coerce_bin(x, y);
}
return rb_float_new(pow(rb_big2dbl(x), d));
}

/*
* call-seq:
*     big & numeric   =>  integer
*
* Performs bitwise +and+ between _big_ and _numeric_.
*/

VALUE
rb_big_and(xx, yy)
VALUE xx, yy;
{
volatile VALUE x, y, z;
BDIGIT *ds1, *ds2, *zds;
long i, l1, l2;
char sign;

x = xx;
y = rb_to_int(yy);
if (FIXNUM_P(y)) {
y = rb_int2big(FIX2LONG(y));
}
if (!RBIGNUM(y)->sign) {
y = rb_big_clone(y);
get2comp(y);
}
if (!RBIGNUM(x)->sign) {
x = rb_big_clone(x);
get2comp(x);
}
if (RBIGNUM(x)->len > RBIGNUM(y)->len) {
l1 = RBIGNUM(y)->len;
l2 = RBIGNUM(x)->len;
ds1 = BDIGITS(y);
ds2 = BDIGITS(x);
sign = RBIGNUM(y)->sign;
}
else {
l1 = RBIGNUM(x)->len;
l2 = RBIGNUM(y)->len;
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
sign = RBIGNUM(x)->sign;
}
z = bignew(l2, RBIGNUM(x)->sign || RBIGNUM(y)->sign);
zds = BDIGITS(z);

for (i=0; i<l1; i++) {
zds[i] = ds1[i] & ds2[i];
}
for (; i<l2; i++) {
zds[i] = sign?0:ds2[i];
}
if (!RBIGNUM(z)->sign) get2comp(z);
return bignorm(z);
}

/*
* call-seq:
*     big | numeric   =>  integer
*
* Performs bitwise +or+ between _big_ and _numeric_.
*/

VALUE
rb_big_or(xx, yy)
VALUE xx, yy;
{
volatile VALUE x, y, z;
BDIGIT *ds1, *ds2, *zds;
long i, l1, l2;
char sign;

x = xx;
y = rb_to_int(yy);
if (FIXNUM_P(y)) {
y = rb_int2big(FIX2LONG(y));
}
if (!RBIGNUM(y)->sign) {
y = rb_big_clone(y);
get2comp(y);
}
if (!RBIGNUM(x)->sign) {
x = rb_big_clone(x);
get2comp(x);
}
if (RBIGNUM(x)->len > RBIGNUM(y)->len) {
l1 = RBIGNUM(y)->len;
l2 = RBIGNUM(x)->len;
ds1 = BDIGITS(y);
ds2 = BDIGITS(x);
sign = RBIGNUM(y)->sign;
}
else {
l1 = RBIGNUM(x)->len;
l2 = RBIGNUM(y)->len;
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
sign = RBIGNUM(x)->sign;
}
z = bignew(l2, RBIGNUM(x)->sign && RBIGNUM(y)->sign);
zds = BDIGITS(z);

for (i=0; i<l1; i++) {
zds[i] = ds1[i] | ds2[i];
}
for (; i<l2; i++) {
zds[i] = sign?ds2[i]:(BIGRAD-1);
}
if (!RBIGNUM(z)->sign) get2comp(z);

return bignorm(z);
}

/*
* call-seq:
*     big ^ numeric   =>  integer
*
* Performs bitwise +exclusive or+ between _big_ and _numeric_.
*/

VALUE
rb_big_xor(xx, yy)
VALUE xx, yy;
{
volatile VALUE x, y;
VALUE z;
BDIGIT *ds1, *ds2, *zds;
long i, l1, l2;
char sign;

x = xx;
y = rb_to_int(yy);
if (FIXNUM_P(y)) {
y = rb_int2big(FIX2LONG(y));
}
if (!RBIGNUM(y)->sign) {
y = rb_big_clone(y);
get2comp(y);
}
if (!RBIGNUM(x)->sign) {
x = rb_big_clone(x);
get2comp(x);
}
if (RBIGNUM(x)->len > RBIGNUM(y)->len) {
l1 = RBIGNUM(y)->len;
l2 = RBIGNUM(x)->len;
ds1 = BDIGITS(y);
ds2 = BDIGITS(x);
sign = RBIGNUM(y)->sign;
}
else {
l1 = RBIGNUM(x)->len;
l2 = RBIGNUM(y)->len;
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
sign = RBIGNUM(x)->sign;
}
RBIGNUM(x)->sign = RBIGNUM(x)->sign?1:0;
RBIGNUM(y)->sign = RBIGNUM(y)->sign?1:0;
z = bignew(l2, !(RBIGNUM(x)->sign ^ RBIGNUM(y)->sign));
zds = BDIGITS(z);

for (i=0; i<l1; i++) {
zds[i] = ds1[i] ^ ds2[i];
}
for (; i<l2; i++) {
zds[i] = sign?ds2[i]:~ds2[i];
}
if (!RBIGNUM(z)->sign) get2comp(z);

return bignorm(z);
}

static VALUE
check_shiftdown(VALUE y, VALUE x)
{
if (!RBIGNUM(x)->len) return INT2FIX(0);
if (RBIGNUM(y)->len > SIZEOF_LONG / SIZEOF_BDIGITS) {
return RBIGNUM(x)->sign ? INT2FIX(0) : INT2FIX(-1);
}
return Qnil;
}

/*
* call-seq:
*     big << numeric   =>  integer
*
* Shifts big left _numeric_ positions (right if _numeric_ is negative).
*/

VALUE
rb_big_lshift(x, y)
VALUE x, y;
{
long shift;
int neg = 0;

for (;;) {
if (FIXNUM_P(y)) {
shift = FIX2LONG(y);
if (shift < 0) {
neg = 1;
shift = -shift;
}
break;
}
else if (TYPE(y) == T_BIGNUM) {
if (!RBIGNUM(y)->sign) {
VALUE t = check_shiftdown(y, x);
if (!NIL_P(t)) return t;
neg = 1;
}
shift = big2ulong(y, "long");
break;
}
y = rb_to_int(y);
}

if (neg) return big_rshift(x, shift);
return big_lshift(x, shift);
}

static VALUE
big_lshift(x, shift)
VALUE x;
unsigned long shift;
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = shift%BITSPERDIG;
VALUE z;
BDIGIT_DBL num = 0;
long len, i;

len = RBIGNUM(x)->len;
z = bignew(len+s1+1, RBIGNUM(x)->sign);
zds = BDIGITS(z);
for (i=0; i<s1; i++) {
*zds++ = 0;
}
xds = BDIGITS(x);
for (i=0; i<len; i++) {
num = num | (BDIGIT_DBL)*xds++<<s2;
*zds++ = BIGLO(num);
num = BIGDN(num);
}
*zds = BIGLO(num);
return bignorm(z);
}

/*
* call-seq:
*     big >> numeric   =>  integer
*
* Shifts big right _numeric_ positions (left if _numeric_ is negative).
*/

VALUE
rb_big_rshift(x, y)
VALUE x, y;
{
long shift;
int neg = 0;

for (;;) {
if (FIXNUM_P(y)) {
shift = FIX2LONG(y);
if (shift < 0) {
neg = 1;
shift = -shift;
}
break;
}
else if (TYPE(y) == T_BIGNUM) {
if (RBIGNUM(y)->sign) {
VALUE t = check_shiftdown(y, x);
if (!NIL_P(t)) return t;
}
else {
neg = 1;
}
shift = big2ulong(y, "long");
break;
}
y = rb_to_int(y);
}

if (neg) return big_lshift(x, shift);
return big_rshift(x, shift);
}

static VALUE
big_rshift(x, shift)
VALUE x;
unsigned long shift;
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = shift%BITSPERDIG;
VALUE z;
BDIGIT_DBL num = 0;
long i, j;
volatile VALUE save_x;

if (s1 > RBIGNUM(x)->len) {
if (RBIGNUM(x)->sign)
return INT2FIX(0);
else
return INT2FIX(-1);
}
if (!RBIGNUM(x)->sign) {
save_x = x = rb_big_clone(x);
get2comp(x);
}
xds = BDIGITS(x);
i = RBIGNUM(x)->len; j = i - s1;
if (j == 0) {
if (RBIGNUM(x)->sign) return INT2FIX(0);
else return INT2FIX(-1);
}
z = bignew(j, RBIGNUM(x)->sign);
if (!RBIGNUM(x)->sign) {
num = ((BDIGIT_DBL)~0) << BITSPERDIG;
}
zds = BDIGITS(z);
while (i--, j--) {
num = (num | xds[i]) >> s2;
zds[j] = BIGLO(num);
num = BIGUP(xds[i]);
}
if (!RBIGNUM(x)->sign) {
get2comp(z);
}
return bignorm(z);
}

/*
*  call-seq:
*     big[n] -> 0, 1
*
*  Bit Reference---Returns the <em>n</em>th bit in the (assumed) binary
*  representation of <i>big</i>, where <i>big</i>[0] is the least
*  significant bit.
*
*     a = 9**15
*     50.downto(0) do |n|
*       print a[n]
*     end
*
*  <em>produces:</em>
*
*     000101110110100000111000011110010100111100010111001
*
*/

static VALUE
rb_big_aref(x, y)
VALUE x, y;
{
BDIGIT *xds;
BDIGIT_DBL num;
unsigned long shift;
long i, s1, s2;

if (TYPE(y) == T_BIGNUM) {
if (!RBIGNUM(y)->sign)
return INT2FIX(0);
if (RBIGNUM(bigtrunc(y))->len > SIZEOF_LONG/SIZEOF_BDIGITS) {
out_of_range:
return RBIGNUM(x)->sign ? INT2FIX(0) : INT2FIX(1);
}
shift = big2ulong(y, "long");
}
else {
i = NUM2LONG(y);
if (i < 0) return INT2FIX(0);
shift = (VALUE)i;
}
s1 = shift/BITSPERDIG;
s2 = shift%BITSPERDIG;

if (s1 >= RBIGNUM(x)->len) goto out_of_range;
if (!RBIGNUM(x)->sign) {
xds = BDIGITS(x);
i = 0; num = 1;
while (num += ~xds[i], ++i <= s1) {
num = BIGDN(num);
}
}
else {
num = BDIGITS(x)[s1];
}
if (num & ((BDIGIT_DBL)1<<s2))
return INT2FIX(1);
return INT2FIX(0);
}

/*
* call-seq:
*   big.hash   => fixnum
*
* Compute a hash based on the value of _big_.
*/

static VALUE
rb_big_hash(x)
VALUE x;
{
long i, len, key;
BDIGIT *digits;

key = 0; digits = BDIGITS(x); len = RBIGNUM(x)->len;
for (i=0; i<len; i++) {
key ^= *digits++;
}
return LONG2FIX(key);
}

/*
* MISSING: documentation
*/

static VALUE
rb_big_coerce(x, y)
VALUE x, y;
{
if (FIXNUM_P(y)) {
return rb_assoc_new(rb_int2big(FIX2LONG(y)), x);
}
else if (TYPE(y) == T_BIGNUM) {
return rb_assoc_new(y, x);
}
else {
rb_raise(rb_eTypeError, "can't coerce %s to Bignum",
rb_obj_classname(y));
}
/* not reached */
return Qnil;
}

/*
*  call-seq:
*     big.abs -> aBignum
*
*  Returns the absolute value of <i>big</i>.
*
*     -1234567890987654321.abs   #=> 1234567890987654321
*/

static VALUE
rb_big_abs(x)
VALUE x;
{
if (!RBIGNUM(x)->sign) {
x = rb_big_clone(x);
RBIGNUM(x)->sign = 1;
}
return x;
}

VALUE
rb_big_rand(max, rand_buf)
VALUE max;
double *rand_buf;
{
VALUE v;
long len = RBIGNUM(max)->len;

if (BIGZEROP(max)) {
return rb_float_new(rand_buf[0]);
}
v = bignew(len,1);
len--;
BDIGITS(v)[len] = BDIGITS(max)[len] * rand_buf[len];
while (len--) {
BDIGITS(v)[len] = ((BDIGIT)~0) * rand_buf[len];
}

return v;
}

/*
*  call-seq:
*     big.size -> integer
*
*  Returns the number of bytes in the machine representation of
*  <i>big</i>.
*
*     (256**10 - 1).size   #=> 12
*     (256**20 - 1).size   #=> 20
*     (256**40 - 1).size   #=> 40
*/

static VALUE
rb_big_size(big)
VALUE big;
{
return LONG2FIX(RBIGNUM(big)->len*SIZEOF_BDIGITS);
}

/*
*  Bignum objects hold integers outside the range of
*  Fixnum. Bignum objects are created
*  automatically when integer calculations would otherwise overflow a
*  Fixnum. When a calculation involving
*  Bignum objects returns a result that will fit in a
*  Fixnum, the result is automatically converted.
*
*  For the purposes of the bitwise operations and <code>[]</code>, a
*  Bignum is treated as if it were an infinite-length
*  bitstring with 2's complement representation.
*
*  While Fixnum values are immediate, Bignum
*  objects are not---assignment and parameter passing work with
*  references to objects, not the objects themselves.
*
*/

void
Init_Bignum()
{
rb_cBignum = rb_define_class("Bignum", rb_cInteger);

rb_define_method(rb_cBignum, "to_s", rb_big_to_s, -1);
rb_define_method(rb_cBignum, "coerce", rb_big_coerce, 1);
rb_define_method(rb_cBignum, "-@", rb_big_uminus, 0);
rb_define_method(rb_cBignum, "+", rb_big_plus, 1);
rb_define_method(rb_cBignum, "-", rb_big_minus, 1);
rb_define_method(rb_cBignum, "*", rb_big_mul, 1);
rb_define_method(rb_cBignum, "/", rb_big_div, 1);
rb_define_method(rb_cBignum, "%", rb_big_modulo, 1);
rb_define_method(rb_cBignum, "div", rb_big_div, 1);
rb_define_method(rb_cBignum, "divmod", rb_big_divmod, 1);
rb_define_method(rb_cBignum, "modulo", rb_big_modulo, 1);
rb_define_method(rb_cBignum, "remainder", rb_big_remainder, 1);
rb_define_method(rb_cBignum, "quo", rb_big_quo, 1);
rb_define_method(rb_cBignum, "fdiv", rb_big_quo, 1);
rb_define_method(rb_cBignum, "**", rb_big_pow, 1);
rb_define_method(rb_cBignum, "&", rb_big_and, 1);
rb_define_method(rb_cBignum, "|", rb_big_or, 1);
rb_define_method(rb_cBignum, "^", rb_big_xor, 1);
rb_define_method(rb_cBignum, "~", rb_big_neg, 0);
rb_define_method(rb_cBignum, "<<", rb_big_lshift, 1);
rb_define_method(rb_cBignum, ">>", rb_big_rshift, 1);
rb_define_method(rb_cBignum, "[]", rb_big_aref, 1);

rb_define_method(rb_cBignum, "<=>", rb_big_cmp, 1);
rb_define_method(rb_cBignum, "==", rb_big_eq, 1);
rb_define_method(rb_cBignum, "eql?", rb_big_eql, 1);
rb_define_method(rb_cBignum, "hash", rb_big_hash, 0);
rb_define_method(rb_cBignum, "to_f", rb_big_to_f, 0);
rb_define_method(rb_cBignum, "abs", rb_big_abs, 0);
rb_define_method(rb_cBignum, "size", rb_big_size, 0);
}
```