ruby--ruby/bignum.c

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

  bignum.c -

  $Author$
  $Date$
  created at: Fri Jun 10 00:48:55 JST 1994

  Copyright (C) 1993-2003 Yukihiro Matsumoto

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

#include "ruby.h"

#include <math.h>
#include <ctype.h>

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 || (RBIGNUM(x)->len == 1 && BDIGITS(x)[0] == 0))

static VALUE
bignew_1(klass, len, sign)
    VALUE klass;
    long len;
    char sign;
{
    NEWOBJ(big, struct RBignum);
    OBJSETUP(big, klass, T_BIGNUM);
    big->sign = sign;
    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;
}

static void
get2comp(x, carry)		/* get 2's complement */
    VALUE x;
    int carry;
{
    long i = RBIGNUM(x)->len;
    BDIGIT *ds = BDIGITS(x);
    BDIGIT_DBL num;

    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 (!carry) return;
    if ((ds[RBIGNUM(x)->len-1] & (1<<(BITSPERDIG-1))) == 0) {
	REALLOC_N(RBIGNUM(x)->digits, BDIGIT, ++RBIGNUM(x)->len);
	ds = BDIGITS(x);
	ds[RBIGNUM(x)->len-1] = ~0;
    }
}

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

static VALUE
bignorm(x)
    VALUE x;
{
    if (!FIXNUM_P(x)) {
	long len = RBIGNUM(x)->len;
	BDIGIT *ds = BDIGITS(x);

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

	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;
}

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;

	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) len = QUAD_SIZE;
    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, c, nondigit = 0;
    BDIGIT_DBL num;
    long len, blen = 1;
    long i;
    VALUE z;
    BDIGIT *zds;

    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 */
	while (*++str == '0');
	--str;
    }
    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++) {
	if (c == '_') {
	    if (badcheck) {
		if (nondigit) goto bad;
		nondigit = c;
	    }
	    continue;
	}
	else if (isdigit(c)) {
	    c -= '0';
	}
	else if (islower(c)) {
	    c -= 'a' - 10;
	}
	else if (isupper(c)) {
	    c -= 'A' - 10;
	}
	else {
	    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_big2str(x, base)
    VALUE x;
    int base;
{
    volatile VALUE t;
    BDIGIT *ds;
    long i, j, hbase;
    VALUE ss;
    char *s, c;

    if (FIXNUM_P(x)) {
	return rb_fix2str(x, base);
    }
    i = RBIGNUM(x)->len;
    if (BIGZEROP(x)) {
	return rb_str_new2("0");
    }
    j = SIZEOF_BDIGITS*CHAR_BIT*i;
    switch (base) {
      case 2: break;
      case 3:
	j = j * 647L / 1024;
	break;
      case 4: case 5: case 6: case 7:
	j /= 2;
	break;
      case 8: case 9:
	j /= 3;
	break;
      case 10: case 11: case 12: case 13: case 14: case 15:
	j = j * 241L / 800;
	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 /= 4;
	break;
      case 32: case 33: case 34: case 35: case 36:
	j /= 5;
	break;
      default:
	rb_raise(rb_eArgError, "illegal radix %d", base);
	break;
    }
    j += 2;

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

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

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

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

    return ss;
}

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

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

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

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

double
rb_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 (isinf(d)) {
	rb_warn("Bignum out of Float range");
	d = HUGE_VAL;
    }
    if (!RBIGNUM(x)->sign) d = -d;
    return d;
}

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

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));
}

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:
	if (rb_big2dbl(x) == RFLOAT(y)->value)
	    return Qtrue;
	else
	    return 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;
}

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;
}

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

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

    return bignorm(z);
}

static VALUE
rb_big_neg(x)
    VALUE x;
{
    VALUE z = rb_big_clone(x);
    long i = RBIGNUM(x)->len;
    BDIGIT *ds = BDIGITS(z);

    if (!RBIGNUM(x)->sign) get2comp(z, Qtrue);
    while (i--) ds[i] = ~ds[i];
    if (RBIGNUM(x)->sign) get2comp(z, Qfalse);
    RBIGNUM(z)->sign = !RBIGNUM(z)->sign;

    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)?1:0);
    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;
    char 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;
}

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);
    }
}

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_mul(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 bignorm(z);
}

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 & (1<<(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;
    }
}

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;

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

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

    return bignorm(z);
}

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);
}

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);
}

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));
}

static VALUE
rb_big_quo(x, y)
    VALUE x, y;
{
    double dx = rb_big2dbl(x);
    double dy;

    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);
}

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 = NUM2LONG(y);
	if (yy > 0) {
	    VALUE z = x;

	    for (;;) {
		yy -= 1;
		if (yy == 0) break;
		while (yy % 2 == 0) {
		    yy /= 2;
		    x = rb_big_mul(x, x);
		}
		z = rb_big_mul(z, 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));
}

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

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else {
	Check_Type(y, T_BIGNUM);
    }

    if (!RBIGNUM(y)->sign) {
	y = rb_big_clone(y);
	get2comp(y, Qtrue);
    }
    if (!RBIGNUM(x)->sign) {
	x = rb_big_clone(x);
	get2comp(x, Qtrue);
    }
    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, Qfalse);
    return bignorm(z);
}

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

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else {
	Check_Type(y, T_BIGNUM);
    }

    if (!RBIGNUM(y)->sign) {
	y = rb_big_clone(y);
	get2comp(y, Qtrue);
    }
    if (!RBIGNUM(x)->sign) {
	x = rb_big_clone(x);
	get2comp(x, Qtrue);
    }
    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, Qfalse);

    return bignorm(z);
}

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

    if (FIXNUM_P(y)) {
	y = rb_int2big(FIX2LONG(y));
    }
    else {
	Check_Type(y, T_BIGNUM);
    }

    if (!RBIGNUM(y)->sign) {
	y = rb_big_clone(y);
	get2comp(y, Qtrue);
    }
    if (!RBIGNUM(x)->sign) {
	x = rb_big_clone(x);
	get2comp(x, Qtrue);
    }
    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, Qfalse);

    return bignorm(z);
}

static VALUE rb_big_rshift _((VALUE,VALUE));

VALUE
rb_big_lshift(x, y)
    VALUE x, y;
{
    BDIGIT *xds, *zds;
    int shift = NUM2INT(y);
    int s1 = shift/BITSPERDIG;
    int s2 = shift%BITSPERDIG;
    VALUE z;
    BDIGIT_DBL num = 0;
    long len, i;

    if (shift < 0) return rb_big_rshift(x, INT2FIX(-shift));
    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);
}

static VALUE
rb_big_rshift(x, y)
    VALUE x, y;
{
    BDIGIT *xds, *zds;
    int shift = NUM2INT(y);
    long s1 = shift/BITSPERDIG;
    long s2 = shift%BITSPERDIG;
    VALUE z;
    BDIGIT_DBL num = 0;
    long i, j;

    if (shift < 0) return rb_big_lshift(x, INT2FIX(-shift));

    if (s1 > RBIGNUM(x)->len) {
	if (RBIGNUM(x)->sign)
	    return INT2FIX(0);
	else
	    return INT2FIX(-1);
    }
    if (!RBIGNUM(x)->sign) {
	x = rb_big_clone(x);
	get2comp(x, Qtrue);
    }
    xds = BDIGITS(x);
    i = RBIGNUM(x)->len; j = i - s1;
    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, Qfalse);
    }
    return bignorm(z);
}

static VALUE
rb_big_aref(x, y)
    VALUE x, y;
{
    BDIGIT *xds;
    int shift;
    long s1, s2;

    if (TYPE(y) == T_BIGNUM) {
	if (!RBIGNUM(y)->sign || RBIGNUM(x)->sign)
	    return INT2FIX(0);
	return INT2FIX(1);
    }
    shift = NUM2INT(y);
    if (shift < 0) return INT2FIX(0);
    s1 = shift/BITSPERDIG;
    s2 = shift%BITSPERDIG;

    if (!RBIGNUM(x)->sign) {
	if (s1 >= RBIGNUM(x)->len) return INT2FIX(1);
	x = rb_big_clone(x);
	get2comp(x, Qtrue);
    }
    else {
	if (s1 >= RBIGNUM(x)->len) return INT2FIX(0);
    }
    xds = BDIGITS(x);
    if (xds[s1] & (1<<s2))
	return INT2FIX(1);
    return INT2FIX(0);
}

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);
}

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

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);
    while (len--) {
	BDIGITS(v)[len] = ((BDIGIT)~0) * rand_buf[len];
    }

    return rb_big_modulo((VALUE)v, max);
}

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

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, "**", 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);
}