зеркало из https://github.com/github/ruby.git
2099 строки
40 KiB
C
2099 строки
40 KiB
C
/**********************************************************************
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bignum.c -
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$Author$
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$Date$
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created at: Fri Jun 10 00:48:55 JST 1994
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Copyright (C) 1993-2003 Yukihiro Matsumoto
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**********************************************************************/
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#include "ruby.h"
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#include <math.h>
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#include <ctype.h>
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#ifdef HAVE_IEEEFP_H
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#include <ieeefp.h>
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#endif
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VALUE rb_cBignum;
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#if defined __MINGW32__
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#define USHORT _USHORT
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#endif
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#define BDIGITS(x) ((BDIGIT*)RBIGNUM(x)->digits)
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#define BITSPERDIG (SIZEOF_BDIGITS*CHAR_BIT)
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#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
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#define DIGSPERLONG ((unsigned int)(SIZEOF_LONG/SIZEOF_BDIGITS))
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#if HAVE_LONG_LONG
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# define DIGSPERLL ((unsigned int)(SIZEOF_LONG_LONG/SIZEOF_BDIGITS))
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#endif
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#define BIGUP(x) ((BDIGIT_DBL)(x) << BITSPERDIG)
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#define BIGDN(x) RSHIFT(x,BITSPERDIG)
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#define BIGLO(x) ((BDIGIT)((x) & (BIGRAD-1)))
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#define BDIGMAX ((BDIGIT)-1)
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#define BIGZEROP(x) (RBIGNUM(x)->len == 0 || (RBIGNUM(x)->len == 1 && BDIGITS(x)[0] == 0))
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static VALUE
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bignew_1(klass, len, sign)
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VALUE klass;
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long len;
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char sign;
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{
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NEWOBJ(big, struct RBignum);
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OBJSETUP(big, klass, T_BIGNUM);
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big->sign = sign;
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big->len = len;
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big->digits = ALLOC_N(BDIGIT, len);
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return (VALUE)big;
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}
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#define bignew(len,sign) bignew_1(rb_cBignum,len,sign)
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VALUE
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rb_big_clone(x)
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VALUE x;
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{
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VALUE z = bignew_1(CLASS_OF(x), RBIGNUM(x)->len, RBIGNUM(x)->sign);
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MEMCPY(BDIGITS(z), BDIGITS(x), BDIGIT, RBIGNUM(x)->len);
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return z;
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}
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static void
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get2comp(x, carry) /* get 2's complement */
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VALUE x;
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int carry;
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{
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long i = RBIGNUM(x)->len;
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BDIGIT *ds = BDIGITS(x);
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BDIGIT_DBL num;
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while (i--) ds[i] = ~ds[i];
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i = 0; num = 1;
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do {
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num += ds[i];
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ds[i++] = BIGLO(num);
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num = BIGDN(num);
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} while (i < RBIGNUM(x)->len);
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if (!carry) return;
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if ((ds[RBIGNUM(x)->len-1] & (1<<(BITSPERDIG-1))) == 0) {
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REALLOC_N(RBIGNUM(x)->digits, BDIGIT, ++RBIGNUM(x)->len);
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ds = BDIGITS(x);
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ds[RBIGNUM(x)->len-1] = ~0;
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}
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}
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void
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rb_big_2comp(x) /* get 2's complement */
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VALUE x;
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{
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get2comp(x, Qtrue);
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}
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static VALUE
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bignorm(x)
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VALUE x;
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{
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if (!FIXNUM_P(x)) {
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long len = RBIGNUM(x)->len;
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BDIGIT *ds = BDIGITS(x);
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while (len-- && !ds[len]) ;
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RBIGNUM(x)->len = ++len;
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if (len*SIZEOF_BDIGITS <= sizeof(VALUE)) {
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long num = 0;
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while (len--) {
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num = BIGUP(num) + ds[len];
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}
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if (num >= 0) {
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if (RBIGNUM(x)->sign) {
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if (POSFIXABLE(num)) return LONG2FIX(num);
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}
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else if (NEGFIXABLE(-(long)num)) return LONG2FIX(-(long)num);
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}
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}
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}
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return x;
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}
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VALUE
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rb_big_norm(x)
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VALUE x;
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{
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return bignorm(x);
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}
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VALUE
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rb_uint2big(n)
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unsigned long n;
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{
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BDIGIT_DBL num = n;
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long i = 0;
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BDIGIT *digits;
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VALUE big;
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big = bignew(DIGSPERLONG, 1);
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digits = BDIGITS(big);
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while (i < DIGSPERLONG) {
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digits[i++] = BIGLO(num);
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num = BIGDN(num);
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}
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i = DIGSPERLONG;
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while (--i && !digits[i]) ;
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RBIGNUM(big)->len = i+1;
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return big;
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}
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VALUE
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rb_int2big(n)
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long n;
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{
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long neg = 0;
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VALUE big;
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if (n < 0) {
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n = -n;
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neg = 1;
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}
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big = rb_uint2big(n);
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if (neg) {
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RBIGNUM(big)->sign = 0;
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}
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return big;
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}
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VALUE
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rb_uint2inum(n)
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unsigned long n;
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{
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if (POSFIXABLE(n)) return LONG2FIX(n);
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return rb_uint2big(n);
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}
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VALUE
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rb_int2inum(n)
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long n;
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{
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if (FIXABLE(n)) return LONG2FIX(n);
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return rb_int2big(n);
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}
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#ifdef HAVE_LONG_LONG
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void
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rb_quad_pack(buf, val)
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char *buf;
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VALUE val;
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{
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LONG_LONG q;
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val = rb_to_int(val);
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if (FIXNUM_P(val)) {
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q = FIX2LONG(val);
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}
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else {
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long len = RBIGNUM(val)->len;
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BDIGIT *ds;
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if (len > SIZEOF_LONG_LONG/SIZEOF_BDIGITS) {
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len = SIZEOF_LONG/SIZEOF_BDIGITS;
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}
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ds = BDIGITS(val);
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q = 0;
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while (len--) {
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q = BIGUP(q);
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q += ds[len];
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}
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if (!RBIGNUM(val)->sign) q = -q;
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}
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memcpy(buf, (char*)&q, SIZEOF_LONG_LONG);
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}
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VALUE
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rb_quad_unpack(buf, sign)
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const char *buf;
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int sign;
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{
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unsigned LONG_LONG q;
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long neg = 0;
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long i;
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BDIGIT *digits;
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VALUE big;
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memcpy(&q, buf, SIZEOF_LONG_LONG);
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if (sign) {
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if (FIXABLE((LONG_LONG)q)) return LONG2FIX((LONG_LONG)q);
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if ((LONG_LONG)q < 0) {
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q = -(LONG_LONG)q;
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neg = 1;
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}
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}
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else {
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if (POSFIXABLE(q)) return LONG2FIX(q);
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}
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i = 0;
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big = bignew(DIGSPERLL, 1);
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digits = BDIGITS(big);
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while (i < DIGSPERLL) {
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digits[i++] = BIGLO(q);
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q = BIGDN(q);
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}
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i = DIGSPERLL;
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while (i-- && !digits[i]) ;
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RBIGNUM(big)->len = i+1;
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if (neg) {
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RBIGNUM(big)->sign = 0;
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}
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return bignorm(big);
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}
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#else
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#define QUAD_SIZE 8
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void
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rb_quad_pack(buf, val)
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char *buf;
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VALUE val;
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{
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long len;
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memset(buf, 0, QUAD_SIZE);
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val = rb_to_int(val);
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if (FIXNUM_P(val)) {
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val = rb_int2big(FIX2LONG(val));
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}
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len = RBIGNUM(val)->len * SIZEOF_BDIGITS;
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if (len > QUAD_SIZE) {
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rb_raise(rb_eRangeError, "bignum too big to convert into `quad int'");
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}
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memcpy(buf, (char*)BDIGITS(val), len);
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if (!RBIGNUM(val)->sign) {
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len = QUAD_SIZE;
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while (len--) {
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*buf = ~*buf;
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buf++;
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}
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}
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}
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#define BNEG(b) (RSHIFT(((BDIGIT*)b)[QUAD_SIZE/SIZEOF_BDIGITS-1],BITSPERDIG-1) != 0)
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VALUE
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rb_quad_unpack(buf, sign)
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const char *buf;
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int sign;
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{
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VALUE big = bignew(QUAD_SIZE/SIZEOF_BDIGITS, 1);
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memcpy((char*)BDIGITS(big), buf, QUAD_SIZE);
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if (sign && BNEG(buf)) {
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long len = QUAD_SIZE;
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char *tmp = (char*)BDIGITS(big);
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RBIGNUM(big)->sign = 0;
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while (len--) {
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*tmp = ~*tmp;
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tmp++;
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}
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}
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return bignorm(big);
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}
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#endif
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VALUE
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rb_cstr_to_inum(str, base, badcheck)
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const char *str;
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int base;
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int badcheck;
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{
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const char *s = str;
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char *end;
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char sign = 1, nondigit = 0;
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int c;
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BDIGIT_DBL num;
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long len, blen = 1;
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long i;
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VALUE z;
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BDIGIT *zds;
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if (!str) {
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if (badcheck) goto bad;
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return INT2FIX(0);
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}
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if (badcheck) {
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while (ISSPACE(*str)) str++;
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}
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else {
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while (ISSPACE(*str) || *str == '_') str++;
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}
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if (str[0] == '+') {
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str++;
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}
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else if (str[0] == '-') {
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str++;
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sign = 0;
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}
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if (str[0] == '+' || str[0] == '-') {
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if (badcheck) goto bad;
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return INT2FIX(0);
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}
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if (base <= 0) {
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if (str[0] == '0') {
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switch (str[1]) {
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case 'x': case 'X':
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base = 16;
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break;
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case 'b': case 'B':
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base = 2;
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break;
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case 'o': case 'O':
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base = 8;
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break;
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case 'd': case 'D':
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base = 10;
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break;
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default:
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base = 8;
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}
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}
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else if (base < -1) {
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base = -base;
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}
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else {
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base = 10;
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}
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}
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switch (base) {
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case 2:
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len = 1;
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if (str[0] == '0' && (str[1] == 'b'||str[1] == 'B')) {
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str += 2;
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}
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break;
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case 3:
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len = 2;
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break;
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case 8:
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if (str[0] == '0' && (str[1] == 'o'||str[1] == 'O')) {
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str += 2;
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}
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case 4: case 5: case 6: case 7:
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len = 3;
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break;
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case 10:
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if (str[0] == '0' && (str[1] == 'd'||str[1] == 'D')) {
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str += 2;
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}
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case 9: case 11: case 12: case 13: case 14: case 15:
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len = 4;
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break;
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case 16:
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len = 4;
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if (str[0] == '0' && (str[1] == 'x'||str[1] == 'X')) {
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str += 2;
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}
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break;
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default:
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if (base < 2 || 36 < base) {
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rb_raise(rb_eArgError, "illegal radix %d", base);
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}
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if (base <= 32) {
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len = 5;
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}
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else {
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len = 6;
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}
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break;
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}
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if (*str == '0') { /* squeeze preceeding 0s */
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while (*++str == '0');
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--str;
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}
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len *= strlen(str)*sizeof(char);
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if (len <= (sizeof(VALUE)*CHAR_BIT)) {
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unsigned long val = strtoul((char*)str, &end, base);
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if (*end == '_') goto bigparse;
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if (badcheck) {
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if (end == str) goto bad; /* no number */
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while (*end && ISSPACE(*end)) end++;
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if (*end) goto bad; /* trailing garbage */
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}
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if (POSFIXABLE(val)) {
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if (sign) return LONG2FIX(val);
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else {
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long result = -(long)val;
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return LONG2FIX(result);
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}
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}
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else {
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VALUE big = rb_uint2big(val);
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RBIGNUM(big)->sign = sign;
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return bignorm(big);
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}
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}
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bigparse:
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len = (len/BITSPERDIG)+1;
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if (badcheck && *str == '_') goto bad;
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z = bignew(len, sign);
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zds = BDIGITS(z);
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for (i=len;i--;) zds[i]=0;
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while (c = *str++) {
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if (c == '_') {
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if (badcheck) {
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if (nondigit) goto bad;
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nondigit = c;
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}
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continue;
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}
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else if (!ISASCII(c)) {
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break;
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}
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else if (isdigit(c)) {
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c -= '0';
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}
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else if (islower(c)) {
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c -= 'a' - 10;
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}
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else if (isupper(c)) {
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c -= 'A' - 10;
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}
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else {
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break;
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}
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if (c >= base) break;
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nondigit = 0;
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i = 0;
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num = c;
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for (;;) {
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while (i<blen) {
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num += (BDIGIT_DBL)zds[i]*base;
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zds[i++] = BIGLO(num);
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num = BIGDN(num);
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}
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if (num) {
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blen++;
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continue;
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}
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break;
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}
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}
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if (badcheck) {
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str--;
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if (s+1 < str && str[-1] == '_') goto bad;
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while (*str && ISSPACE(*str)) str++;
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if (*str) {
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bad:
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rb_invalid_str(s, "Integer");
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}
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}
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return bignorm(z);
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}
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VALUE
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rb_str_to_inum(str, base, badcheck)
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VALUE str;
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int base;
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int badcheck;
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{
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char *s;
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long len;
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StringValue(str);
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if (badcheck) {
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s = StringValueCStr(str);
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}
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else {
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s = RSTRING(str)->ptr;
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}
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if (s) {
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len = RSTRING(str)->len;
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if (s[len]) { /* no sentinel somehow */
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char *p = ALLOCA_N(char, len+1);
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MEMCPY(p, s, char, len);
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p[len] = '\0';
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s = p;
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}
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}
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return rb_cstr_to_inum(s, base, badcheck);
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}
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#if HAVE_LONG_LONG
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VALUE
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rb_ull2big(n)
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unsigned LONG_LONG n;
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{
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BDIGIT_DBL num = n;
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long i = 0;
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BDIGIT *digits;
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VALUE big;
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big = bignew(DIGSPERLL, 1);
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digits = BDIGITS(big);
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while (i < DIGSPERLL) {
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digits[i++] = BIGLO(num);
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num = BIGDN(num);
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}
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i = DIGSPERLL;
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while (i-- && !digits[i]) ;
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RBIGNUM(big)->len = i+1;
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return big;
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}
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VALUE
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rb_ll2big(n)
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LONG_LONG n;
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{
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long neg = 0;
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VALUE big;
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if (n < 0) {
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n = -n;
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neg = 1;
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}
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big = rb_ull2big(n);
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if (neg) {
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RBIGNUM(big)->sign = 0;
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}
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return big;
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}
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VALUE
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rb_ull2inum(n)
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unsigned LONG_LONG n;
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{
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if (POSFIXABLE(n)) return LONG2FIX(n);
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return rb_ull2big(n);
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}
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VALUE
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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;
|
|
}
|
|
|
|
/*
|
|
* 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, check)
|
|
VALUE x;
|
|
char *type;
|
|
int check;
|
|
{
|
|
long len = RBIGNUM(x)->len;
|
|
BDIGIT_DBL num;
|
|
BDIGIT *ds;
|
|
|
|
if (len > SIZEOF_LONG/SIZEOF_BDIGITS) {
|
|
if (check)
|
|
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
|
|
len = SIZEOF_LONG/SIZEOF_BDIGITS;
|
|
}
|
|
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", Qfalse);
|
|
if (!RBIGNUM(x)->sign) {
|
|
return -num;
|
|
}
|
|
return num;
|
|
}
|
|
|
|
unsigned long
|
|
rb_big2ulong(x)
|
|
VALUE x;
|
|
{
|
|
unsigned long num = big2ulong(x, "unsigned long", Qtrue);
|
|
|
|
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", Qtrue);
|
|
|
|
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));
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
b = rb_big2dbl(x);
|
|
if (isnan(a) || isnan(b)) return Qfalse;
|
|
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 = 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;
|
|
}
|
|
|
|
/*
|
|
* 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);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* big * other => Numeric
|
|
*
|
|
* Multiplies big and other, returning the result.
|
|
*/
|
|
|
|
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;
|
|
}
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* 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);
|
|
}
|
|
|
|
/*
|
|
* 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
|
|
*
|
|
* 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 = 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);
|
|
}
|
|
|
|
/*
|
|
* 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 = 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));
|
|
}
|
|
|
|
/*
|
|
* 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, 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);
|
|
}
|
|
|
|
/*
|
|
* 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, 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);
|
|
}
|
|
|
|
/*
|
|
* 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, 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));
|
|
|
|
/*
|
|
* call-seq:
|
|
* big << numeric => integer
|
|
*
|
|
* Shifts big left _numeric_ positions (right if _numeric_ is negative).
|
|
*/
|
|
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* big >> numeric => integer
|
|
*
|
|
* Shifts big right _numeric_ positions (left if _numeric_ is negative).
|
|
*/
|
|
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* 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 {
|
|
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, "**", 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);
|
|
}
|