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ruby/bignum.c

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C
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/**********************************************************************
bignum.c -
$Author$
$Date$
created at: Fri Jun 10 00:48:55 JST 1994
Copyright (C) 1993-2002 Yukihiro Matsumoto
**********************************************************************/
#include <math.h>
#include <ctype.h>
#include "ruby.h"
VALUE rb_cBignum;
#if defined __MINGW32__
#define USHORT _USHORT
#endif
#if SIZEOF_INT*2 <= SIZEOF_LONG_LONG
typedef unsigned int BDIGIT;
typedef unsigned LONG_LONG BDIGIT_DBL;
typedef LONG_LONG BDIGIT_DBL_SIGNED;
#elif SIZEOF_INT*2 <= SIZEOF_LONG
typedef unsigned int BDIGIT;
typedef unsigned long BDIGIT_DBL;
typedef LONG_LONG BDIGIT_DBL_SIGNED;
#else
typedef unsigned short BDIGIT;
typedef unsigned long BDIGIT_DBL;
typedef long BDIGIT_DBL_SIGNED;
#endif
#define BDIGITS(x) ((BDIGIT*)RBIGNUM(x)->digits)
#define BITSPERDIG (sizeof(BDIGIT)*CHAR_BIT)
#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
#define DIGSPERLONG ((unsigned int)(sizeof(long)/sizeof(BDIGIT)))
#if HAVE_LONG_LONG
# define DIGSPERLL ((unsigned int)(sizeof(LONG_LONG)/sizeof(BDIGIT)))
#endif
#define BIGUP(x) ((BDIGIT_DBL)(x) << BITSPERDIG)
#define BIGDN(x) RSHIFT(x,BITSPERDIG)
#define BIGLO(x) ((BDIGIT)((x) & (BIGRAD-1)))
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[0] == 1 || ds[0] == 0) {
if (RBIGNUM(x)->len == 1) return;
for (i=1; i<RBIGNUM(x)->len; i++) {
if (ds[i] != 0) return;
}
REALLOC_N(RBIGNUM(x)->digits, BDIGIT, RBIGNUM(x)->len++);
ds = BDIGITS(x);
ds[RBIGNUM(x)->len-1] = 1;
}
}
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(BDIGIT) <= sizeof(VALUE)) {
long num = 0;
while (len--) {
num = BIGUP(num) + ds[len];
}
if (num >= 0) {
if (RBIGNUM(x)->sign) {
if (POSFIXABLE(num)) return INT2FIX(num);
}
else if (NEGFIXABLE(-(long)num)) return INT2FIX(-(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;
i = 0;
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 INT2FIX(n);
return rb_uint2big(n);
}
VALUE
rb_int2inum(n)
long n;
{
if (FIXABLE(n)) return INT2FIX(n);
return rb_int2big(n);
}
#ifdef HAVE_LONG_LONG
#define DIGSPERLONGLONG ((unsigned int)(sizeof(LONG_LONG)/sizeof(BDIGIT)))
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];
}
}
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 = 0;
BDIGIT *digits;
VALUE big;
memcpy(&q, buf, sizeof(LONG_LONG));
if (sign) {
if (FIXABLE((LONG_LONG)q)) return INT2FIX((LONG_LONG)q);
if ((LONG_LONG)q < 0) {
q = -(LONG_LONG)q;
neg = 1;
}
}
else {
if (POSFIXABLE(q)) return INT2FIX(q);
}
i = 0;
big = bignew(DIGSPERLONGLONG, 1);
digits = BDIGITS(big);
while (i < DIGSPERLONGLONG) {
digits[i++] = BIGLO(q);
q = BIGDN(q);
}
i = DIGSPERLONGLONG;
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(BDIGIT);
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(BDIGIT)-1],BITSPERDIG-1) != 0)
VALUE
rb_quad_unpack(buf, sign)
const char *buf;
int sign;
{
VALUE big = bignew(QUAD_SIZE/sizeof(BDIGIT), 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 (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') {
if (str[1] == 'x' || str[1] == 'X') {
base = 16;
}
else if (str[1] == 'b' || str[1] == 'B') {
base = 2;
}
else {
base = 8;
}
}
else if (base < -1) {
base = -base;
}
else {
base = 10;
}
}
if (base == 8) {
len = 3;
}
else { /* base == 10, 2 or 16 */
if (base == 16 && str[0] == '0' && (str[1] == 'x'||str[1] == 'X')) {
str += 2;
}
else if (base == 2 && str[0] == '0' && (str[1] == 'b'||str[1] == 'B')) {
str += 2;
}
len = 4;
}
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) { /* trailing garbage */
bad:
rb_invalid_str(s, "Integer");
}
}
if (POSFIXABLE(val)) {
if (sign) return INT2FIX(val);
else {
long result = -(long)val;
return INT2FIX(result);
}
}
else {
VALUE big = rb_uint2big(val);
RBIGNUM(big)->sign = sign;
return 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++) {
switch (c) {
case '8': case '9':
if (base == 8) {
c = base;
break;
}
case '0': case '1': case '2': case '3': case '4':
case '5': case '6': case '7':
c = c - '0';
nondigit = 0;
break;
case 'a': case 'b': case 'c':
case 'd': case 'e': case 'f':
c -= 'a' - 'A';
case 'A': case 'B': case 'C':
case 'D': case 'E': case 'F':
if (base != 16) {
nondigit = c;
c = base;
}
else {
c = c - 'A' + 10;
nondigit = 0;
}
break;
case '_':
if (badcheck) {
if (nondigit) goto bad;
nondigit = c;
}
continue;
default:
c = base;
break;
}
if (c >= base) break;
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) goto bad;
}
return bignorm(z);
}
VALUE
rb_str_to_inum(str, base, badcheck)
VALUE str;
int base;
int badcheck;
{
char *s;
int len;
StringValue(str);
s = RSTRING(str)->ptr;
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;
}
if (badcheck && len != strlen(s)) {
rb_raise(rb_eArgError, "string for Integer contains null byte");
}
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;
i = 0;
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 INT2FIX(n);
return rb_ull2big(n);
}
VALUE
rb_ll2inum(n)
LONG_LONG n;
{
if (FIXABLE(n)) return INT2FIX(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);
}
static char hexmap[] = "0123456789abcdef";
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 (i == 0) return rb_str_new2("0");
if (base == 10) {
j = (sizeof(BDIGIT)/sizeof(char)*CHAR_BIT*i*241L)/800+2;
hbase = 10000;
}
else if (base == 16) {
j = (sizeof(BDIGIT)/sizeof(char)*CHAR_BIT*i)/4+2;
hbase = 0x10000;
}
else if (base == 8) {
j = (sizeof(BDIGIT)/sizeof(char)*CHAR_BIT*i)+2;
hbase = 010000;
}
else if (base == 2) {
j = (sizeof(BDIGIT)*CHAR_BIT*i)+2;
hbase = 020;
}
else {
rb_raise(rb_eArgError, "illegal radix %d", base);
}
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 = 4;
while (k--) {
c = (char)(num % base);
s[--j] = hexmap[(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(BDIGIT))
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(BDIGIT))
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 (!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:
{
double d = rb_big2dbl(x);
if (d == RFLOAT(y)->value) return INT2FIX(0);
if (d > RFLOAT(y)->value) return INT2FIX(1);
if (d < RFLOAT(y)->value) return INT2FIX(-1);
}
break;
default:
return rb_num_coerce_bin(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:
return (rb_big2dbl(x) == RFLOAT(y)->value)?Qtrue:Qfalse;
default:
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_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;
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;
yds = BDIGITS(y);
if (ny == 0 && yds[0] == 0) rb_num_zerodiv();
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) { /* just 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 && RBIGNUM(mod)->len > 0) {
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));
}
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;
z = x;
for (;;) {
yy = yy - 1;
if (yy == 0) break;
while (yy % 2 == 0) {
yy = yy / 2;
x = rb_big_mul(x, x);
}
z = rb_big_mul(z, x);
}
if (!FIXNUM_P(z)) z = bignorm(z);
return 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);
int s1 = shift/BITSPERDIG;
int s2 = shift%BITSPERDIG;
VALUE z;
BDIGIT_DBL num = 0;
long i = RBIGNUM(x)->len;
long 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);
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;
int 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 INT2FIX(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_class2name(CLASS_OF(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;
}
/* !!!warnig!!!!
this is not really a random number!!
*/
VALUE
rb_big_rand(max, rand)
VALUE max;
double rand;
{
VALUE v;
long len;
len = RBIGNUM(max)->len;
v = bignew(len,1);
while (len--) {
BDIGITS(v)[len] = ((BDIGIT)~0) * rand;
}
return rb_big_modulo((VALUE)v, max);
}
static VALUE
rb_big_size(big)
VALUE big;
{
return INT2FIX(RBIGNUM(big)->len*sizeof(BDIGIT));
}
static VALUE
rb_big_zero_p(big)
VALUE big;
{
return Qfalse;
}
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, "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, "**", 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, "===", 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);
rb_define_method(rb_cBignum, "zero?", rb_big_zero_p, 0);
}
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