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ruby/bignum.c

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70 KiB
C
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/**********************************************************************
bignum.c -
$Author$
created at: Fri Jun 10 00:48:55 JST 1994
Copyright (C) 1993-2007 Yukihiro Matsumoto
**********************************************************************/
#include "ruby/ruby.h"
#include "ruby/util.h"
#include <math.h>
#include <float.h>
#include <ctype.h>
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
#include <assert.h>
VALUE rb_cBignum;
#if defined __MINGW32__
#define USHORT _USHORT
#endif
#define BDIGITS(x) (RBIGNUM_DIGITS(x))
#define BITSPERDIG (SIZEOF_BDIGITS*CHAR_BIT)
#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
#define DIGSPERLONG (SIZEOF_LONG/SIZEOF_BDIGITS)
#if HAVE_LONG_LONG
# define DIGSPERLL (SIZEOF_LONG_LONG/SIZEOF_BDIGITS)
#endif
#define BIGUP(x) ((BDIGIT_DBL)(x) << BITSPERDIG)
#define BIGDN(x) RSHIFT(x,BITSPERDIG)
#define BIGLO(x) ((BDIGIT)((x) & (BIGRAD-1)))
#define BDIGMAX ((BDIGIT)-1)
#define BIGZEROP(x) (RBIGNUM_LEN(x) == 0 || \
(BDIGITS(x)[0] == 0 && \
(RBIGNUM_LEN(x) == 1 || bigzero_p(x))))
static int
bigzero_p(VALUE x)
{
long i;
BDIGIT *ds = BDIGITS(x);
for (i = RBIGNUM_LEN(x) - 1; 0 <= i; i--) {
if (ds[i]) return 0;
}
return 1;
}
int
rb_bigzero_p(VALUE x)
{
return BIGZEROP(x);
}
int
rb_cmpint(VALUE val, VALUE a, VALUE b)
{
if (NIL_P(val)) {
rb_cmperr(a, b);
}
if (FIXNUM_P(val)) {
long l = FIX2LONG(val);
if (l > 0) return 1;
if (l < 0) return -1;
return 0;
}
if (TYPE(val) == T_BIGNUM) {
if (BIGZEROP(val)) return 0;
if (RBIGNUM_SIGN(val)) return 1;
return -1;
}
if (RTEST(rb_funcall(val, '>', 1, INT2FIX(0)))) return 1;
if (RTEST(rb_funcall(val, '<', 1, INT2FIX(0)))) return -1;
return 0;
}
#define RBIGNUM_SET_LEN(b,l) \
((RBASIC(b)->flags & RBIGNUM_EMBED_FLAG) ? \
(void)(RBASIC(b)->flags = \
(RBASIC(b)->flags & ~RBIGNUM_EMBED_LEN_MASK) | \
((l) << RBIGNUM_EMBED_LEN_SHIFT)) : \
(void)(RBIGNUM(b)->as.heap.len = (l)))
static void
rb_big_realloc(VALUE big, long len)
{
BDIGIT *ds;
if (RBASIC(big)->flags & RBIGNUM_EMBED_FLAG) {
if (RBIGNUM_EMBED_LEN_MAX < len) {
ds = ALLOC_N(BDIGIT, len);
MEMCPY(ds, RBIGNUM(big)->as.ary, BDIGIT, RBIGNUM_EMBED_LEN_MAX);
RBIGNUM(big)->as.heap.len = RBIGNUM_LEN(big);
RBIGNUM(big)->as.heap.digits = ds;
RBASIC(big)->flags &= ~RBIGNUM_EMBED_FLAG;
}
}
else {
if (len <= RBIGNUM_EMBED_LEN_MAX) {
ds = RBIGNUM(big)->as.heap.digits;
RBASIC(big)->flags |= RBIGNUM_EMBED_FLAG;
RBIGNUM_SET_LEN(big, len);
if (ds) {
MEMCPY(RBIGNUM(big)->as.ary, ds, BDIGIT, len);
xfree(ds);
}
}
else {
if (RBIGNUM_LEN(big) == 0) {
RBIGNUM(big)->as.heap.digits = ALLOC_N(BDIGIT, len);
}
else {
REALLOC_N(RBIGNUM(big)->as.heap.digits, BDIGIT, len);
}
}
}
}
void
rb_big_resize(VALUE big, long len)
{
rb_big_realloc(big, len);
RBIGNUM_SET_LEN(big, len);
}
static VALUE
bignew_1(VALUE klass, long len, int sign)
{
NEWOBJ(big, struct RBignum);
OBJSETUP(big, klass, T_BIGNUM);
RBIGNUM_SET_SIGN(big, sign?1:0);
if (len <= RBIGNUM_EMBED_LEN_MAX) {
RBASIC(big)->flags |= RBIGNUM_EMBED_FLAG;
RBIGNUM_SET_LEN(big, len);
}
else {
RBIGNUM(big)->as.heap.digits = ALLOC_N(BDIGIT, len);
RBIGNUM(big)->as.heap.len = len;
}
return (VALUE)big;
}
#define bignew(len,sign) bignew_1(rb_cBignum,len,sign)
VALUE
rb_big_new(long len, int sign)
{
return bignew(len, sign != 0);
}
VALUE
rb_big_clone(VALUE x)
{
long len = RBIGNUM_LEN(x);
VALUE z = bignew_1(CLASS_OF(x), len, RBIGNUM_SIGN(x));
MEMCPY(BDIGITS(z), BDIGITS(x), BDIGIT, len);
return z;
}
/* modify a bignum by 2's complement */
static void
get2comp(VALUE x)
{
long i = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
BDIGIT_DBL num;
if (!i) return;
while (i--) ds[i] = ~ds[i];
i = 0; num = 1;
do {
num += ds[i];
ds[i++] = BIGLO(num);
num = BIGDN(num);
} while (i < RBIGNUM_LEN(x));
if (num != 0) {
rb_big_resize(x, RBIGNUM_LEN(x)+1);
ds = BDIGITS(x);
ds[RBIGNUM_LEN(x)-1] = 1;
}
}
void
rb_big_2comp(VALUE x) /* get 2's complement */
{
get2comp(x);
}
static inline VALUE
bigtrunc(VALUE x)
{
long len = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
if (len == 0) return x;
while (--len && !ds[len]);
if (RBIGNUM_LEN(x) > len+1) {
rb_big_resize(x, len+1);
}
return x;
}
static inline VALUE
bigfixize(VALUE x)
{
long len = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
if (len == 0) return INT2FIX(0);
if ((size_t)(len*SIZEOF_BDIGITS) <= sizeof(long)) {
long num = 0;
#if 2*SIZEOF_BDIGITS > SIZEOF_LONG
num = (long)ds[0];
#else
while (len--) {
num = (long)(BIGUP(num) + ds[len]);
}
#endif
if (num >= 0) {
if (RBIGNUM_SIGN(x)) {
if (POSFIXABLE(num)) return LONG2FIX(num);
}
else {
if (NEGFIXABLE(-num)) return LONG2FIX(-num);
}
}
}
return x;
}
static VALUE
bignorm(VALUE x)
{
if (!FIXNUM_P(x) && TYPE(x) == T_BIGNUM) {
x = bigfixize(bigtrunc(x));
}
return x;
}
VALUE
rb_big_norm(VALUE x)
{
return bignorm(x);
}
VALUE
rb_uint2big(VALUE n)
{
BDIGIT_DBL num = n;
long i = 0;
BDIGIT *digits;
VALUE big;
big = bignew(DIGSPERLONG, 1);
digits = BDIGITS(big);
while (i < DIGSPERLONG) {
digits[i++] = BIGLO(num);
num = BIGDN(num);
}
i = DIGSPERLONG;
while (--i && !digits[i]) ;
RBIGNUM_SET_LEN(big, i+1);
return big;
}
VALUE
rb_int2big(SIGNED_VALUE n)
{
long neg = 0;
VALUE big;
if (n < 0) {
n = -n;
neg = 1;
}
big = rb_uint2big(n);
if (neg) {
RBIGNUM_SET_SIGN(big, 0);
}
return big;
}
VALUE
rb_uint2inum(VALUE n)
{
if (POSFIXABLE(n)) return LONG2FIX(n);
return rb_uint2big(n);
}
VALUE
rb_int2inum(SIGNED_VALUE n)
{
if (FIXABLE(n)) return LONG2FIX(n);
return rb_int2big(n);
}
#if SIZEOF_LONG % SIZEOF_BDIGITS != 0
# error unexpected SIZEOF_LONG : SIZEOF_BDIGITS ratio
#endif
/*
* buf is an array of long integers.
* buf is ordered from least significant word to most significant word.
* buf[0] is the least significant word and
* buf[num_longs-1] is the most significant word.
* This means words in buf is little endian.
* However each word in buf is native endian.
* (buf[i]&1) is the least significant bit and
* (buf[i]&(1<<(SIZEOF_LONG*CHAR_BIT-1))) is the most significant bit
* for each 0 <= i < num_longs.
* So buf is little endian at whole on a little endian machine.
* But buf is mixed endian on a big endian machine.
*/
void
rb_big_pack(VALUE val, unsigned long *buf, long num_longs)
{
val = rb_to_int(val);
if (num_longs == 0)
return;
if (FIXNUM_P(val)) {
long i;
long tmp = FIX2LONG(val);
buf[0] = (unsigned long)tmp;
tmp = tmp < 0 ? ~0L : 0;
for (i = 1; i < num_longs; i++)
buf[i] = (unsigned long)tmp;
return;
}
else {
long len = RBIGNUM_LEN(val);
BDIGIT *ds = BDIGITS(val), *dend = ds + len;
long i, j;
for (i = 0; i < num_longs && ds < dend; i++) {
unsigned long l = 0;
for (j = 0; j < DIGSPERLONG && ds < dend; j++, ds++) {
l |= ((unsigned long)*ds << (j * BITSPERDIG));
}
buf[i] = l;
}
for (; i < num_longs; i++)
buf[i] = 0;
if (RBIGNUM_NEGATIVE_P(val)) {
for (i = 0; i < num_longs; i++) {
buf[i] = ~buf[i];
}
for (i = 0; i < num_longs; i++) {
buf[i]++;
if (buf[i] != 0)
return;
}
}
}
}
/* See rb_big_pack comment for endianness of buf. */
VALUE
rb_big_unpack(unsigned long *buf, long num_longs)
{
while (2 <= num_longs) {
if (buf[num_longs-1] == 0 && (long)buf[num_longs-2] >= 0)
num_longs--;
else if (buf[num_longs-1] == ~0UL && (long)buf[num_longs-2] < 0)
num_longs--;
else
break;
}
if (num_longs == 0)
return INT2FIX(0);
else if (num_longs == 1)
return LONG2NUM((long)buf[0]);
else {
VALUE big;
BDIGIT *ds;
long len = num_longs * DIGSPERLONG;
long i;
big = bignew(len, 1);
ds = BDIGITS(big);
for (i = 0; i < num_longs; i++) {
unsigned long d = buf[i];
#if SIZEOF_LONG == SIZEOF_BDIGITS
*ds++ = d;
#else
int j;
for (j = 0; j < DIGSPERLONG; j++) {
*ds++ = BIGLO(d);
d = BIGDN(d);
}
#endif
}
if ((long)buf[num_longs-1] < 0) {
get2comp(big);
RBIGNUM_SET_SIGN(big, 0);
}
return bignorm(big);
}
}
#define QUAD_SIZE 8
#if SIZEOF_LONG_LONG == QUAD_SIZE && SIZEOF_BDIGITS*2 == SIZEOF_LONG_LONG
void
rb_quad_pack(char *buf, VALUE val)
{
LONG_LONG q;
val = rb_to_int(val);
if (FIXNUM_P(val)) {
q = FIX2LONG(val);
}
else {
long len = RBIGNUM_LEN(val);
BDIGIT *ds;
if (len > SIZEOF_LONG_LONG/SIZEOF_BDIGITS) {
len = SIZEOF_LONG_LONG/SIZEOF_BDIGITS;
}
ds = BDIGITS(val);
q = 0;
while (len--) {
q = BIGUP(q);
q += ds[len];
}
if (!RBIGNUM_SIGN(val)) q = -q;
}
memcpy(buf, (char*)&q, SIZEOF_LONG_LONG);
}
VALUE
rb_quad_unpack(const char *buf, int sign)
{
unsigned LONG_LONG q;
long neg = 0;
long i;
BDIGIT *digits;
VALUE big;
memcpy(&q, buf, SIZEOF_LONG_LONG);
if (sign) {
if (FIXABLE((LONG_LONG)q)) return LONG2FIX((LONG_LONG)q);
if ((LONG_LONG)q < 0) {
q = -(LONG_LONG)q;
neg = 1;
}
}
else {
if (POSFIXABLE(q)) return LONG2FIX(q);
}
i = 0;
big = bignew(DIGSPERLL, 1);
digits = BDIGITS(big);
while (i < DIGSPERLL) {
digits[i++] = BIGLO(q);
q = BIGDN(q);
}
i = DIGSPERLL;
while (i-- && !digits[i]) ;
RBIGNUM_SET_LEN(big, i+1);
if (neg) {
RBIGNUM_SET_SIGN(big, 0);
}
return bignorm(big);
}
#else
static int
quad_buf_complement(char *buf, size_t len)
{
size_t i;
for (i = 0; i < len; i++)
buf[i] = ~buf[i];
for (i = 0; i < len; i++) {
buf[i]++;
if (buf[i] != 0)
return 0;
}
return 1;
}
void
rb_quad_pack(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_LEN(val) * SIZEOF_BDIGITS;
if (len > QUAD_SIZE) {
len = QUAD_SIZE;
}
memcpy(buf, (char*)BDIGITS(val), len);
if (RBIGNUM_NEGATIVE_P(val)) {
quad_buf_complement(buf, QUAD_SIZE);
}
}
#define BNEG(b) (RSHIFT(((BDIGIT*)b)[QUAD_SIZE/SIZEOF_BDIGITS-1],BITSPERDIG-1) != 0)
VALUE
rb_quad_unpack(const char *buf, int sign)
{
VALUE big = bignew(QUAD_SIZE/SIZEOF_BDIGITS, 1);
memcpy((char*)BDIGITS(big), buf, QUAD_SIZE);
if (sign && BNEG(buf)) {
char *tmp = (char*)BDIGITS(big);
RBIGNUM_SET_SIGN(big, 0);
quad_buf_complement(tmp, QUAD_SIZE);
}
return bignorm(big);
}
#endif
VALUE
rb_cstr_to_inum(const char *str, int base, int badcheck)
{
const char *s = str;
char *end;
char sign = 1, nondigit = 0;
int c;
BDIGIT_DBL num;
long len, blen = 1;
long i;
VALUE z;
BDIGIT *zds;
#undef ISDIGIT
#define ISDIGIT(c) ('0' <= (c) && (c) <= '9')
#define conv_digit(c) \
(!ISASCII(c) ? -1 : \
ISDIGIT(c) ? ((c) - '0') : \
ISLOWER(c) ? ((c) - 'a' + 10) : \
ISUPPER(c) ? ((c) - 'A' + 10) : \
-1)
if (!str) {
if (badcheck) goto bad;
return INT2FIX(0);
}
while (ISSPACE(*str)) str++;
if (str[0] == '+') {
str++;
}
else if (str[0] == '-') {
str++;
sign = 0;
}
if (str[0] == '+' || str[0] == '-') {
if (badcheck) goto bad;
return INT2FIX(0);
}
if (base <= 0) {
if (str[0] == '0') {
switch (str[1]) {
case 'x': case 'X':
base = 16;
break;
case 'b': case 'B':
base = 2;
break;
case 'o': case 'O':
base = 8;
break;
case 'd': case 'D':
base = 10;
break;
default:
base = 8;
}
}
else if (base < -1) {
base = -base;
}
else {
base = 10;
}
}
switch (base) {
case 2:
len = 1;
if (str[0] == '0' && (str[1] == 'b'||str[1] == 'B')) {
str += 2;
}
break;
case 3:
len = 2;
break;
case 8:
if (str[0] == '0' && (str[1] == 'o'||str[1] == 'O')) {
str += 2;
}
case 4: case 5: case 6: case 7:
len = 3;
break;
case 10:
if (str[0] == '0' && (str[1] == 'd'||str[1] == 'D')) {
str += 2;
}
case 9: case 11: case 12: case 13: case 14: case 15:
len = 4;
break;
case 16:
len = 4;
if (str[0] == '0' && (str[1] == 'x'||str[1] == 'X')) {
str += 2;
}
break;
default:
if (base < 2 || 36 < base) {
rb_raise(rb_eArgError, "invalid radix %d", base);
}
if (base <= 32) {
len = 5;
}
else {
len = 6;
}
break;
}
if (*str == '0') { /* squeeze preceding 0s */
int us = 0;
while ((c = *++str) == '0' || c == '_') {
if (c == '_') {
if (++us >= 2)
break;
} else
us = 0;
}
if (!(c = *str) || ISSPACE(c)) --str;
}
c = *str;
c = conv_digit(c);
if (c < 0 || c >= base) {
if (badcheck) goto bad;
return INT2FIX(0);
}
len *= strlen(str)*sizeof(char);
if ((size_t)len <= (sizeof(long)*CHAR_BIT)) {
unsigned long val = STRTOUL(str, &end, base);
if (str < end && *end == '_') goto bigparse;
if (badcheck) {
if (end == str) goto bad; /* no number */
while (*end && ISSPACE(*end)) end++;
if (*end) goto bad; /* trailing garbage */
}
if (POSFIXABLE(val)) {
if (sign) return LONG2FIX(val);
else {
long result = -(long)val;
return LONG2FIX(result);
}
}
else {
VALUE big = rb_uint2big(val);
RBIGNUM_SET_SIGN(big, sign);
return bignorm(big);
}
}
bigparse:
len = (len/BITSPERDIG)+1;
if (badcheck && *str == '_') goto bad;
z = bignew(len, sign);
zds = BDIGITS(z);
for (i=len;i--;) zds[i]=0;
while ((c = *str++) != 0) {
if (c == '_') {
if (nondigit) {
if (badcheck) goto bad;
break;
}
nondigit = c;
continue;
}
else if ((c = conv_digit(c)) < 0) {
break;
}
if (c >= base) break;
nondigit = 0;
i = 0;
num = c;
for (;;) {
while (i<blen) {
num += (BDIGIT_DBL)zds[i]*base;
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
if (num) {
blen++;
continue;
}
break;
}
}
if (badcheck) {
str--;
if (s+1 < str && str[-1] == '_') goto bad;
while (*str && ISSPACE(*str)) str++;
if (*str) {
bad:
rb_invalid_str(s, "Integer()");
}
}
return bignorm(z);
}
VALUE
rb_str_to_inum(VALUE str, int base, int badcheck)
{
char *s;
long len;
StringValue(str);
if (badcheck) {
s = StringValueCStr(str);
}
else {
s = RSTRING_PTR(str);
}
if (s) {
len = RSTRING_LEN(str);
if (s[len]) { /* no sentinel somehow */
char *p = ALLOCA_N(char, len+1);
MEMCPY(p, s, char, len);
p[len] = '\0';
s = p;
}
}
return rb_cstr_to_inum(s, base, badcheck);
}
#if HAVE_LONG_LONG
static VALUE
rb_ull2big(unsigned LONG_LONG n)
{
BDIGIT_DBL num = n;
long i = 0;
BDIGIT *digits;
VALUE big;
big = bignew(DIGSPERLL, 1);
digits = BDIGITS(big);
while (i < DIGSPERLL) {
digits[i++] = BIGLO(num);
num = BIGDN(num);
}
i = DIGSPERLL;
while (i-- && !digits[i]) ;
RBIGNUM_SET_LEN(big, i+1);
return big;
}
static VALUE
rb_ll2big(LONG_LONG n)
{
long neg = 0;
VALUE big;
if (n < 0) {
n = -n;
neg = 1;
}
big = rb_ull2big(n);
if (neg) {
RBIGNUM_SET_SIGN(big, 0);
}
return big;
}
VALUE
rb_ull2inum(unsigned LONG_LONG n)
{
if (POSFIXABLE(n)) return LONG2FIX(n);
return rb_ull2big(n);
}
VALUE
rb_ll2inum(LONG_LONG n)
{
if (FIXABLE(n)) return LONG2FIX(n);
return rb_ll2big(n);
}
#endif /* HAVE_LONG_LONG */
VALUE
rb_cstr2inum(const char *str, int base)
{
return rb_cstr_to_inum(str, base, base==0);
}
VALUE
rb_str2inum(VALUE str, int base)
{
return rb_str_to_inum(str, base, base==0);
}
const char ruby_digitmap[] = "0123456789abcdefghijklmnopqrstuvwxyz";
static VALUE bigsqr(VALUE x);
static void bigdivmod(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp);
#define POW2_P(x) (((x)&((x)-1))==0)
static inline int
ones(register unsigned long x)
{
#if SIZEOF_LONG == 8
# define MASK_55 0x5555555555555555UL
# define MASK_33 0x3333333333333333UL
# define MASK_0f 0x0f0f0f0f0f0f0f0fUL
#else
# define MASK_55 0x55555555UL
# define MASK_33 0x33333333UL
# define MASK_0f 0x0f0f0f0fUL
#endif
x -= (x >> 1) & MASK_55;
x = ((x >> 2) & MASK_33) + (x & MASK_33);
x = ((x >> 4) + x) & MASK_0f;
x += (x >> 8);
x += (x >> 16);
#if SIZEOF_LONG == 8
x += (x >> 32);
#endif
return (int)(x & 0x7f);
#undef MASK_0f
#undef MASK_33
#undef MASK_55
}
static inline unsigned long
next_pow2(register unsigned long x)
{
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
#if SIZEOF_LONG == 8
x |= x >> 32;
#endif
return x + 1;
}
static inline int
floor_log2(register unsigned long x)
{
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
#if SIZEOF_LONG == 8
x |= x >> 32;
#endif
return (int)ones(x) - 1;
}
static inline int
ceil_log2(register unsigned long x)
{
return floor_log2(x) + !POW2_P(x);
}
#define LOG2_KARATSUBA_DIGITS 7
#define KARATSUBA_DIGITS (1L<<LOG2_KARATSUBA_DIGITS)
#define MAX_BIG2STR_TABLE_ENTRIES 64
static VALUE big2str_power_cache[35][MAX_BIG2STR_TABLE_ENTRIES];
static void
power_cache_init(void)
{
int i, j;
for (i = 0; i < 35; ++i) {
for (j = 0; j < MAX_BIG2STR_TABLE_ENTRIES; ++j) {
big2str_power_cache[i][j] = Qnil;
}
}
}
static inline VALUE
power_cache_get_power0(int base, int i)
{
if (NIL_P(big2str_power_cache[base - 2][i])) {
big2str_power_cache[base - 2][i] =
i == 0 ? rb_big_pow(rb_int2big(base), INT2FIX(KARATSUBA_DIGITS))
: bigsqr(power_cache_get_power0(base, i - 1));
rb_gc_register_mark_object(big2str_power_cache[base - 2][i]);
}
return big2str_power_cache[base - 2][i];
}
static VALUE
power_cache_get_power(int base, long n1, long* m1)
{
int i, m;
long j;
VALUE t;
if (n1 <= KARATSUBA_DIGITS)
rb_bug("n1 > KARATSUBA_DIGITS");
m = ceil_log2(n1);
if (m1) *m1 = 1 << m;
i = m - LOG2_KARATSUBA_DIGITS;
if (i >= MAX_BIG2STR_TABLE_ENTRIES)
i = MAX_BIG2STR_TABLE_ENTRIES - 1;
t = power_cache_get_power0(base, i);
j = KARATSUBA_DIGITS*(1 << i);
while (n1 > j) {
t = bigsqr(t);
j *= 2;
}
return t;
}
/* big2str_muraken_find_n1
*
* Let a natural number x is given by:
* x = 2^0 * x_0 + 2^1 * x_1 + ... + 2^(B*n_0 - 1) * x_{B*n_0 - 1},
* where B is BITSPERDIG (i.e. BDIGITS*CHAR_BIT) and n_0 is
* RBIGNUM_LEN(x).
*
* Now, we assume n_1 = min_n \{ n | 2^(B*n_0/2) <= b_1^(n_1) \}, so
* it is realized that 2^(B*n_0) <= {b_1}^{2*n_1}, where b_1 is a
* given radix number. And then, we have n_1 <= (B*n_0) /
* (2*log_2(b_1)), therefore n_1 is given by ceil((B*n_0) /
* (2*log_2(b_1))).
*/
static long
big2str_find_n1(VALUE x, int base)
{
static const double log_2[] = {
1.0, 1.58496250072116, 2.0,
2.32192809488736, 2.58496250072116, 2.8073549220576,
3.0, 3.16992500144231, 3.32192809488736,
3.4594316186373, 3.58496250072116, 3.70043971814109,
3.8073549220576, 3.90689059560852, 4.0,
4.08746284125034, 4.16992500144231, 4.24792751344359,
4.32192809488736, 4.39231742277876, 4.4594316186373,
4.52356195605701, 4.58496250072116, 4.64385618977472,
4.70043971814109, 4.75488750216347, 4.8073549220576,
4.85798099512757, 4.90689059560852, 4.95419631038688,
5.0, 5.04439411935845, 5.08746284125034,
5.12928301694497, 5.16992500144231
};
long bits;
if (base < 2 || 36 < base)
rb_bug("invalid radix %d", base);
if (FIXNUM_P(x)) {
bits = (SIZEOF_LONG*CHAR_BIT - 1)/2 + 1;
}
else if (BIGZEROP(x)) {
return 0;
}
else if (RBIGNUM_LEN(x) >= LONG_MAX/BITSPERDIG) {
rb_raise(rb_eRangeError, "bignum too big to convert into `string'");
}
else {
bits = BITSPERDIG*RBIGNUM_LEN(x);
}
return (long)ceil(bits/log_2[base - 2]);
}
static long
big2str_orig(VALUE x, int base, char* ptr, long len, long hbase, int trim)
{
long i = RBIGNUM_LEN(x), j = len;
BDIGIT* ds = BDIGITS(x);
while (i && j > 0) {
long k = i;
BDIGIT_DBL num = 0;
while (k--) { /* x / hbase */
num = BIGUP(num) + ds[k];
ds[k] = (BDIGIT)(num / hbase);
num %= hbase;
}
if (trim && ds[i-1] == 0) i--;
k = SIZEOF_BDIGITS;
while (k--) {
ptr[--j] = ruby_digitmap[num % base];
num /= base;
if (j <= 0) break;
if (trim && i == 0 && num == 0) break;
}
}
if (trim) {
while (j < len && ptr[j] == '0') j++;
MEMMOVE(ptr, ptr + j, char, len - j);
len -= j;
}
return len;
}
static long
big2str_karatsuba(VALUE x, int base, char* ptr,
long n1, long len, long hbase, int trim)
{
long lh, ll, m1;
VALUE b, q, r;
if (BIGZEROP(x)) {
if (trim) return 0;
else {
memset(ptr, '0', len);
return len;
}
}
if (n1 <= KARATSUBA_DIGITS) {
return big2str_orig(x, base, ptr, len, hbase, trim);
}
b = power_cache_get_power(base, n1, &m1);
bigdivmod(x, b, &q, &r);
lh = big2str_karatsuba(q, base, ptr, (len - m1)/2,
len - m1, hbase, trim);
rb_big_resize(q, 0);
ll = big2str_karatsuba(r, base, ptr + lh, m1/2,
m1, hbase, !lh && trim);
rb_big_resize(r, 0);
return lh + ll;
}
VALUE
rb_big2str0(VALUE x, int base, int trim)
{
int off;
VALUE ss, xx;
long n1, n2, len, hbase;
char* ptr;
if (FIXNUM_P(x)) {
return rb_fix2str(x, base);
}
if (BIGZEROP(x)) {
return rb_usascii_str_new2("0");
}
if (base < 2 || 36 < base)
rb_raise(rb_eArgError, "invalid radix %d", base);
n2 = big2str_find_n1(x, base);
n1 = (n2 + 1) / 2;
ss = rb_usascii_str_new(0, n2 + 1); /* plus one for sign */
ptr = RSTRING_PTR(ss);
ptr[0] = RBIGNUM_SIGN(x) ? '+' : '-';
hbase = base*base;
#if SIZEOF_BDIGITS > 2
hbase *= hbase;
#endif
off = !(trim && RBIGNUM_SIGN(x)); /* erase plus sign if trim */
xx = rb_big_clone(x);
RBIGNUM_SET_SIGN(xx, 1);
if (n1 <= KARATSUBA_DIGITS) {
len = off + big2str_orig(xx, base, ptr + off, n2, hbase, trim);
}
else {
len = off + big2str_karatsuba(xx, base, ptr + off, n1,
n2, hbase, trim);
}
rb_big_resize(xx, 0);
ptr[len] = '\0';
rb_str_resize(ss, len);
return ss;
}
VALUE
rb_big2str(VALUE x, int base)
{
return rb_big2str0(x, base, 1);
}
/*
* 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(int argc, VALUE *argv, VALUE x)
{
int base;
if (argc == 0) base = 10;
else {
VALUE b;
rb_scan_args(argc, argv, "01", &b);
base = NUM2INT(b);
}
return rb_big2str(x, base);
}
static VALUE
big2ulong(VALUE x, const char *type, int check)
{
long len = RBIGNUM_LEN(x);
BDIGIT_DBL num;
BDIGIT *ds;
if (len > DIGSPERLONG) {
if (check)
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
len = DIGSPERLONG;
}
ds = BDIGITS(x);
num = 0;
while (len--) {
num = BIGUP(num);
num += ds[len];
}
return (VALUE)num;
}
VALUE
rb_big2ulong_pack(VALUE x)
{
VALUE num = big2ulong(x, "unsigned long", FALSE);
if (!RBIGNUM_SIGN(x)) {
return (VALUE)(-(SIGNED_VALUE)num);
}
return num;
}
VALUE
rb_big2ulong(VALUE x)
{
VALUE num = big2ulong(x, "unsigned long", TRUE);
if (!RBIGNUM_SIGN(x)) {
if ((SIGNED_VALUE)num < 0) {
rb_raise(rb_eRangeError, "bignum out of range of unsigned long");
}
return (VALUE)(-(SIGNED_VALUE)num);
}
return num;
}
SIGNED_VALUE
rb_big2long(VALUE x)
{
VALUE num = big2ulong(x, "long", TRUE);
if ((SIGNED_VALUE)num < 0 &&
(RBIGNUM_SIGN(x) || (SIGNED_VALUE)num != LONG_MIN)) {
rb_raise(rb_eRangeError, "bignum too big to convert into `long'");
}
if (!RBIGNUM_SIGN(x)) return -(SIGNED_VALUE)num;
return num;
}
#if HAVE_LONG_LONG
static unsigned LONG_LONG
big2ull(VALUE x, const char *type)
{
long len = RBIGNUM_LEN(x);
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(VALUE x)
{
unsigned LONG_LONG num = big2ull(x, "unsigned long long");
if (!RBIGNUM_SIGN(x))
return (VALUE)(-(SIGNED_VALUE)num);
return num;
}
LONG_LONG
rb_big2ll(VALUE x)
{
unsigned LONG_LONG num = big2ull(x, "long long");
if ((LONG_LONG)num < 0 && (RBIGNUM_SIGN(x)
|| (LONG_LONG)num != LLONG_MIN)) {
rb_raise(rb_eRangeError, "bignum too big to convert into `long long'");
}
if (!RBIGNUM_SIGN(x)) return -(LONG_LONG)num;
return num;
}
#endif /* HAVE_LONG_LONG */
static VALUE
dbl2big(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(double d)
{
return bignorm(dbl2big(d));
}
static int
nlz(BDIGIT x)
{
BDIGIT y;
int n = BITSPERDIG;
#if BITSPERDIG > 64
y = x >> 64; if (y) {n -= 64; x = y;}
#endif
#if BITSPERDIG > 32
y = x >> 32; if (y) {n -= 32; x = y;}
#endif
#if BITSPERDIG > 16
y = x >> 16; if (y) {n -= 16; x = y;}
#endif
y = x >> 8; if (y) {n -= 8; x = y;}
y = x >> 4; if (y) {n -= 4; x = y;}
y = x >> 2; if (y) {n -= 2; x = y;}
y = x >> 1; if (y) {return n - 2;}
return n - x;
}
static double
big2dbl(VALUE x)
{
double d = 0.0;
long i = (bigtrunc(x), RBIGNUM_LEN(x)), lo = 0, bits;
BDIGIT *ds = BDIGITS(x), dl;
if (i) {
bits = i * BITSPERDIG - nlz(ds[i-1]);
if (bits > DBL_MANT_DIG+DBL_MAX_EXP) {
d = HUGE_VAL;
}
else {
if (bits > DBL_MANT_DIG+1)
lo = (bits -= DBL_MANT_DIG+1) / BITSPERDIG;
else
bits = 0;
while (--i > lo) {
d = ds[i] + BIGRAD*d;
}
dl = ds[i];
if (bits && (dl & (1UL << (bits %= BITSPERDIG)))) {
int carry = dl & ~(~(BDIGIT)0 << bits);
if (!carry) {
while (i-- > 0) {
if ((carry = ds[i]) != 0) break;
}
}
if (carry) {
dl &= (BDIGIT)~0 << bits;
dl += (BDIGIT)1 << bits;
if (!dl) d += 1;
}
}
d = dl + BIGRAD*d;
if (lo) {
if (lo > INT_MAX / BITSPERDIG)
d = HUGE_VAL;
else if (lo < INT_MIN / BITSPERDIG)
d = 0.0;
else
d = ldexp(d, (int)(lo * BITSPERDIG));
}
}
}
if (!RBIGNUM_SIGN(x)) d = -d;
return d;
}
double
rb_big2dbl(VALUE x)
{
double d = big2dbl(x);
if (isinf(d)) {
rb_warning("Bignum out of Float range");
if (d < 0.0)
d = -HUGE_VAL;
else
d = HUGE_VAL;
}
return d;
}
/*
* call-seq:
* big.to_f -> float
*
* Converts <i>big</i> to a <code>Float</code>. If <i>big</i> doesn't
* fit in a <code>Float</code>, the result is infinity.
*
*/
static VALUE
rb_big_to_f(VALUE x)
{
return DBL2NUM(rb_big2dbl(x));
}
/*
* call-seq:
* big <=> numeric => -1, 0, +1 or nil
*
* 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>.
*
*/
VALUE
rb_big_cmp(VALUE x, VALUE y)
{
long xlen = RBIGNUM_LEN(x);
BDIGIT *xds, *yds;
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
{
double a = RFLOAT_VALUE(y);
if (isinf(a)) {
if (a > 0.0) return INT2FIX(-1);
else return INT2FIX(1);
}
return rb_dbl_cmp(rb_big2dbl(x), a);
}
default:
return rb_num_coerce_cmp(x, y, rb_intern("<=>"));
}
if (RBIGNUM_SIGN(x) > RBIGNUM_SIGN(y)) return INT2FIX(1);
if (RBIGNUM_SIGN(x) < RBIGNUM_SIGN(y)) return INT2FIX(-1);
if (xlen < RBIGNUM_LEN(y))
return (RBIGNUM_SIGN(x)) ? INT2FIX(-1) : INT2FIX(1);
if (xlen > RBIGNUM_LEN(y))
return (RBIGNUM_SIGN(x)) ? INT2FIX(1) : INT2FIX(-1);
xds = BDIGITS(x);
yds = BDIGITS(y);
while(xlen-- && (xds[xlen]==yds[xlen]));
if (-1 == xlen) return INT2FIX(0);
return (xds[xlen] > yds[xlen]) ?
(RBIGNUM_SIGN(x) ? INT2FIX(1) : INT2FIX(-1)) :
(RBIGNUM_SIGN(x) ? INT2FIX(-1) : INT2FIX(1));
}
static VALUE
big_op(VALUE x, VALUE y, int op)
{
VALUE rel;
int n;
switch (TYPE(y)) {
case T_FIXNUM:
case T_BIGNUM:
rel = rb_big_cmp(x, y);
break;
case T_FLOAT:
{
double a = RFLOAT_VALUE(y);
if (isinf(a)) {
if (a > 0.0) return INT2FIX(-1);
else return INT2FIX(1);
}
rel = rb_dbl_cmp(rb_big2dbl(x), a);
break;
}
default:
{
ID id = 0;
switch (op) {
case 0: id = '>'; break;
case 1: id = rb_intern(">="); break;
case 2: id = '<'; break;
case 3: id = rb_intern("<="); break;
}
return rb_num_coerce_relop(x, y, id);
}
}
if (NIL_P(rel)) return Qfalse;
n = FIX2INT(rel);
switch (op) {
case 0: return n > 0 ? Qtrue : Qfalse;
case 1: return n >= 0 ? Qtrue : Qfalse;
case 2: return n < 0 ? Qtrue : Qfalse;
case 3: return n <= 0 ? Qtrue : Qfalse;
}
return Qundef;
}
/*
* call-seq:
* big > real -> true or false
*
* Returns <code>true</code> if the value of <code>big</code> is
* greater than that of <code>real</code>.
*/
static VALUE
big_gt(VALUE x, VALUE y)
{
return big_op(x, y, 0);
}
/*
* call-seq:
* big >= real -> true or false
*
* Returns <code>true</code> if the value of <code>big</code> is
* greater than or equal to that of <code>real</code>.
*/
static VALUE
big_ge(VALUE x, VALUE y)
{
return big_op(x, y, 1);
}
/*
* call-seq:
* big < real -> true or false
*
* Returns <code>true</code> if the value of <code>big</code> is
* less than that of <code>real</code>.
*/
static VALUE
big_lt(VALUE x, VALUE y)
{
return big_op(x, y, 2);
}
/*
* call-seq:
* big <= real -> true or false
*
* Returns <code>true</code> if the value of <code>big</code> is
* less than or equal to that of <code>real</code>.
*/
static VALUE
big_le(VALUE x, VALUE y)
{
return big_op(x, y, 3);
}
/*
* 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
*/
VALUE
rb_big_eq(VALUE x, VALUE 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_VALUE(y);
if (isnan(a)) return Qfalse;
b = rb_big2dbl(x);
return (a == b)?Qtrue:Qfalse;
}
default:
return rb_equal(y, x);
}
if (RBIGNUM_SIGN(x) != RBIGNUM_SIGN(y)) return Qfalse;
if (RBIGNUM_LEN(x) != RBIGNUM_LEN(y)) return Qfalse;
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM_LEN(y)) != 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(VALUE x, VALUE y)
{
if (TYPE(y) != T_BIGNUM) return Qfalse;
if (RBIGNUM_SIGN(x) != RBIGNUM_SIGN(y)) return Qfalse;
if (RBIGNUM_LEN(x) != RBIGNUM_LEN(y)) return Qfalse;
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM_LEN(y)) != 0) return Qfalse;
return Qtrue;
}
/*
* call-seq:
* -big => integer
*
* Unary minus (returns an integer whose value is 0-big)
*/
static VALUE
rb_big_uminus(VALUE x)
{
VALUE z = rb_big_clone(x);
RBIGNUM_SET_SIGN(z, !RBIGNUM_SIGN(x));
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(VALUE x)
{
VALUE z = rb_big_clone(x);
BDIGIT *ds;
long i;
if (!RBIGNUM_SIGN(x)) get2comp(z);
ds = BDIGITS(z);
i = RBIGNUM_LEN(x);
if (!i) return INT2FIX(~(SIGNED_VALUE)0);
while (i--) {
ds[i] = ~ds[i];
}
RBIGNUM_SET_SIGN(z, !RBIGNUM_SIGN(z));
if (RBIGNUM_SIGN(x)) get2comp(z);
return bignorm(z);
}
static void
bigsub_core(BDIGIT *xds, long xn, BDIGIT *yds, long yn, BDIGIT *zds, long zn)
{
BDIGIT_DBL_SIGNED num;
long i;
for (i = 0, num = 0; i < yn; i++) {
num += (BDIGIT_DBL_SIGNED)xds[i] - yds[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
while (num && i < xn) {
num += xds[i];
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
while (i < xn) {
zds[i] = xds[i];
i++;
}
assert(i <= zn);
while (i < zn) {
zds[i++] = 0;
}
}
static VALUE
bigsub(VALUE x, VALUE y)
{
VALUE z = 0;
long i = RBIGNUM_LEN(x);
BDIGIT *xds, *yds;
/* if x is larger than y, swap */
if (RBIGNUM_LEN(x) < RBIGNUM_LEN(y)) {
z = x; x = y; y = z; /* swap x y */
}
else if (RBIGNUM_LEN(x) == RBIGNUM_LEN(y)) {
xds = BDIGITS(x);
yds = BDIGITS(y);
while (i > 0) {
i--;
if (xds[i] > yds[i]) {
break;
}
if (xds[i] < yds[i]) {
z = x; x = y; y = z; /* swap x y */
break;
}
}
}
z = bignew(RBIGNUM_LEN(x), z==0);
bigsub_core(BDIGITS(x), RBIGNUM_LEN(x),
BDIGITS(y), RBIGNUM_LEN(y),
BDIGITS(z), RBIGNUM_LEN(z));
return z;
}
static VALUE bigadd_int(VALUE x, long y);
static VALUE
bigsub_int(VALUE x, long y0)
{
VALUE z;
BDIGIT *xds, *zds;
long xn;
BDIGIT_DBL_SIGNED num;
long i, y;
y = y0;
xds = BDIGITS(x);
xn = RBIGNUM_LEN(x);
z = bignew(xn, RBIGNUM_SIGN(x));
zds = BDIGITS(z);
#if SIZEOF_BDIGITS == SIZEOF_LONG
num = (BDIGIT_DBL_SIGNED)xds[0] - y;
if (xn == 1 && num < 0) {
RBIGNUM_SET_SIGN(z, !RBIGNUM_SIGN(x));
zds[0] = (BDIGIT)-num;
return bignorm(z);
}
zds[0] = BIGLO(num);
num = BIGDN(num);
i = 1;
#else
num = 0;
for (i=0; i<(int)(sizeof(y)/sizeof(BDIGIT)); i++) {
num += (BDIGIT_DBL_SIGNED)xds[i] - BIGLO(y);
zds[i] = BIGLO(num);
num = BIGDN(num);
y = BIGDN(y);
}
#endif
while (num && i < xn) {
num += xds[i];
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
while (i < xn) {
zds[i] = xds[i];
i++;
}
if (num < 0) {
z = bigsub(x, rb_int2big(y0));
}
return bignorm(z);
}
static VALUE
bigadd_int(VALUE x, long y)
{
VALUE z;
BDIGIT *xds, *zds;
long xn, zn;
BDIGIT_DBL num;
long i;
xds = BDIGITS(x);
xn = RBIGNUM_LEN(x);
if (xn < 2) {
zn = 3;
}
else {
zn = xn + 1;
}
z = bignew(zn, RBIGNUM_SIGN(x));
zds = BDIGITS(z);
#if SIZEOF_BDIGITS == SIZEOF_LONG
num = (BDIGIT_DBL)xds[0] + y;
zds[0] = BIGLO(num);
num = BIGDN(num);
i = 1;
#else
num = 0;
for (i=0; i<(int)(sizeof(y)/sizeof(BDIGIT)); i++) {
num += (BDIGIT_DBL)xds[i] + BIGLO(y);
zds[i] = BIGLO(num);
num = BIGDN(num);
y = BIGDN(y);
}
#endif
while (num && i < xn) {
num += xds[i];
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
if (num) zds[i++] = (BDIGIT)num;
else while (i < xn) {
zds[i] = xds[i];
i++;
}
assert(i <= zn);
while (i < zn) {
zds[i++] = 0;
}
return bignorm(z);
}
static void
bigadd_core(BDIGIT *xds, long xn, BDIGIT *yds, long yn, BDIGIT *zds, long zn)
{
BDIGIT_DBL num = 0;
long i;
if (xn > yn) {
BDIGIT *tds;
tds = xds; xds = yds; yds = tds;
i = xn; xn = yn; yn = i;
}
i = 0;
while (i < xn) {
num += (BDIGIT_DBL)xds[i] + yds[i];
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
while (num && i < yn) {
num += yds[i];
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
while (i < yn) {
zds[i] = yds[i];
i++;
}
if (num) zds[i++] = (BDIGIT)num;
assert(i <= zn);
while (i < zn) {
zds[i++] = 0;
}
}
static VALUE
bigadd(VALUE x, VALUE y, int sign)
{
VALUE z;
long len;
sign = (sign == RBIGNUM_SIGN(y));
if (RBIGNUM_SIGN(x) != sign) {
if (sign) return bigsub(y, x);
return bigsub(x, y);
}
if (RBIGNUM_LEN(x) > RBIGNUM_LEN(y)) {
len = RBIGNUM_LEN(x) + 1;
}
else {
len = RBIGNUM_LEN(y) + 1;
}
z = bignew(len, sign);
bigadd_core(BDIGITS(x), RBIGNUM_LEN(x),
BDIGITS(y), RBIGNUM_LEN(y),
BDIGITS(z), RBIGNUM_LEN(z));
return z;
}
/*
* call-seq:
* big + other => Numeric
*
* Adds big and other, returning the result.
*/
VALUE
rb_big_plus(VALUE x, VALUE y)
{
long n;
switch (TYPE(y)) {
case T_FIXNUM:
n = FIX2LONG(y);
if ((n > 0) != RBIGNUM_SIGN(x)) {
if (n < 0) {
n = -n;
}
return bigsub_int(x, n);
}
if (n < 0) {
n = -n;
}
return bigadd_int(x, n);
case T_BIGNUM:
return bignorm(bigadd(x, y, 1));
case T_FLOAT:
return DBL2NUM(rb_big2dbl(x) + RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, y, '+');
}
}
/*
* call-seq:
* big - other => Numeric
*
* Subtracts other from big, returning the result.
*/
VALUE
rb_big_minus(VALUE x, VALUE y)
{
long n;
switch (TYPE(y)) {
case T_FIXNUM:
n = FIX2LONG(y);
if ((n > 0) != RBIGNUM_SIGN(x)) {
if (n < 0) {
n = -n;
}
return bigadd_int(x, n);
}
if (n < 0) {
n = -n;
}
return bigsub_int(x, n);
case T_BIGNUM:
return bignorm(bigadd(x, y, 0));
case T_FLOAT:
return DBL2NUM(rb_big2dbl(x) - RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, y, '-');
}
}
static long
big_real_len(VALUE x)
{
long i = RBIGNUM_LEN(x);
BDIGIT *xds = BDIGITS(x);
while (--i && !xds[i]);
return i + 1;
}
static VALUE
bigmul1_single(VALUE x, VALUE y)
{
BDIGIT_DBL n;
VALUE z = bignew(2, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
BDIGIT *xds, *yds, *zds;
xds = BDIGITS(x);
yds = BDIGITS(y);
zds = BDIGITS(z);
n = (BDIGIT_DBL)xds[0] * yds[0];
zds[0] = BIGLO(n);
zds[1] = (BDIGIT)BIGDN(n);
return z;
}
static VALUE
bigmul1_normal(VALUE x, VALUE y)
{
long xl = RBIGNUM_LEN(x), yl = RBIGNUM_LEN(y), i, j = xl + yl + 1;
BDIGIT_DBL n = 0;
VALUE z = bignew(j, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
BDIGIT *xds, *yds, *zds;
xds = BDIGITS(x);
yds = BDIGITS(y);
zds = BDIGITS(z);
while (j--) zds[j] = 0;
for (i = 0; i < xl; i++) {
BDIGIT_DBL dd;
dd = xds[i];
if (dd == 0) continue;
n = 0;
for (j = 0; j < yl; j++) {
BDIGIT_DBL ee = n + (BDIGIT_DBL)dd * yds[j];
n = zds[i + j] + ee;
if (ee) zds[i + j] = BIGLO(n);
n = BIGDN(n);
}
if (n) {
zds[i + j] = (BDIGIT)n;
}
}
rb_thread_check_ints();
return z;
}
static VALUE bigmul0(VALUE x, VALUE y);
/* balancing multiplication by slicing larger argument */
static VALUE
bigmul1_balance(VALUE x, VALUE y)
{
VALUE z, t1, t2;
long i, xn, yn, r, n;
BDIGIT *yds, *zds, *t1ds;
xn = RBIGNUM_LEN(x);
yn = RBIGNUM_LEN(y);
assert(2 * xn <= yn);
z = bignew(xn + yn, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
t1 = bignew(xn, 1);
yds = BDIGITS(y);
zds = BDIGITS(z);
t1ds = BDIGITS(t1);
for (i = 0; i < xn + yn; i++) zds[i] = 0;
n = 0;
while (yn > 0) {
r = xn > yn ? yn : xn;
MEMCPY(t1ds, yds + n, BDIGIT, r);
RBIGNUM_SET_LEN(t1, r);
t2 = bigmul0(x, t1);
bigadd_core(zds + n, RBIGNUM_LEN(z) - n,
BDIGITS(t2), big_real_len(t2),
zds + n, RBIGNUM_LEN(z) - n);
yn -= r;
n += r;
}
return z;
}
/* split a bignum into high and low bignums */
static void
big_split(VALUE v, long n, volatile VALUE *ph, volatile VALUE *pl)
{
long hn = 0, ln = RBIGNUM_LEN(v);
VALUE h, l;
BDIGIT *vds = BDIGITS(v);
if (ln > n) {
hn = ln - n;
ln = n;
}
while (--hn && !vds[hn + ln]);
h = bignew(hn += 2, 1);
MEMCPY(BDIGITS(h), vds + ln, BDIGIT, hn - 1);
BDIGITS(h)[hn - 1] = 0; /* margin for carry */
while (--ln && !vds[ln]);
l = bignew(ln += 2, 1);
MEMCPY(BDIGITS(l), vds, BDIGIT, ln - 1);
BDIGITS(l)[ln - 1] = 0; /* margin for carry */
*pl = l;
*ph = h;
}
/* multiplication by karatsuba method */
static VALUE
bigmul1_karatsuba(VALUE x, VALUE y)
{
long i, n, xn, yn, t1n, t2n;
VALUE xh, xl, yh, yl, z, t1, t2;
BDIGIT *zds;
xn = RBIGNUM_LEN(x);
yn = RBIGNUM_LEN(y);
n = yn / 2;
big_split(x, n, &xh, &xl);
if (x == y) {
yh = xh; yl = xl;
}
else big_split(y, n, &yh, &yl);
/* x = xh * b + xl
* y = yh * b + yl
*
* Karatsuba method:
* x * y = z2 * b^2 + z1 * b + z0
* where
* z2 = xh * yh
* z0 = xl * yl
* z1 = (xh + xl) * (yh + yl) - z2 - z0
*
* ref: http://en.wikipedia.org/wiki/Karatsuba_algorithm
*/
/* allocate a result bignum */
z = bignew(xn + yn, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
zds = BDIGITS(z);
/* t1 <- xh * yh */
t1 = bigmul0(xh, yh);
t1n = big_real_len(t1);
/* copy t1 into high bytes of the result (z2) */
MEMCPY(zds + 2 * n, BDIGITS(t1), BDIGIT, t1n);
for (i = 2 * n + t1n; i < xn + yn; i++) zds[i] = 0;
if (!BIGZEROP(xl) && !BIGZEROP(yl)) {
/* t2 <- xl * yl */
t2 = bigmul0(xl, yl);
t2n = big_real_len(t2);
/* copy t2 into low bytes of the result (z0) */
MEMCPY(zds, BDIGITS(t2), BDIGIT, t2n);
for (i = t2n; i < 2 * n; i++) zds[i] = 0;
/* subtract t2 from middle bytes of the result (z1) */
i = xn + yn - n;
bigsub_core(zds + n, i, BDIGITS(t2), t2n, zds + n, i);
}
else {
/* copy 0 into low bytes of the result (z0) */
for (i = 0; i < 2 * n; i++) zds[i] = 0;
}
/* subtract t1 from middle bytes of the result (z1) */
i = xn + yn - n;
bigsub_core(zds + n, i, BDIGITS(t1), t1n, zds + n, i);
/* xh <- xh + xl */
if (RBIGNUM_LEN(xl) > RBIGNUM_LEN(xh)) {
t1 = xl; xl = xh; xh = t1;
}
bigadd_core(BDIGITS(xh), RBIGNUM_LEN(xh),
BDIGITS(xl), RBIGNUM_LEN(xl),
BDIGITS(xh), RBIGNUM_LEN(xh));
/* yh <- yh + yl */
if (x != y) {
if (RBIGNUM_LEN(yl) > RBIGNUM_LEN(yh)) {
t1 = yl; yl = yh; yh = t1;
}
bigadd_core(BDIGITS(yh), RBIGNUM_LEN(yh),
BDIGITS(yl), RBIGNUM_LEN(yl),
BDIGITS(yh), RBIGNUM_LEN(yh));
}
else yh = xh;
/* t1 <- xh * yh */
t1 = bigmul0(xh, yh);
/* add t1 to middle bytes of the result (z1) */
bigadd_core(zds + n, i, BDIGITS(t1), big_real_len(t1), zds + n, i);
return z;
}
/* efficient squaring (2 times faster than normal multiplication)
* ref: Handbook of Applied Cryptography, Algorithm 14.16
* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
*/
static VALUE
bigsqr_fast(VALUE x)
{
long len = RBIGNUM_LEN(x), i, j;
VALUE z = bignew(2 * len + 1, 1);
BDIGIT *xds = BDIGITS(x), *zds = BDIGITS(z);
BDIGIT_DBL c, v, w;
for (i = 2 * len + 1; i--; ) zds[i] = 0;
for (i = 0; i < len; i++) {
v = (BDIGIT_DBL)xds[i];
if (!v) continue;
c = (BDIGIT_DBL)zds[i + i] + v * v;
zds[i + i] = BIGLO(c);
c = BIGDN(c);
v *= 2;
for (j = i + 1; j < len; j++) {
w = (BDIGIT_DBL)xds[j];
c += (BDIGIT_DBL)zds[i + j] + BIGLO(v) * w;
zds[i + j] = BIGLO(c);
c = BIGDN(c);
if (BIGDN(v)) c += w;
}
if (c) {
c += (BDIGIT_DBL)zds[i + len];
zds[i + len] = BIGLO(c);
c = BIGDN(c);
}
if (c) zds[i + len + 1] += (BDIGIT)c;
}
return z;
}
#define KARATSUBA_MUL_DIGITS 70
/* determine whether a bignum is sparse or not by random sampling */
static inline VALUE
big_sparse_p(VALUE x)
{
long c = 0, n = RBIGNUM_LEN(x);
unsigned long rb_rand_internal(unsigned long i);
if ( BDIGITS(x)[rb_rand_internal(n / 2) + n / 4]) c++;
if (c <= 1 && BDIGITS(x)[rb_rand_internal(n / 2) + n / 4]) c++;
if (c <= 1 && BDIGITS(x)[rb_rand_internal(n / 2) + n / 4]) c++;
return (c <= 1) ? Qtrue : Qfalse;
}
#if 0
static void
dump_bignum(VALUE x)
{
long i;
printf("0x0");
for (i = RBIGNUM_LEN(x); i--; ) {
printf("_%08x", BDIGITS(x)[i]);
}
puts("");
}
#endif
static VALUE
bigmul0(VALUE x, VALUE y)
{
long xn, yn;
xn = RBIGNUM_LEN(x);
yn = RBIGNUM_LEN(y);
/* make sure that y is longer than x */
if (xn > yn) {
VALUE t;
long tn;
t = x; x = y; y = t;
tn = xn; xn = yn; yn = tn;
}
assert(xn <= yn);
/* normal multiplication when x is small */
if (xn < KARATSUBA_MUL_DIGITS) {
normal:
if (x == y) return bigsqr_fast(x);
if (xn == 1 && yn == 1) return bigmul1_single(x, y);
return bigmul1_normal(x, y);
}
/* normal multiplication when x or y is a sparse bignum */
if (big_sparse_p(x)) goto normal;
if (big_sparse_p(y)) return bigmul1_normal(y, x);
/* balance multiplication by slicing y when x is much smaller than y */
if (2 * xn <= yn) return bigmul1_balance(x, y);
/* multiplication by karatsuba method */
return bigmul1_karatsuba(x, y);
}
/*
* call-seq:
* big * other => Numeric
*
* Multiplies big and other, returning the result.
*/
VALUE
rb_big_mul(VALUE x, VALUE y)
{
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
return DBL2NUM(rb_big2dbl(x) * RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, y, '*');
}
return bignorm(bigmul0(x, y));
}
struct big_div_struct {
long nx, ny;
BDIGIT *yds, *zds;
VALUE stop;
};
static VALUE
bigdivrem1(void *ptr)
{
struct big_div_struct *bds = (struct big_div_struct*)ptr;
long nx = bds->nx, ny = bds->ny;
long i, j, nyzero;
BDIGIT *yds = bds->yds, *zds = bds->zds;
BDIGIT_DBL t2;
BDIGIT_DBL_SIGNED num;
BDIGIT q;
j = nx==ny?nx+1:nx;
for (nyzero = 0; !yds[nyzero]; nyzero++);
do {
if (bds->stop) return Qnil;
if (zds[j] == yds[ny-1]) q = (BDIGIT)BIGRAD-1;
else q = (BDIGIT)((BIGUP(zds[j]) + zds[j-1])/yds[ny-1]);
if (q) {
i = nyzero; 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);
return Qnil;
}
static void
rb_big_stop(void *ptr)
{
VALUE *stop = (VALUE*)ptr;
*stop = Qtrue;
}
static VALUE
bigdivrem(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp)
{
struct big_div_struct bds;
long nx = RBIGNUM_LEN(x), ny = RBIGNUM_LEN(y);
long i, j;
VALUE z, yy, zz;
BDIGIT *xds, *yds, *zds, *tds;
BDIGIT_DBL t2;
BDIGIT dd, q;
if (BIGZEROP(y)) rb_num_zerodiv();
xds = BDIGITS(x);
yds = BDIGITS(y);
if (nx < ny || (nx == ny && xds[nx - 1] < yds[ny - 1])) {
if (divp) *divp = rb_int2big(0);
if (modp) *modp = x;
return Qnil;
}
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_SET_SIGN(z, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
if (modp) {
*modp = rb_uint2big((VALUE)t2);
RBIGNUM_SET_SIGN(*modp, RBIGNUM_SIGN(x));
}
if (divp) *divp = z;
return Qnil;
}
z = bignew(nx==ny?nx+2:nx+1, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
zds = BDIGITS(z);
if (nx==ny) zds[nx+1] = 0;
while (!yds[ny-1]) ny--;
dd = 0;
q = yds[ny-1];
while ((q & (BDIGIT)(1UL<<(BITSPERDIG-1))) == 0) {
q <<= 1UL;
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;
RB_GC_GUARD(y) = yy;
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];
}
bds.nx = nx;
bds.ny = ny;
bds.zds = zds;
bds.yds = yds;
bds.stop = Qfalse;
if (nx > 10000 || ny > 10000) {
rb_thread_blocking_region(bigdivrem1, &bds, rb_big_stop, &bds.stop);
}
else {
bigdivrem1(&bds);
}
if (divp) { /* move quotient down in z */
*divp = zz = rb_big_clone(z);
zds = BDIGITS(zz);
j = (nx==ny ? nx+2 : nx+1) - ny;
for (i = 0;i < j;i++) zds[i] = zds[i+ny];
if (!zds[i-1]) i--;
RBIGNUM_SET_LEN(zz, i);
}
if (modp) { /* normalize remainder */
*modp = zz = rb_big_clone(z);
zds = BDIGITS(zz);
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);
}
}
if (!zds[ny-1]) ny--;
RBIGNUM_SET_LEN(zz, ny);
RBIGNUM_SET_SIGN(zz, RBIGNUM_SIGN(x));
}
return z;
}
static void
bigdivmod(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp)
{
VALUE mod;
bigdivrem(x, y, divp, &mod);
if (RBIGNUM_SIGN(x) != RBIGNUM_SIGN(y) && !BIGZEROP(mod)) {
if (divp) *divp = bigadd(*divp, rb_int2big(1), 0);
if (modp) *modp = bigadd(mod, y, 1);
}
else if (modp) {
*modp = mod;
}
}
static VALUE
rb_big_divide(VALUE x, VALUE y, ID op)
{
VALUE z;
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
{
double div = rb_big2dbl(x) / RFLOAT_VALUE(y);
if (op == '/') {
return DBL2NUM(div);
}
else {
return rb_dbl2big(div);
}
}
default:
return rb_num_coerce_bin(x, y, op);
}
bigdivmod(x, y, &z, 0);
return bignorm(z);
}
/*
* call-seq:
* big / other => Numeric
*
* Performs division: the class of the resulting object depends on
* the class of <code>numeric</code> and on the magnitude of the
* result.
*/
VALUE
rb_big_div(VALUE x, VALUE y)
{
return rb_big_divide(x, y, '/');
}
/*
* call-seq:
* big.div(other) => integer
*
* Performs integer division: returns integer value.
*/
VALUE
rb_big_idiv(VALUE x, VALUE y)
{
return rb_big_divide(x, y, rb_intern("div"));
}
/*
* call-seq:
* big % other => Numeric
* big.modulo(other) => Numeric
*
* Returns big modulo other. See Numeric.divmod for more
* information.
*/
VALUE
rb_big_modulo(VALUE x, VALUE 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(VALUE x, VALUE 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, rb_intern("remainder"));
}
bigdivrem(x, y, 0, &z);
return bignorm(z);
}
/*
* call-seq:
* big.divmod(numeric) => array
*
* See <code>Numeric#divmod</code>.
*
*/
VALUE
rb_big_divmod(VALUE x, VALUE 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, rb_intern("divmod"));
}
bigdivmod(x, y, &div, &mod);
return rb_assoc_new(bignorm(div), bignorm(mod));
}
static int
bdigbitsize(BDIGIT x)
{
int size = 1;
int nb = BITSPERDIG / 2;
BDIGIT bits = (~0 << nb);
if (!x) return 0;
while (x > 1) {
if (x & bits) {
size += nb;
x >>= nb;
}
x &= ~bits;
nb /= 2;
bits >>= nb;
}
return size;
}
static VALUE big_lshift(VALUE, unsigned long);
static VALUE big_rshift(VALUE, unsigned long);
static VALUE
big_shift(VALUE x, long n)
{
if (n < 0)
return big_lshift(x, (unsigned long)-n);
else if (n > 0)
return big_rshift(x, (unsigned long)n);
return x;
}
static VALUE
big_fdiv(VALUE x, VALUE y)
{
#define DBL_BIGDIG ((DBL_MANT_DIG + BITSPERDIG) / BITSPERDIG)
VALUE z;
long l, ex, ey;
int i;
bigtrunc(x);
l = RBIGNUM_LEN(x) - 1;
ex = l * BITSPERDIG;
ex += bdigbitsize(BDIGITS(x)[l]);
ex -= 2 * DBL_BIGDIG * BITSPERDIG;
if (ex) x = big_shift(x, ex);
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
case T_BIGNUM: {
bigtrunc(y);
l = RBIGNUM_LEN(y) - 1;
ey = l * BITSPERDIG;
ey += bdigbitsize(BDIGITS(y)[l]);
ey -= DBL_BIGDIG * BITSPERDIG;
if (ey) y = big_shift(y, ey);
bignum:
bigdivrem(x, y, &z, 0);
l = ex - ey;
#if SIZEOF_LONG > SIZEOF_INT
{
/* Visual C++ can't be here */
if (l > INT_MAX) return DBL2NUM(INFINITY);
if (l < INT_MIN) return DBL2NUM(0.0);
}
#endif
return DBL2NUM(ldexp(big2dbl(z), (int)l));
}
case T_FLOAT:
y = dbl2big(ldexp(frexp(RFLOAT_VALUE(y), &i), DBL_MANT_DIG));
ey = i - DBL_MANT_DIG;
goto bignum;
}
rb_bug("big_fdiv");
/* NOTREACHED */
}
/*
* call-seq:
* big.fdiv(numeric) -> float
*
* Returns the floating point result of dividing <i>big</i> by
* <i>numeric</i>.
*
* -1234567890987654321.fdiv(13731) #=> -89910996357705.5
* -1234567890987654321.fdiv(13731.24) #=> -89909424858035.7
*
*/
VALUE
rb_big_fdiv(VALUE x, VALUE y)
{
double dx, dy;
dx = big2dbl(x);
switch (TYPE(y)) {
case T_FIXNUM:
dy = (double)FIX2LONG(y);
if (isinf(dx))
return big_fdiv(x, y);
break;
case T_BIGNUM:
dy = rb_big2dbl(y);
if (isinf(dx) || isinf(dy))
return big_fdiv(x, y);
break;
case T_FLOAT:
dy = RFLOAT_VALUE(y);
if (isnan(dy))
return y;
if (isinf(dx))
return big_fdiv(x, y);
break;
default:
return rb_num_coerce_bin(x, y, rb_intern("fdiv"));
}
return DBL2NUM(dx / dy);
}
static VALUE
bigsqr(VALUE x)
{
return bigtrunc(bigmul0(x, x));
}
/*
* 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(VALUE x, VALUE y)
{
double d;
SIGNED_VALUE yy;
if (y == INT2FIX(0)) return INT2FIX(1);
switch (TYPE(y)) {
case T_FLOAT:
d = RFLOAT_VALUE(y);
if ((!RBIGNUM_SIGN(x) && !BIGZEROP(x)) && d != round(d))
return rb_funcall(rb_complex_raw1(x), rb_intern("**"), 1, y);
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)
return rb_funcall(rb_rational_raw1(x), rb_intern("**"), 1, y);
else {
VALUE z = 0;
SIGNED_VALUE mask;
const long BIGLEN_LIMIT = 1024*1024 / SIZEOF_BDIGITS;
if ((RBIGNUM_LEN(x) > BIGLEN_LIMIT) ||
(RBIGNUM_LEN(x) > BIGLEN_LIMIT / yy)) {
rb_warn("in a**b, b may be too big");
d = (double)yy;
break;
}
for (mask = FIXNUM_MAX + 1; mask; mask >>= 1) {
if (z) z = bigsqr(z);
if (yy & mask) {
z = z ? bigtrunc(bigmul0(z, x)) : x;
}
}
return bignorm(z);
}
/* NOTREACHED */
break;
default:
return rb_num_coerce_bin(x, y, rb_intern("**"));
}
return DBL2NUM(pow(rb_big2dbl(x), d));
}
static inline VALUE
bit_coerce(VALUE x)
{
while (!FIXNUM_P(x) && TYPE(x) != T_BIGNUM) {
if (TYPE(x) == T_FLOAT) {
rb_raise(rb_eTypeError, "can't convert Float into Integer");
}
x = rb_to_int(x);
}
return x;
}
static VALUE
bigand_int(VALUE x, long y)
{
VALUE z;
BDIGIT *xds, *zds;
long xn, zn;
long i;
char sign;
if (y == 0) return INT2FIX(0);
sign = (y > 0);
xds = BDIGITS(x);
zn = xn = RBIGNUM_LEN(x);
#if SIZEOF_BDIGITS == SIZEOF_LONG
if (sign) {
y &= xds[0];
return LONG2NUM(y);
}
#endif
z = bignew(zn, RBIGNUM_SIGN(x) || sign);
zds = BDIGITS(z);
#if SIZEOF_BDIGITS == SIZEOF_LONG
i = 1;
zds[0] = xds[0] & y;
#else
{
BDIGIT_DBL num = y;
for (i=0; i<(int)(sizeof(y)/sizeof(BDIGIT)); i++) {
zds[i] = xds[i] & BIGLO(num);
num = BIGDN(num);
}
}
#endif
while (i < xn) {
zds[i] = sign?0:xds[i];
i++;
}
if (!RBIGNUM_SIGN(z)) get2comp(z);
return bignorm(z);
}
/*
* call-seq:
* big & numeric => integer
*
* Performs bitwise +and+ between _big_ and _numeric_.
*/
VALUE
rb_big_and(VALUE xx, VALUE yy)
{
volatile VALUE x, y, z;
BDIGIT *ds1, *ds2, *zds;
long i, l1, l2;
char sign;
x = xx;
y = bit_coerce(yy);
if (!RBIGNUM_SIGN(x)) {
x = rb_big_clone(x);
get2comp(x);
}
if (FIXNUM_P(y)) {
return bigand_int(x, FIX2LONG(y));
}
if (!RBIGNUM_SIGN(y)) {
y = rb_big_clone(y);
get2comp(y);
}
if (RBIGNUM_LEN(x) > RBIGNUM_LEN(y)) {
l1 = RBIGNUM_LEN(y);
l2 = RBIGNUM_LEN(x);
ds1 = BDIGITS(y);
ds2 = BDIGITS(x);
sign = RBIGNUM_SIGN(y);
}
else {
l1 = RBIGNUM_LEN(x);
l2 = RBIGNUM_LEN(y);
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
sign = RBIGNUM_SIGN(x);
}
z = bignew(l2, RBIGNUM_SIGN(x) || RBIGNUM_SIGN(y));
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_SIGN(z)) get2comp(z);
return bignorm(z);
}
static VALUE
bigor_int(VALUE x, long y)
{
VALUE z;
BDIGIT *xds, *zds;
long xn, zn;
long i;
char sign;
sign = (y >= 0);
xds = BDIGITS(x);
zn = xn = RBIGNUM_LEN(x);
z = bignew(zn, RBIGNUM_SIGN(x) && sign);
zds = BDIGITS(z);
#if SIZEOF_BDIGITS == SIZEOF_LONG
i = 1;
zds[0] = xds[0] | y;
#else
{
BDIGIT_DBL num = y;
for (i=0; i<(int)(sizeof(y)/sizeof(BDIGIT)); i++) {
zds[i] = xds[i] | BIGLO(num);
num = BIGDN(num);
}
}
#endif
while (i < xn) {
zds[i] = sign?xds[i]:(BDIGIT)(BIGRAD-1);
i++;
}
if (!RBIGNUM_SIGN(z)) get2comp(z);
return bignorm(z);
}
/*
* call-seq:
* big | numeric => integer
*
* Performs bitwise +or+ between _big_ and _numeric_.
*/
VALUE
rb_big_or(VALUE xx, VALUE yy)
{
volatile VALUE x, y, z;
BDIGIT *ds1, *ds2, *zds;
long i, l1, l2;
char sign;
x = xx;
y = bit_coerce(yy);
if (!RBIGNUM_SIGN(x)) {
x = rb_big_clone(x);
get2comp(x);
}
if (FIXNUM_P(y)) {
return bigor_int(x, FIX2LONG(y));
}
if (!RBIGNUM_SIGN(y)) {
y = rb_big_clone(y);
get2comp(y);
}
if (RBIGNUM_LEN(x) > RBIGNUM_LEN(y)) {
l1 = RBIGNUM_LEN(y);
l2 = RBIGNUM_LEN(x);
ds1 = BDIGITS(y);
ds2 = BDIGITS(x);
sign = RBIGNUM_SIGN(y);
}
else {
l1 = RBIGNUM_LEN(x);
l2 = RBIGNUM_LEN(y);
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
sign = RBIGNUM_SIGN(x);
}
z = bignew(l2, RBIGNUM_SIGN(x) && RBIGNUM_SIGN(y));
zds = BDIGITS(z);
for (i=0; i<l1; i++) {
zds[i] = ds1[i] | ds2[i];
}
for (; i<l2; i++) {
zds[i] = sign?ds2[i]:(BDIGIT)(BIGRAD-1);
}
if (!RBIGNUM_SIGN(z)) get2comp(z);
return bignorm(z);
}
static VALUE
bigxor_int(VALUE x, long y)
{
VALUE z;
BDIGIT *xds, *zds;
long xn, zn;
long i;
char sign;
sign = (y >= 0) ? 1 : 0;
xds = BDIGITS(x);
zn = xn = RBIGNUM_LEN(x);
z = bignew(zn, !(RBIGNUM_SIGN(x) ^ sign));
zds = BDIGITS(z);
#if SIZEOF_BDIGITS == SIZEOF_LONG
i = 1;
zds[0] = xds[0] ^ y;
#else
{
BDIGIT_DBL num = y;
for (i=0; i<(int)(sizeof(y)/sizeof(BDIGIT)); i++) {
zds[i] = xds[i] ^ BIGLO(num);
num = BIGDN(num);
}
}
#endif
while (i < xn) {
zds[i] = sign?xds[i]:~xds[i];
i++;
}
if (!RBIGNUM_SIGN(z)) get2comp(z);
return bignorm(z);
}
/*
* call-seq:
* big ^ numeric => integer
*
* Performs bitwise +exclusive or+ between _big_ and _numeric_.
*/
VALUE
rb_big_xor(VALUE xx, VALUE yy)
{
volatile VALUE x, y;
VALUE z;
BDIGIT *ds1, *ds2, *zds;
long i, l1, l2;
char sign;
x = xx;
y = bit_coerce(yy);
if (!RBIGNUM_SIGN(x)) {
x = rb_big_clone(x);
get2comp(x);
}
if (FIXNUM_P(y)) {
return bigxor_int(x, FIX2LONG(y));
}
if (!RBIGNUM_SIGN(y)) {
y = rb_big_clone(y);
get2comp(y);
}
if (RBIGNUM_LEN(x) > RBIGNUM_LEN(y)) {
l1 = RBIGNUM_LEN(y);
l2 = RBIGNUM_LEN(x);
ds1 = BDIGITS(y);
ds2 = BDIGITS(x);
sign = RBIGNUM_SIGN(y);
}
else {
l1 = RBIGNUM_LEN(x);
l2 = RBIGNUM_LEN(y);
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
sign = RBIGNUM_SIGN(x);
}
RBIGNUM_SET_SIGN(x, RBIGNUM_SIGN(x)?1:0);
RBIGNUM_SET_SIGN(y, RBIGNUM_SIGN(y)?1:0);
z = bignew(l2, !(RBIGNUM_SIGN(x) ^ RBIGNUM_SIGN(y)));
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_SIGN(z)) get2comp(z);
return bignorm(z);
}
static VALUE
check_shiftdown(VALUE y, VALUE x)
{
if (!RBIGNUM_LEN(x)) return INT2FIX(0);
if (RBIGNUM_LEN(y) > SIZEOF_LONG / SIZEOF_BDIGITS) {
return RBIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(-1);
}
return Qnil;
}
/*
* call-seq:
* big << numeric => integer
*
* Shifts big left _numeric_ positions (right if _numeric_ is negative).
*/
VALUE
rb_big_lshift(VALUE x, VALUE y)
{
long shift;
int neg = 0;
for (;;) {
if (FIXNUM_P(y)) {
shift = FIX2LONG(y);
if (shift < 0) {
neg = 1;
shift = -shift;
}
break;
}
else if (TYPE(y) == T_BIGNUM) {
if (!RBIGNUM_SIGN(y)) {
VALUE t = check_shiftdown(y, x);
if (!NIL_P(t)) return t;
neg = 1;
}
shift = big2ulong(y, "long", TRUE);
break;
}
y = rb_to_int(y);
}
x = neg ? big_rshift(x, shift) : big_lshift(x, shift);
return bignorm(x);
}
static VALUE
big_lshift(VALUE x, unsigned long shift)
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = (int)(shift%BITSPERDIG);
VALUE z;
BDIGIT_DBL num = 0;
long len, i;
len = RBIGNUM_LEN(x);
z = bignew(len+s1+1, RBIGNUM_SIGN(x));
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 z;
}
/*
* call-seq:
* big >> numeric => integer
*
* Shifts big right _numeric_ positions (left if _numeric_ is negative).
*/
VALUE
rb_big_rshift(VALUE x, VALUE y)
{
long shift;
int neg = 0;
for (;;) {
if (FIXNUM_P(y)) {
shift = FIX2LONG(y);
if (shift < 0) {
neg = 1;
shift = -shift;
}
break;
}
else if (TYPE(y) == T_BIGNUM) {
if (RBIGNUM_SIGN(y)) {
VALUE t = check_shiftdown(y, x);
if (!NIL_P(t)) return t;
}
else {
neg = 1;
}
shift = big2ulong(y, "long", TRUE);
break;
}
y = rb_to_int(y);
}
x = neg ? big_lshift(x, shift) : big_rshift(x, shift);
return bignorm(x);
}
static VALUE
big_rshift(VALUE x, unsigned long shift)
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = (int)(shift%BITSPERDIG);
VALUE z;
BDIGIT_DBL num = 0;
long i, j;
volatile VALUE save_x;
if (s1 > RBIGNUM_LEN(x)) {
if (RBIGNUM_SIGN(x))
return INT2FIX(0);
else
return INT2FIX(-1);
}
if (!RBIGNUM_SIGN(x)) {
save_x = x = rb_big_clone(x);
get2comp(x);
}
xds = BDIGITS(x);
i = RBIGNUM_LEN(x); j = i - s1;
if (j == 0) {
if (RBIGNUM_SIGN(x)) return INT2FIX(0);
else return INT2FIX(-1);
}
z = bignew(j, RBIGNUM_SIGN(x));
if (!RBIGNUM_SIGN(x)) {
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_SIGN(x)) {
get2comp(z);
}
return 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(VALUE x, VALUE y)
{
BDIGIT *xds;
BDIGIT_DBL num;
VALUE shift;
long i, s1, s2;
if (TYPE(y) == T_BIGNUM) {
if (!RBIGNUM_SIGN(y))
return INT2FIX(0);
bigtrunc(y);
if (RBIGNUM_LEN(y) > DIGSPERLONG) {
out_of_range:
return RBIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
}
shift = big2ulong(y, "long", FALSE);
}
else {
i = NUM2LONG(y);
if (i < 0) return INT2FIX(0);
shift = (VALUE)i;
}
s1 = shift/BITSPERDIG;
s2 = shift%BITSPERDIG;
if (s1 >= RBIGNUM_LEN(x)) goto out_of_range;
if (!RBIGNUM_SIGN(x)) {
xds = BDIGITS(x);
i = 0; num = 1;
while (num += ~xds[i], ++i <= s1) {
num = BIGDN(num);
}
}
else {
num = BDIGITS(x)[s1];
}
if (num & ((BDIGIT_DBL)1<<s2))
return INT2FIX(1);
return INT2FIX(0);
}
/*
* call-seq:
* big.hash => fixnum
*
* Compute a hash based on the value of _big_.
*/
static VALUE
rb_big_hash(VALUE x)
{
st_index_t hash;
hash = rb_memhash(BDIGITS(x), sizeof(BDIGIT)*RBIGNUM_LEN(x)) ^ RBIGNUM_SIGN(x);
return INT2FIX(hash);
}
/*
* MISSING: documentation
*/
static VALUE
rb_big_coerce(VALUE x, VALUE y)
{
if (FIXNUM_P(y)) {
return rb_assoc_new(rb_int2big(FIX2LONG(y)), x);
}
else if (TYPE(y) == T_BIGNUM) {
return rb_assoc_new(y, x);
}
else {
rb_raise(rb_eTypeError, "can't coerce %s to Bignum",
rb_obj_classname(y));
}
/* not reached */
return Qnil;
}
/*
* call-seq:
* big.abs -> aBignum
*
* Returns the absolute value of <i>big</i>.
*
* -1234567890987654321.abs #=> 1234567890987654321
*/
static VALUE
rb_big_abs(VALUE x)
{
if (!RBIGNUM_SIGN(x)) {
x = rb_big_clone(x);
RBIGNUM_SET_SIGN(x, 1);
}
return x;
}
/*
* 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(VALUE big)
{
return LONG2FIX(RBIGNUM_LEN(big)*SIZEOF_BDIGITS);
}
/*
* call-seq:
* big.odd? -> true or false
*
* Returns <code>true</code> if <i>big</i> is an odd number.
*/
static VALUE
rb_big_odd_p(VALUE num)
{
if (BDIGITS(num)[0] & 1) {
return Qtrue;
}
return Qfalse;
}
/*
* call-seq:
* big.even? -> true or false
*
* Returns <code>true</code> if <i>big</i> is an even number.
*/
static VALUE
rb_big_even_p(VALUE num)
{
if (BDIGITS(num)[0] & 1) {
return Qfalse;
}
return Qtrue;
}
/*
* 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(void)
{
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_idiv, 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, "fdiv", rb_big_fdiv, 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, ">", big_gt, 1);
rb_define_method(rb_cBignum, ">=", big_ge, 1);
rb_define_method(rb_cBignum, "<", big_lt, 1);
rb_define_method(rb_cBignum, "<=", big_le, 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, "magnitude", rb_big_abs, 0);
rb_define_method(rb_cBignum, "size", rb_big_size, 0);
rb_define_method(rb_cBignum, "odd?", rb_big_odd_p, 0);
rb_define_method(rb_cBignum, "even?", rb_big_even_p, 0);
power_cache_init();
}
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