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ruby/bignum.c

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52 KiB
C
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/**********************************************************************
bignum.c -
$Author$
$Date$
created at: Fri Jun 10 00:48:55 JST 1994
Copyright (C) 1993-2007 Yukihiro Matsumoto
**********************************************************************/
#include "ruby/ruby.h"
#include <math.h>
#include <float.h>
#include <ctype.h>
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
VALUE rb_cBignum;
#if defined __MINGW32__
#define USHORT _USHORT
#endif
#define BDIGITS(x) (RBIGNUM_DIGITS(x))
#define BITSPERDIG (SIZEOF_BDIGITS*CHAR_BIT)
#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
#define DIGSPERLONG ((unsigned int)(SIZEOF_LONG/SIZEOF_BDIGITS))
#if HAVE_LONG_LONG
# define DIGSPERLL ((unsigned int)(SIZEOF_LONG_LONG/SIZEOF_BDIGITS))
#endif
#define BIGUP(x) ((BDIGIT_DBL)(x) << BITSPERDIG)
#define BIGDN(x) RSHIFT(x,BITSPERDIG)
#define BIGLO(x) ((BDIGIT)((x) & (BIGRAD-1)))
#define BDIGMAX ((BDIGIT)-1)
#define BIGZEROP(x) (RBIGNUM_LEN(x) == 0 || (RBIGNUM_LEN(x) == 1 && BDIGITS(x)[0] == 0))
#define RBIGNUM_SET_LEN(b,l) \
((RBASIC(b)->flags & RBIGNUM_EMBED_FLAG) ? \
(RBASIC(b)->flags = (RBASIC(b)->flags & ~RBIGNUM_EMBED_LEN_MASK) | \
((l) << RBIGNUM_EMBED_LEN_SHIFT)) : \
(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);
free(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 {
rb_big_resize((VALUE)big, len);
}
return (VALUE)big;
}
#define bignew(len,sign) bignew_1(rb_cBignum,len,sign)
VALUE
rb_big_clone(VALUE x)
{
VALUE z = bignew_1(CLASS_OF(x), RBIGNUM_LEN(x), RBIGNUM_SIGN(x));
MEMCPY(BDIGITS(z), BDIGITS(x), BDIGIT, RBIGNUM_LEN(x));
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 VALUE
bigtrunc(VALUE x)
{
long len = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
if (len == 0) return x;
while (--len && !ds[len]);
rb_big_resize(x, len+1);
return x;
}
static VALUE
bigfixize(VALUE x)
{
long len = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
if (len*SIZEOF_BDIGITS <= sizeof(long)) {
long num = 0;
while (len--) {
num = BIGUP(num) + ds[len];
}
if (num >= 0) {
if (RBIGNUM_SIGN(x)) {
if (POSFIXABLE(num)) return LONG2FIX(num);
}
else {
if (NEGFIXABLE(-(long)num)) return LONG2FIX(-(long)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);
}
#ifdef HAVE_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
#define QUAD_SIZE 8
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) {
rb_raise(rb_eRangeError, "bignum too big to convert into `quad int'");
}
memcpy(buf, (char*)BDIGITS(val), len);
if (!RBIGNUM_SIGN(val)) {
len = QUAD_SIZE;
while (len--) {
*buf = ~*buf;
buf++;
}
}
}
#define BNEG(b) (RSHIFT(((BDIGIT*)b)[QUAD_SIZE/SIZEOF_BDIGITS-1],BITSPERDIG-1) != 0)
VALUE
rb_quad_unpack(const char *buf, int sign)
{
VALUE big = bignew(QUAD_SIZE/SIZEOF_BDIGITS, 1);
memcpy((char*)BDIGITS(big), buf, QUAD_SIZE);
if (sign && BNEG(buf)) {
long len = QUAD_SIZE;
char *tmp = (char*)BDIGITS(big);
RBIGNUM_SET_SIGN(big, 0);
while (len--) {
*tmp = ~*tmp;
tmp++;
}
}
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;
#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[1] == '_')) {
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 preceeding 0s */
while (*++str == '0');
if (!(c = *str) || ISSPACE(c)) --str;
}
c = *str;
c = conv_digit(c);
if (c < 0 || c >= base) {
if (badcheck) goto bad;
return INT2FIX(0);
}
len *= strlen(str)*sizeof(char);
if (len <= (sizeof(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 (badcheck) {
if (nondigit) goto bad;
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, VALUE *divp, 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) {
big2str_power_cache[i][0] =
rb_big_pow(rb_int2big(i+2), INT2FIX(KARATSUBA_DIGITS));
rb_global_variable(&big2str_power_cache[i][0]);
for (j = 1; 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] =
bigsqr(power_cache_get_power0(base, i - 1));
rb_global_variable(&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)
{
long i, j, m;
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 {
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 (FIXNUM_P(x)) {
VALUE str = rb_fix2str(x, base);
char* str_ptr = RSTRING_PTR(str);
long str_len = RSTRING_LEN(str);
if (trim) {
if (FIX2INT(x) == 0) return 0;
MEMCPY(ptr, str_ptr, char, str_len);
return str_len;
}
else {
memset(ptr, '0', len - str_len);
MEMCPY(ptr + len - str_len, str_ptr, char, str_len);
return len;
}
}
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);
ll = big2str_karatsuba(r, base, ptr + lh, m1/2,
m1, hbase, !lh && trim);
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_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_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);
}
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)
{
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 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 num;
}
VALUE
rb_big2ulong_pack(VALUE x)
{
VALUE num = big2ulong(x, "unsigned long", Qfalse);
if (!RBIGNUM_SIGN(x)) {
return -num;
}
return num;
}
VALUE
rb_big2ulong(VALUE x)
{
VALUE num = big2ulong(x, "unsigned long", Qtrue);
if (!RBIGNUM_SIGN(x)) {
if ((SIGNED_VALUE)num < 0) {
rb_raise(rb_eRangeError, "bignum out of range of unsigned long");
}
return -num;
}
return num;
}
SIGNED_VALUE
rb_big2long(VALUE x)
{
VALUE num = big2ulong(x, "long", Qtrue);
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 -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 double
big2dbl(VALUE x)
{
double d = 0.0;
long i = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
while (i--) {
d = ds[i] + BIGRAD*d;
}
if (!RBIGNUM_SIGN(x)) d = -d;
return d;
}
double
rb_big2dbl(VALUE x)
{
double d = big2dbl(x);
if (isinf(d)) {
rb_warn("Bignum out of Float range");
d = HUGE_VAL;
}
return d;
}
/*
* call-seq:
* big.to_f -> float
*
* Converts <i>big</i> to a <code>Float</code>. If <i>big</i> doesn't
* fit in a <code>Float</code>, the result is infinity.
*
*/
static VALUE
rb_big_to_f(VALUE x)
{
return DOUBLE2NUM(rb_big2dbl(x));
}
/*
* call-seq:
* big <=> numeric => -1, 0, +1
*
* Comparison---Returns -1, 0, or +1 depending on whether <i>big</i> is
* less than, equal to, or greater than <i>numeric</i>. This is the
* basis for the tests in <code>Comparable</code>.
*
*/
VALUE
rb_big_cmp(VALUE x, VALUE y)
{
long xlen = RBIGNUM_LEN(x);
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
return rb_dbl_cmp(rb_big2dbl(x), RFLOAT_VALUE(y));
default:
return rb_num_coerce_cmp(x, y);
}
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);
while(xlen-- && (BDIGITS(x)[xlen]==BDIGITS(y)[xlen]));
if (-1 == xlen) return INT2FIX(0);
return (BDIGITS(x)[xlen] > BDIGITS(y)[xlen]) ?
(RBIGNUM_SIGN(x) ? INT2FIX(1) : INT2FIX(-1)) :
(RBIGNUM_SIGN(x) ? INT2FIX(-1) : INT2FIX(1));
}
/*
* call-seq:
* big == obj => true or false
*
* Returns <code>true</code> only if <i>obj</i> has the same value
* as <i>big</i>. Contrast this with <code>Bignum#eql?</code>, which
* requires <i>obj</i> to be a <code>Bignum</code>.
*
* 68719476736 == 68719476736.0 #=> true
*/
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 => other_big
*
* Unary minus (returns a new Bignum 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 VALUE
bigsub(VALUE x, VALUE y)
{
VALUE z = 0;
BDIGIT *zds;
BDIGIT_DBL_SIGNED num;
long i = RBIGNUM_LEN(x);
/* 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)) {
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_LEN(x), z==0);
zds = BDIGITS(z);
for (i = 0, num = 0; i < RBIGNUM_LEN(y); i++) {
num += (BDIGIT_DBL_SIGNED)BDIGITS(x)[i] - BDIGITS(y)[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
while (num && i < RBIGNUM_LEN(x)) {
num += BDIGITS(x)[i];
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
while (i < RBIGNUM_LEN(x)) {
zds[i] = BDIGITS(x)[i];
i++;
}
return z;
}
static VALUE
bigadd(VALUE x, VALUE y, int sign)
{
VALUE z;
BDIGIT_DBL num;
long i, 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;
z = x; x = y; y = z;
}
else {
len = RBIGNUM_LEN(y) + 1;
}
z = bignew(len, sign);
len = RBIGNUM_LEN(x);
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_LEN(y);
while (num && i < len) {
num += BDIGITS(y)[i];
BDIGITS(z)[i++] = BIGLO(num);
num = BIGDN(num);
}
while (i < len) {
BDIGITS(z)[i] = BDIGITS(y)[i];
i++;
}
BDIGITS(z)[i] = (BDIGIT)num;
return z;
}
/*
* call-seq:
* big + other => Numeric
*
* Adds big and other, returning the result.
*/
VALUE
rb_big_plus(VALUE x, VALUE 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 DOUBLE2NUM(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)
{
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 DOUBLE2NUM(rb_big2dbl(x) - RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, y);
}
}
static void
rb_big_stop(void *ptr)
{
VALUE *stop = (VALUE*)ptr;
*stop = Qtrue;
}
struct big_mul_struct {
VALUE x, y, stop;
};
static VALUE
bigmul1(void *ptr)
{
struct big_mul_struct *bms = (struct big_mul_struct*)ptr;
long i, j;
BDIGIT_DBL n = 0;
VALUE x = bms->x, y = bms->y, z;
BDIGIT *zds;
j = RBIGNUM_LEN(x) + RBIGNUM_LEN(y) + 1;
z = bignew(j, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
zds = BDIGITS(z);
while (j--) zds[j] = 0;
for (i = 0; i < RBIGNUM_LEN(x); i++) {
BDIGIT_DBL dd;
if (bms->stop) return Qnil;
dd = BDIGITS(x)[i];
if (dd == 0) continue;
n = 0;
for (j = 0; j < RBIGNUM_LEN(y); j++) {
BDIGIT_DBL ee = n + (BDIGIT_DBL)dd * BDIGITS(y)[j];
n = zds[i + j] + ee;
if (ee) zds[i + j] = BIGLO(n);
n = BIGDN(n);
}
if (n) {
zds[i + j] = n;
}
}
return z;
}
static VALUE
rb_big_mul0(VALUE x, VALUE y)
{
struct big_mul_struct bms;
VALUE z;
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
return DOUBLE2NUM(rb_big2dbl(x) * RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, y);
}
bms.x = x;
bms.y = y;
bms.stop = Qfalse;
if (RBIGNUM_LEN(x) + RBIGNUM_LEN(y) > 10000) {
z = rb_thread_blocking_region(bigmul1, &bms, rb_big_stop, &bms.stop);
}
else {
z = bigmul1(&bms);
}
return z;
}
/*
* call-seq:
* big * other => Numeric
*
* Multiplies big and other, returning the result.
*/
VALUE
rb_big_mul(VALUE x, VALUE y)
{
return bignorm(rb_big_mul0(x, y));
}
struct big_div_struct {
VALUE x, y, *divp, *modp, stop;
};
static VALUE
bigdivrem1(void *ptr)
{
struct big_div_struct *bds = (struct big_div_struct*)ptr;
VALUE x = bds->x, y = bds->y, *divp = bds->divp, *modp = bds->modp;
long nx = RBIGNUM_LEN(x), ny = RBIGNUM_LEN(y);
long i, j;
VALUE yy, z;
BDIGIT *xds, *yds, *zds, *tds;
BDIGIT_DBL t2;
BDIGIT_DBL_SIGNED num;
BDIGIT dd, q;
if (BIGZEROP(y)) rb_num_zerodiv();
yds = BDIGITS(y);
if (nx < ny || (nx == ny && BDIGITS(x)[nx - 1] < BDIGITS(y)[ny - 1])) {
if (divp) *divp = rb_int2big(0);
if (modp) *modp = x;
return Qnil;
}
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_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 & (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;
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 (bds->stop) return Qnil;
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_SET_LEN(*divp, i);
}
if (modp) { /* normalize remainder */
*modp = rb_big_clone(z);
zds = BDIGITS(*modp);
while (--ny && !zds[ny]); ++ny;
if (dd) {
t2 = 0; i = ny;
while(i--) {
t2 = (t2 | zds[i]) >> dd;
q = zds[i];
zds[i] = BIGLO(t2);
t2 = BIGUP(q);
}
}
RBIGNUM_SET_LEN(*modp, ny);
RBIGNUM_SET_SIGN(*modp, RBIGNUM_SIGN(x));
}
return Qnil;
}
static VALUE
bigdivrem(VALUE x, VALUE y, VALUE *divp, VALUE *modp)
{
struct big_div_struct bds;
VALUE z;
bds.x = x;
bds.y = y;
bds.divp = divp;
bds.modp = modp;
bds.stop = Qfalse;
if (RBIGNUM_LEN(x) > 10000 || RBIGNUM_LEN(y) > 10000) {
z = rb_thread_blocking_region(bigdivrem1, &bds, rb_big_stop, &bds.stop);
}
else {
z = bigdivrem1(&bds);
}
return z;
}
static void
bigdivmod(VALUE x, VALUE y, VALUE *divp, 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 (divp) *divp = *divp;
if (modp) *modp = mod;
}
}
/*
* call-seq:
* big / other => Numeric
* big.div(other) => Numeric
*
* Divides big by other, returning the result.
*/
VALUE
rb_big_div(VALUE x, VALUE y)
{
VALUE z;
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
return DOUBLE2NUM(rb_big2dbl(x) / RFLOAT_VALUE(y));
default:
return rb_num_coerce_bin(x, y);
}
bigdivmod(x, y, &z, 0);
return bignorm(z);
}
/*
* call-seq:
* big % other => Numeric
* big.modulo(other) => Numeric
*
* Returns big modulo other. See Numeric.divmod for more
* information.
*/
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);
}
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);
}
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, int n)
{
if (n < 0)
return big_lshift(x, (unsigned int)n);
else if (n > 0)
return big_rshift(x, (unsigned int)n);
return x;
}
/*
* call-seq:
* big.quo(numeric) -> float
* big.fdiv(numeric) -> float
*
* Returns the floating point result of dividing <i>big</i> by
* <i>numeric</i>.
*
* -1234567890987654321.quo(13731) #=> -89910996357705.5
* -1234567890987654321.quo(13731.24) #=> -89909424858035.7
*
*/
static VALUE
rb_big_quo(VALUE x, VALUE y)
{
double dx = big2dbl(x);
double dy;
if (isinf(dx)) {
#define DBL_BIGDIG ((DBL_MANT_DIG + BITSPERDIG) / BITSPERDIG)
VALUE z;
int ex, ey;
ex = (RBIGNUM_LEN(bigtrunc(x)) - 1) * BITSPERDIG;
ex += bdigbitsize(BDIGITS(x)[RBIGNUM_LEN(x) - 1]);
ex -= 2 * DBL_BIGDIG * BITSPERDIG;
if (ex) x = big_shift(x, ex);
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
case T_BIGNUM: {
ey = (RBIGNUM_LEN(bigtrunc(y)) - 1) * BITSPERDIG;
ey += bdigbitsize(BDIGITS(y)[RBIGNUM_LEN(y) - 1]);
ey -= DBL_BIGDIG * BITSPERDIG;
if (ey) y = big_shift(y, ey);
bignum:
bigdivrem(x, y, &z, 0);
return DOUBLE2NUM(ldexp(big2dbl(z), ex - ey));
}
case T_FLOAT:
y = dbl2big(ldexp(frexp(RFLOAT_VALUE(y), &ey), DBL_MANT_DIG));
ey -= DBL_MANT_DIG;
goto bignum;
}
}
switch (TYPE(y)) {
case T_FIXNUM:
dy = (double)FIX2LONG(y);
break;
case T_BIGNUM:
dy = rb_big2dbl(y);
break;
case T_FLOAT:
dy = RFLOAT_VALUE(y);
break;
default:
return rb_num_coerce_bin(x, y);
}
return DOUBLE2NUM(dx / dy);
}
static VALUE
bigsqr(VALUE x)
{
long len = RBIGNUM_LEN(x), k = len / 2, i;
VALUE a, b, a2, z;
BDIGIT_DBL num;
if (len < 4000 / BITSPERDIG) {
return bigtrunc(rb_big_mul0(x, x));
}
a = bignew(len - k, 1);
MEMCPY(BDIGITS(a), BDIGITS(x) + k, BDIGIT, len - k);
b = bignew(k, 1);
MEMCPY(BDIGITS(b), BDIGITS(x), BDIGIT, k);
a2 = bigtrunc(bigsqr(a));
z = bigsqr(b);
rb_big_realloc(z, (len = 2 * k + RBIGNUM_LEN(a2)) + 1);
while (RBIGNUM_LEN(z) < 2 * k) {
BDIGITS(z)[RBIGNUM_LEN(z)] = 0;
RBIGNUM_SET_LEN(z, RBIGNUM_LEN(z)+1);
}
MEMCPY(BDIGITS(z) + 2 * k, BDIGITS(a2), BDIGIT, RBIGNUM_LEN(a2));
RBIGNUM_SET_LEN(z, len);
a2 = bigtrunc(rb_big_mul0(a, b));
len = RBIGNUM_LEN(a2);
for (i = 0, num = 0; i < len; i++) {
num += (BDIGIT_DBL)BDIGITS(z)[i + k] + ((BDIGIT_DBL)BDIGITS(a2)[i] << 1);
BDIGITS(z)[i + k] = BIGLO(num);
num = BIGDN(num);
}
if (num) {
len = RBIGNUM_LEN(z);
for (i += k; i < len && num; ++i) {
num += (BDIGIT_DBL)BDIGITS(z)[i];
BDIGITS(z)[i] = BIGLO(num);
num = BIGDN(num);
}
if (num) {
BDIGITS(z)[RBIGNUM_LEN(z)] = BIGLO(num);
RBIGNUM_SET_LEN(z, RBIGNUM_LEN(z)+1);
}
}
return bigtrunc(z);
}
/*
* call-seq:
* big ** exponent #=> numeric
*
* Raises _big_ to the _exponent_ power (which may be an integer, float,
* or anything that will coerce to a number). The result may be
* a Fixnum, Bignum, or Float
*
* 123456789 ** 2 #=> 15241578750190521
* 123456789 ** 1.2 #=> 5126464716.09932
* 123456789 ** -2 #=> 6.5610001194102e-17
*/
VALUE
rb_big_pow(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);
break;
case T_BIGNUM:
rb_warn("in a**b, b may be too big");
d = rb_big2dbl(y);
break;
case T_FIXNUM:
yy = FIX2LONG(y);
if (yy > 0) {
VALUE z = 0;
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 = bigtrunc(bigsqr(z));
if (yy & mask) {
z = z ? bigtrunc(rb_big_mul0(z, x)) : x;
}
}
return bignorm(z);
}
d = (double)yy;
break;
default:
return rb_num_coerce_bin(x, y);
}
return DOUBLE2NUM(pow(rb_big2dbl(x), d));
}
/*
* 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 = rb_to_int(yy);
if (FIXNUM_P(y)) {
y = rb_int2big(FIX2LONG(y));
}
if (!RBIGNUM_SIGN(y)) {
y = rb_big_clone(y);
get2comp(y);
}
if (!RBIGNUM_SIGN(x)) {
x = rb_big_clone(x);
get2comp(x);
}
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);
}
/*
* 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 = rb_to_int(yy);
if (FIXNUM_P(y)) {
y = rb_int2big(FIX2LONG(y));
}
if (!RBIGNUM_SIGN(y)) {
y = rb_big_clone(y);
get2comp(y);
}
if (!RBIGNUM_SIGN(x)) {
x = rb_big_clone(x);
get2comp(x);
}
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]:(BIGRAD-1);
}
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 = rb_to_int(yy);
if (FIXNUM_P(y)) {
y = rb_int2big(FIX2LONG(y));
}
if (!RBIGNUM_SIGN(y)) {
y = rb_big_clone(y);
get2comp(y);
}
if (!RBIGNUM_SIGN(x)) {
x = rb_big_clone(x);
get2comp(x);
}
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", Qtrue);
break;
}
y = rb_to_int(y);
}
if (neg) return big_rshift(x, shift);
return big_lshift(x, shift);
}
static VALUE
big_lshift(VALUE x, unsigned long shift)
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = shift%BITSPERDIG;
VALUE z;
BDIGIT_DBL num = 0;
long len, i;
len = RBIGNUM_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 bignorm(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", Qtrue);
break;
}
y = rb_to_int(y);
}
if (neg) return big_lshift(x, shift);
return big_rshift(x, shift);
}
static VALUE
big_rshift(VALUE x, unsigned long shift)
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = shift%BITSPERDIG;
VALUE z;
BDIGIT_DBL num = 0;
long i, j;
volatile VALUE save_x;
if (s1 > RBIGNUM_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 bignorm(z);
}
/*
* call-seq:
* big[n] -> 0, 1
*
* Bit Reference---Returns the <em>n</em>th bit in the (assumed) binary
* representation of <i>big</i>, where <i>big</i>[0] is the least
* significant bit.
*
* a = 9**15
* 50.downto(0) do |n|
* print a[n]
* end
*
* <em>produces:</em>
*
* 000101110110100000111000011110010100111100010111001
*
*/
static VALUE
rb_big_aref(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);
if (RBIGNUM_LEN(bigtrunc(y)) > DIGSPERLONG) {
out_of_range:
return RBIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
}
shift = big2ulong(y, "long", Qfalse);
}
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)
{
int 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_div, 1);
rb_define_method(rb_cBignum, "divmod", rb_big_divmod, 1);
rb_define_method(rb_cBignum, "modulo", rb_big_modulo, 1);
rb_define_method(rb_cBignum, "remainder", rb_big_remainder, 1);
rb_define_method(rb_cBignum, "quo", rb_big_quo, 1);
rb_define_method(rb_cBignum, "fdiv", rb_big_quo, 1);
rb_define_method(rb_cBignum, "**", rb_big_pow, 1);
rb_define_method(rb_cBignum, "&", rb_big_and, 1);
rb_define_method(rb_cBignum, "|", rb_big_or, 1);
rb_define_method(rb_cBignum, "^", rb_big_xor, 1);
rb_define_method(rb_cBignum, "~", rb_big_neg, 0);
rb_define_method(rb_cBignum, "<<", rb_big_lshift, 1);
rb_define_method(rb_cBignum, ">>", rb_big_rshift, 1);
rb_define_method(rb_cBignum, "[]", rb_big_aref, 1);
rb_define_method(rb_cBignum, "<=>", rb_big_cmp, 1);
rb_define_method(rb_cBignum, "==", rb_big_eq, 1);
rb_define_method(rb_cBignum, "eql?", rb_big_eql, 1);
rb_define_method(rb_cBignum, "hash", rb_big_hash, 0);
rb_define_method(rb_cBignum, "to_f", rb_big_to_f, 0);
rb_define_method(rb_cBignum, "abs", rb_big_abs, 0);
rb_define_method(rb_cBignum, "size", rb_big_size, 0);
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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