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bignum.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 <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 ((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 || \
(BDIGITS(x)[0] == 0 && \
(RBIGNUM_LEN(x) == 1 || bigzero_p(x))))
static int
bigzero_p(VALUE x)
{
long i;
for (i = RBIGNUM_LEN(x) - 1; 0 <= i; i--) {
if (BDIGITS(x)[i]) return 0;
}
return 1;
}
int
rb_cmpint(VALUE val, VALUE a, VALUE b)
{
if (NIL_P(val)) {
rb_cmperr(a, b);
}
if (FIXNUM_P(val)) return FIX2INT(val);
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) ? \
(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);
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 {
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 += 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 (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, 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) {
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)
{
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 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);
}