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bignum.c
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/**********************************************************************
bignum.c -
$Author$
$Date$
created at: Fri Jun 10 00:48:55 JST 1994
Copyright (C) 1993-2003 Yukihiro Matsumoto
**********************************************************************/
#include "ruby.h"
#include <math.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) ((BDIGIT*)RBIGNUM(x)->digits)
#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(x)->len == 0 || (RBIGNUM(x)->len == 1 && BDIGITS(x)[0] == 0))
static VALUE
bignew_1(VALUE klass, long len, int sign)
{
NEWOBJ(big, struct RBignum);
OBJSETUP(big, klass, T_BIGNUM);
big->sign = sign?1:0;
big->len = len;
big->digits = ALLOC_N(BDIGIT, len);
return (VALUE)big;
}
#define bignew(len,sign) bignew_1(rb_cBignum,len,sign)
VALUE
rb_big_clone(VALUE x)
{
VALUE z = bignew_1(CLASS_OF(x), RBIGNUM(x)->len, RBIGNUM(x)->sign);
MEMCPY(BDIGITS(z), BDIGITS(x), BDIGIT, RBIGNUM(x)->len);
return z;
}
/* modify a bignum by 2's complement */
static void
get2comp(VALUE x)
{
long i = RBIGNUM(x)->len;
BDIGIT *ds = BDIGITS(x);
BDIGIT_DBL num;
while (i--) ds[i] = ~ds[i];
i = 0; num = 1;
do {
num += ds[i];
ds[i++] = BIGLO(num);
num = BIGDN(num);
} while (i < RBIGNUM(x)->len);
if (num != 0) {
REALLOC_N(RBIGNUM(x)->digits, BDIGIT, ++RBIGNUM(x)->len);
ds = BDIGITS(x);
ds[RBIGNUM(x)->len-1] = 1;
}
}
void
rb_big_2comp(VALUE x) /* get 2's complement */
{
get2comp(x);
}
static VALUE
bignorm(VALUE x)
{
if (FIXNUM_P(x)) {
return x;
}
else if (TYPE(x) == T_BIGNUM) {
long len = RBIGNUM(x)->len;
BDIGIT *ds = BDIGITS(x);
while (len-- && !ds[len]) ;
RBIGNUM(x)->len = ++len;
if (len*SIZEOF_BDIGITS <= sizeof(VALUE)) {
long num = 0;
while (len--) {
num = BIGUP(num) + ds[len];
}
if (num >= 0) {
if (RBIGNUM(x)->sign) {
if (POSFIXABLE(num)) return LONG2FIX(num);
}
else if (NEGFIXABLE(-(long)num)) return LONG2FIX(-(long)num);
}
}
}
return x;
}
VALUE
rb_big_norm(VALUE x)
{
return bignorm(x);
}
VALUE
rb_uint2big(unsigned long 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(big)->len = i+1;
return big;
}
VALUE
rb_int2big(long n)
{
long neg = 0;
VALUE big;
if (n < 0) {
n = -n;
neg = 1;
}
big = rb_uint2big(n);
if (neg) {
RBIGNUM(big)->sign = 0;
}
return big;
}
VALUE
rb_uint2inum(unsigned long n)
{
if (POSFIXABLE(n)) return LONG2FIX(n);
return rb_uint2big(n);
}
VALUE
rb_int2inum(long 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(val)->len;
BDIGIT *ds;
if (len > SIZEOF_LONG_LONG/SIZEOF_BDIGITS) {
len = SIZEOF_LONG/SIZEOF_BDIGITS;
}
ds = BDIGITS(val);
q = 0;
while (len--) {
q = BIGUP(q);
q += ds[len];
}
if (!RBIGNUM(val)->sign) 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(big)->len = i+1;
if (neg) {
RBIGNUM(big)->sign = 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(val)->len * 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(val)->sign) {
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(big)->sign = 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;
if (!str) {
if (badcheck) goto bad;
return INT2FIX(0);
}
if (badcheck) {
while (ISSPACE(*str)) str++;
}
else {
while (ISSPACE(*str) || *str == '_') str++;
}
if (str[0] == '+') {
str++;
}
else if (str[0] == '-') {
str++;
sign = 0;
}
if (str[0] == '+' || str[0] == '-') {
if (badcheck) goto bad;
return INT2FIX(0);
}
if (base <= 0) {
if (str[0] == '0') {
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, "illegal radix %d", base);
}
if (base <= 32) {
len = 5;
}
else {
len = 6;
}
break;
}
if (*str == '0') { /* squeeze preceeding 0s */
while (*++str == '0');
--str;
}
len *= strlen(str)*sizeof(char);
if (len <= (sizeof(VALUE)*CHAR_BIT)) {
unsigned long val = strtoul((char*)str, &end, base);
if (*end == '_') goto bigparse;
if (badcheck) {
if (end == str) goto bad; /* no number */
while (*end && ISSPACE(*end)) end++;
if (*end) 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(big)->sign = 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++) {
if (c == '_') {
if (badcheck) {
if (nondigit) goto bad;
nondigit = c;
}
continue;
}
else if (!ISASCII(c)) {
break;
}
else if (isdigit(c)) {
c -= '0';
}
else if (islower(c)) {
c -= 'a' - 10;
}
else if (isupper(c)) {
c -= 'A' - 10;
}
else {
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(str)->ptr;
}
if (s) {
len = RSTRING(str)->len;
if (s[len]) { /* no sentinel somehow */
char *p = ALLOCA_N(char, len+1);
MEMCPY(p, s, char, len);
p[len] = '\0';
s = p;
}
}
return rb_cstr_to_inum(s, base, badcheck);
}
#if HAVE_LONG_LONG
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(big)->len = i+1;
return big;
}
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(big)->sign = 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";
VALUE
rb_big2str(VALUE x, int base)
{
volatile VALUE t;
BDIGIT *ds;
long i, j, hbase;
VALUE ss;
char *s, c;
if (FIXNUM_P(x)) {
return rb_fix2str(x, base);
}
i = RBIGNUM(x)->len;
if (BIGZEROP(x)) {
return rb_str_new2("0");
}
j = SIZEOF_BDIGITS*CHAR_BIT*i;
switch (base) {
case 2: break;
case 3:
j = j * 647L / 1024;
break;
case 4: case 5: case 6: case 7:
j /= 2;
break;
case 8: case 9:
j /= 3;
break;
case 10: case 11: case 12: case 13: case 14: case 15:
j = j * 241L / 800;
break;
case 16: case 17: case 18: case 19: case 20: case 21:
case 22: case 23: case 24: case 25: case 26: case 27:
case 28: case 29: case 30: case 31:
j /= 4;
break;
case 32: case 33: case 34: case 35: case 36:
j /= 5;
break;
default:
rb_raise(rb_eArgError, "illegal radix %d", base);
break;
}
j += 2;
hbase = base * base;
#if SIZEOF_BDIGITS > 2
hbase *= hbase;
#endif
t = rb_big_clone(x);
ds = BDIGITS(t);
ss = rb_str_new(0, j);
s = RSTRING(ss)->ptr;
s[0] = RBIGNUM(x)->sign ? '+' : '-';
while (i && j) {
long k = i;
BDIGIT_DBL num = 0;
while (k--) {
num = BIGUP(num) + ds[k];
ds[k] = (BDIGIT)(num / hbase);
num %= hbase;
}
if (ds[i-1] == 0) i--;
k = SIZEOF_BDIGITS;
while (k--) {
c = (char)(num % base);
s[--j] = ruby_digitmap[(int)c];
num /= base;
if (i == 0 && num == 0) break;
}
}
while (s[j] == '0') j++;
RSTRING(ss)->len -= RBIGNUM(x)->sign?j:j-1;
memmove(RBIGNUM(x)->sign?s:s+1, s+j, RSTRING(ss)->len);
s[RSTRING(ss)->len] = '\0';
return ss;
}
/*
* call-seq:
* big.to_s(base=10) => string
*
* Returns a string containing the representation of <i>big</i> radix
* <i>base</i> (2 through 36).
*
* 12345654321.to_s #=> "12345654321"
* 12345654321.to_s(2) #=> "1011011111110110111011110000110001"
* 12345654321.to_s(8) #=> "133766736061"
* 12345654321.to_s(16) #=> "2dfdbbc31"
* 78546939656932.to_s(36) #=> "rubyrules"
*/
static VALUE
rb_big_to_s(int argc, VALUE *argv, VALUE x)
{
VALUE b;
int base;
rb_scan_args(argc, argv, "01", &b);
if (argc == 0) base = 10;
else base = NUM2INT(b);
return rb_big2str(x, base);
}
static unsigned long
big2ulong(VALUE x, const char *type, int check)
{
long len = RBIGNUM(x)->len;
BDIGIT_DBL num;
BDIGIT *ds;
if (len > SIZEOF_LONG/SIZEOF_BDIGITS) {
if (check)
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
len = SIZEOF_LONG/SIZEOF_BDIGITS;
}
ds = BDIGITS(x);
num = 0;
while (len--) {
num = BIGUP(num);
num += ds[len];
}
return num;
}
unsigned long
rb_big2ulong_pack(VALUE x)
{
unsigned long num = big2ulong(x, "unsigned long", Qfalse);
if (!RBIGNUM(x)->sign) {
return -num;
}
return num;
}
unsigned long
rb_big2ulong(VALUE x)
{
unsigned long num = big2ulong(x, "unsigned long", Qtrue);
if (!RBIGNUM(x)->sign) {
if ((long)num < 0) {
rb_raise(rb_eRangeError, "bignum out of range of unsigned long");
}
return -num;
}
return num;
}
long
rb_big2long(VALUE x)
{
unsigned long num = big2ulong(x, "long", Qtrue);
if ((long)num < 0 && (RBIGNUM(x)->sign || (long)num != LONG_MIN)) {
rb_raise(rb_eRangeError, "bignum too big to convert into `long'");
}
if (!RBIGNUM(x)->sign) return -(long)num;
return num;
}
#if HAVE_LONG_LONG
static unsigned LONG_LONG
big2ull(VALUE x, const char *type)
{
long len = RBIGNUM(x)->len;
BDIGIT_DBL num;
BDIGIT *ds;
if (len > SIZEOF_LONG_LONG/SIZEOF_BDIGITS)
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
ds = BDIGITS(x);
num = 0;
while (len--) {
num = BIGUP(num);
num += ds[len];
}
return num;
}
unsigned LONG_LONG
rb_big2ull(VALUE x)
{
unsigned LONG_LONG num = big2ull(x, "unsigned long long");
if (!RBIGNUM(x)->sign) return -num;
return num;
}
LONG_LONG
rb_big2ll(VALUE x)
{
unsigned LONG_LONG num = big2ull(x, "long long");
if ((LONG_LONG)num < 0 && (RBIGNUM(x)->sign
|| (LONG_LONG)num != LLONG_MIN)) {
rb_raise(rb_eRangeError, "bignum too big to convert into `long long'");
}
if (!RBIGNUM(x)->sign) return -(LONG_LONG)num;
return num;
}
#endif /* HAVE_LONG_LONG */
static VALUE
dbl2big(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));
}
double
rb_big2dbl(VALUE x)
{
double d = 0.0;
long i = RBIGNUM(x)->len;
BDIGIT *ds = BDIGITS(x);
while (i--) {
d = ds[i] + BIGRAD*d;
}
if (isinf(d)) {
rb_warn("Bignum out of Float range");
d = HUGE_VAL;
}
if (!RBIGNUM(x)->sign) d = -d;
return d;
}
/*
* call-seq:
* big.to_f -> float
*
* Converts <i>big</i> to a <code>Float</code>. If <i>big</i> doesn't
* fit in a <code>Float</code>, the result is infinity.
*
*/
static VALUE
rb_big_to_f(VALUE x)
{
return rb_float_new(rb_big2dbl(x));
}
/*
* call-seq:
* big <=> numeric => -1, 0, +1
*
* Comparison---Returns -1, 0, or +1 depending on whether <i>big</i> is
* less than, equal to, or greater than <i>numeric</i>. This is the
* basis for the tests in <code>Comparable</code>.
*
*/
VALUE
rb_big_cmp(VALUE x, VALUE y)
{
long xlen = RBIGNUM(x)->len;
switch (TYPE(y)) {
case T_FIXNUM:
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
return rb_dbl_cmp(rb_big2dbl(x), RFLOAT(y)->value);
default:
return rb_num_coerce_cmp(x, y);
}
if (RBIGNUM(x)->sign > RBIGNUM(y)->sign) return INT2FIX(1);
if (RBIGNUM(x)->sign < RBIGNUM(y)->sign) return INT2FIX(-1);
if (xlen < RBIGNUM(y)->len)
return (RBIGNUM(x)->sign) ? INT2FIX(-1) : INT2FIX(1);
if (xlen > RBIGNUM(y)->len)
return (RBIGNUM(x)->sign) ? INT2FIX(1) : INT2FIX(-1);
while(xlen-- && (BDIGITS(x)[xlen]==BDIGITS(y)[xlen]));
if (-1 == xlen) return INT2FIX(0);
return (BDIGITS(x)[xlen] > BDIGITS(y)[xlen]) ?
(RBIGNUM(x)->sign ? INT2FIX(1) : INT2FIX(-1)) :
(RBIGNUM(x)->sign ? INT2FIX(-1) : INT2FIX(1));
}
/*
* call-seq:
* big == obj => true or false
*
* Returns <code>true</code> only if <i>obj</i> has the same value
* as <i>big</i>. Contrast this with <code>Bignum#eql?</code>, which
* requires <i>obj</i> to be a <code>Bignum</code>.
*
* 68719476736 == 68719476736.0 #=> true
*/
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(y)->value;
if (isnan(a)) return Qfalse;
b = rb_big2dbl(x);
return (a == b)?Qtrue:Qfalse;
}
default:
return rb_equal(y, x);
}
if (RBIGNUM(x)->sign != RBIGNUM(y)->sign) return Qfalse;
if (RBIGNUM(x)->len != RBIGNUM(y)->len) return Qfalse;
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM(y)->len) != 0) return Qfalse;
return Qtrue;
}
/*
* call-seq:
* big.eql?(obj) => true or false
*
* Returns <code>true</code> only if <i>obj</i> is a
* <code>Bignum</code> with the same value as <i>big</i>. Contrast this
* with <code>Bignum#==</code>, which performs type conversions.
*
* 68719476736.eql?(68719476736.0) #=> false
*/
static VALUE
rb_big_eql(VALUE x, VALUE y)
{
if (TYPE(y) != T_BIGNUM) return Qfalse;
if (RBIGNUM(x)->sign != RBIGNUM(y)->sign) return Qfalse;
if (RBIGNUM(x)->len != RBIGNUM(y)->len) return Qfalse;
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,RBIGNUM(y)->len) != 0) return Qfalse;
return Qtrue;
}
/*
* call-seq:
* -big => other_big
*
* Unary minus (returns a new Bignum whose value is 0-big)
*/
static VALUE
rb_big_uminus(VALUE x)
{
VALUE z = rb_big_clone(x);
RBIGNUM(z)->sign = !RBIGNUM(x)->sign;
return bignorm(z);
}
/*
* call-seq:
* ~big => integer
*
* Inverts the bits in big. As Bignums are conceptually infinite
* length, the result acts as if it had an infinite number of one
* bits to the left. In hex representations, this is displayed
* as two periods to the left of the digits.
*
* sprintf("%X", ~0x1122334455) #=> "..FEEDDCCBBAA"
*/
static VALUE
rb_big_neg(VALUE x)
{