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ruby--ruby/bignum.c
akr fa343a796f * bignum.c (biglsh_bang): Don't shift a BDIGIT with BITSPERDIG bits. 
(bigrsh_bang): Ditto.




git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@41842 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2013-07-08 16:50:04 +00:00

6056 lines
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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/thread.h"
#include "ruby/util.h"
#include "internal.h"
#ifdef HAVE_STRINGS_H
#include <strings.h>
#endif
#include <math.h>
#include <float.h>
#include <ctype.h>
#ifdef HAVE_IEEEFP_H
#include <ieeefp.h>
#endif
#include <assert.h>
VALUE rb_cBignum;
const char ruby_digitmap[] = "0123456789abcdefghijklmnopqrstuvwxyz";
static VALUE big_three = Qnil;
#if defined __MINGW32__
#define USHORT _USHORT
#endif
#ifdef WORDS_BIGENDIAN
# define HOST_BIGENDIAN_P 1
#else
# define HOST_BIGENDIAN_P 0
#endif
#define ALIGNOF(type) ((int)offsetof(struct { char f1; type f2; }, f2))
/* (sizeof(d) * CHAR_BIT <= (n) ? 0 : (n)) is same as n but suppress a warning, C4293, by Visual Studio. */
#define LSHIFTABLE(d, n) ((n) < sizeof(d) * CHAR_BIT)
#define LSHIFTX(d, n) (!LSHIFTABLE(d, n) ? 0 : ((d) << (!LSHIFTABLE(d, n) ? 0 : (n))))
#define CLEAR_LOWBITS(d, numbits) ((d) & LSHIFTX(~((d)*0), (numbits)))
#define FILL_LOWBITS(d, numbits) ((d) | (LSHIFTX(((d)*0+1), (numbits))-1))
#define POW2_P(x) (((x)&((x)-1))==0)
#define BDIGITS(x) (RBIGNUM_DIGITS(x))
#define BITSPERDIG (SIZEOF_BDIGITS*CHAR_BIT)
#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
#define BIGRAD_HALF ((BDIGIT)(BIGRAD >> 1))
#define BDIGIT_MSB(d) (((d) & BIGRAD_HALF) != 0)
#if SIZEOF_LONG >= SIZEOF_BDIGITS
# define DIGSPERLONG (SIZEOF_LONG/SIZEOF_BDIGITS)
#endif
#if defined(HAVE_LONG_LONG) && SIZEOF_LONG_LONG >= SIZEOF_BDIGITS
# define DIGSPERLL (SIZEOF_LONG_LONG/SIZEOF_BDIGITS)
#endif
#define BIGUP(x) LSHIFTX(((x) + (BDIGIT_DBL)0), BITSPERDIG)
#define BIGDN(x) RSHIFT((x),BITSPERDIG)
#define BIGLO(x) ((BDIGIT)((x) & BDIGMAX))
#define BDIGMAX ((BDIGIT)(BIGRAD-1))
#define BDIGIT_DBL_MAX (~(BDIGIT_DBL)0)
#if SIZEOF_BDIGITS == 2
# define swap_bdigit(x) swap16(x)
#elif SIZEOF_BDIGITS == 4
# define swap_bdigit(x) swap32(x)
#elif SIZEOF_BDIGITS == 8
# define swap_bdigit(x) swap64(x)
#endif
#define BIGZEROP(x) (RBIGNUM_LEN(x) == 0 || \
(BDIGITS(x)[0] == 0 && \
(RBIGNUM_LEN(x) == 1 || bigzero_p(x))))
#define BIGSIZE(x) (RBIGNUM_LEN(x) == 0 ? (size_t)0 : \
BDIGITS(x)[RBIGNUM_LEN(x)-1] ? \
(size_t)(RBIGNUM_LEN(x)*SIZEOF_BDIGITS - nlz(BDIGITS(x)[RBIGNUM_LEN(x)-1])/CHAR_BIT) : \
rb_absint_size(x, NULL))
#define BIGDIVREM_EXTRA_WORDS 2
#define roomof(n, m) ((long)(((n)+(m)-1) / (m)))
#define bdigit_roomof(n) roomof(n, SIZEOF_BDIGITS)
#define BARY_ARGS(ary) ary, numberof(ary)
#define BARY_ADD(z, x, y) bary_add(BARY_ARGS(z), BARY_ARGS(x), BARY_ARGS(y))
#define BARY_SUB(z, x, y) bary_sub(BARY_ARGS(z), BARY_ARGS(x), BARY_ARGS(y))
#define BARY_MUL1(z, x, y) bary_mul1(BARY_ARGS(z), BARY_ARGS(x), BARY_ARGS(y))
#define BARY_DIVMOD(q, r, x, y) bary_divmod(BARY_ARGS(q), BARY_ARGS(r), BARY_ARGS(x), BARY_ARGS(y))
#define BARY_ZERO_P(x) bary_zero_p(BARY_ARGS(x))
#define RBIGNUM_SET_NEGATIVE_SIGN(b) RBIGNUM_SET_SIGN(b, 0)
#define RBIGNUM_SET_POSITIVE_SIGN(b) RBIGNUM_SET_SIGN(b, 1)
#define bignew(len,sign) bignew_1(rb_cBignum,(len),(sign))
#define KARATSUBA_MUL_DIGITS 70
#define TOOM3_MUL_DIGITS 150
static BDIGIT bary_small_lshift(BDIGIT *zds, BDIGIT *xds, long n, int shift);
static void bary_small_rshift(BDIGIT *zds, BDIGIT *xds, long n, int shift, int sign_bit);
static void bary_mul(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl);
static void bary_divmod(BDIGIT *qds, size_t nq, BDIGIT *rds, size_t nr, BDIGIT *xds, size_t nx, BDIGIT *yds, size_t ny);
static VALUE bigmul0(VALUE x, VALUE y);
static VALUE bigmul1_toom3(VALUE x, VALUE y);
static VALUE bignew_1(VALUE klass, long len, int sign);
static inline VALUE bigtrunc(VALUE x);
static VALUE bigsqr(VALUE x);
static void bigdivmod(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp);
static int
nlz16(uint16_t x)
{
uint16_t y;
int n = 16;
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 (int)(n - x);
}
static int
nlz32(uint32_t x)
{
uint32_t y;
int n = 32;
y = x >> 16; if (y) {n -= 16; x = y;}
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 (int)(n - x);
}
#if defined(HAVE_UINT64_T)
static int
nlz64(uint64_t x)
{
uint64_t y;
int n = 64;
y = x >> 32; if (y) {n -= 32; x = y;}
y = x >> 16; if (y) {n -= 16; x = y;}
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 (int)(n - x);
}
#endif
#if defined(HAVE_UINT128_T)
static int
nlz128(uint128_t x)
{
uint128_t y;
int n = 128;
y = x >> 64; if (y) {n -= 64; x = y;}
y = x >> 32; if (y) {n -= 32; x = y;}
y = x >> 16; if (y) {n -= 16; x = y;}
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 (int)(n - x);
}
#endif
#if SIZEOF_BDIGITS == 2
static int nlz(BDIGIT x) { return nlz16((uint16_t)x); }
#elif SIZEOF_BDIGITS == 4
static int nlz(BDIGIT x) { return nlz32((uint32_t)x); }
#elif SIZEOF_BDIGITS == 8
static int nlz(BDIGIT x) { return nlz64((uint64_t)x); }
#elif SIZEOF_BDIGITS == 16
static int nlz(BDIGIT x) { return nlz128((uint128_t)x); }
#endif
#if defined(HAVE_UINT128_T)
# define bitsize(x) \
(sizeof(x) <= 2 ? 16 - nlz16(x) : \
sizeof(x) <= 4 ? 32 - nlz32(x) : \
sizeof(x) <= 8 ? 64 - nlz64(x) : \
128 - nlz128(x))
#elif defined(HAVE_UINT64_T)
# define bitsize(x) \
(sizeof(x) <= 2 ? 16 - nlz16(x) : \
sizeof(x) <= 4 ? 32 - nlz32(x) : \
64 - nlz64(x))
#else
# define bitsize(x) \
(sizeof(x) <= 2 ? 16 - nlz16(x) : \
32 - nlz32(x))
#endif
#define U16(a) ((uint16_t)(a))
#define U32(a) ((uint32_t)(a))
#ifdef HAVE_UINT64_T
#define U64(a,b) (((uint64_t)(a) << 32) | (b))
#endif
#ifdef HAVE_UINT128_T
#define U128(a,b,c,d) (((uint128_t)U64(a,b) << 64) | U64(c,d))
#endif
/* The following scirpt, maxpow.rb, generates the tables follows.
def big(n, bits)
ns = []
((bits+31)/32).times {
ns << sprintf("0x%08x", n & 0xffff_ffff)
n >>= 32
}
"U#{bits}(" + ns.reverse.join(",") + ")"
end
def values(ary, width, indent)
lines = [""]
ary.each {|e|
lines << "" if !ary.last.empty? && width < (lines.last + e + ", ").length
lines.last << e + ", "
}
lines.map {|line| " " * indent + line.chomp(" ") + "\n" }.join
end
[16,32,64,128].each {|bits|
max = 2**bits-1
exps = []
nums = []
2.upto(36) {|base|
exp = 0
n = 1
while n * base <= max
exp += 1
n *= base
end
exps << exp.to_s
nums << big(n, bits)
}
puts "#ifdef HAVE_UINT#{bits}_T"
puts "static const int maxpow#{bits}_exp[35] = {"
print values(exps, 70, 4)
puts "};"
puts "static const uint#{bits}_t maxpow#{bits}_num[35] = {"
print values(nums, 70, 4)
puts "};"
puts "#endif"
}
*/
#ifdef HAVE_UINT16_T
static const int maxpow16_exp[35] = {
15, 10, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
};
static const uint16_t maxpow16_num[35] = {
U16(0x00008000), U16(0x0000e6a9), U16(0x00004000), U16(0x00003d09),
U16(0x0000b640), U16(0x000041a7), U16(0x00008000), U16(0x0000e6a9),
U16(0x00002710), U16(0x00003931), U16(0x00005100), U16(0x00006f91),
U16(0x00009610), U16(0x0000c5c1), U16(0x00001000), U16(0x00001331),
U16(0x000016c8), U16(0x00001acb), U16(0x00001f40), U16(0x0000242d),
U16(0x00002998), U16(0x00002f87), U16(0x00003600), U16(0x00003d09),
U16(0x000044a8), U16(0x00004ce3), U16(0x000055c0), U16(0x00005f45),
U16(0x00006978), U16(0x0000745f), U16(0x00008000), U16(0x00008c61),
U16(0x00009988), U16(0x0000a77b), U16(0x0000b640),
};
#endif
#ifdef HAVE_UINT32_T
static const int maxpow32_exp[35] = {
31, 20, 15, 13, 12, 11, 10, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7,
7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
};
static const uint32_t maxpow32_num[35] = {
U32(0x80000000), U32(0xcfd41b91), U32(0x40000000), U32(0x48c27395),
U32(0x81bf1000), U32(0x75db9c97), U32(0x40000000), U32(0xcfd41b91),
U32(0x3b9aca00), U32(0x8c8b6d2b), U32(0x19a10000), U32(0x309f1021),
U32(0x57f6c100), U32(0x98c29b81), U32(0x10000000), U32(0x18754571),
U32(0x247dbc80), U32(0x3547667b), U32(0x4c4b4000), U32(0x6b5a6e1d),
U32(0x94ace180), U32(0xcaf18367), U32(0x0b640000), U32(0x0e8d4a51),
U32(0x1269ae40), U32(0x17179149), U32(0x1cb91000), U32(0x23744899),
U32(0x2b73a840), U32(0x34e63b41), U32(0x40000000), U32(0x4cfa3cc1),
U32(0x5c13d840), U32(0x6d91b519), U32(0x81bf1000),
};
#endif
#ifdef HAVE_UINT64_T
static const int maxpow64_exp[35] = {
63, 40, 31, 27, 24, 22, 21, 20, 19, 18, 17, 17, 16, 16, 15, 15, 15,
15, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12,
12,
};
static const uint64_t maxpow64_num[35] = {
U64(0x80000000,0x00000000), U64(0xa8b8b452,0x291fe821),
U64(0x40000000,0x00000000), U64(0x6765c793,0xfa10079d),
U64(0x41c21cb8,0xe1000000), U64(0x36427987,0x50226111),
U64(0x80000000,0x00000000), U64(0xa8b8b452,0x291fe821),
U64(0x8ac72304,0x89e80000), U64(0x4d28cb56,0xc33fa539),
U64(0x1eca170c,0x00000000), U64(0x780c7372,0x621bd74d),
U64(0x1e39a505,0x7d810000), U64(0x5b27ac99,0x3df97701),
U64(0x10000000,0x00000000), U64(0x27b95e99,0x7e21d9f1),
U64(0x5da0e1e5,0x3c5c8000), U64(0xd2ae3299,0xc1c4aedb),
U64(0x16bcc41e,0x90000000), U64(0x2d04b7fd,0xd9c0ef49),
U64(0x5658597b,0xcaa24000), U64(0xa0e20737,0x37609371),
U64(0x0c29e980,0x00000000), U64(0x14adf4b7,0x320334b9),
U64(0x226ed364,0x78bfa000), U64(0x383d9170,0xb85ff80b),
U64(0x5a3c23e3,0x9c000000), U64(0x8e651373,0x88122bcd),
U64(0xdd41bb36,0xd259e000), U64(0x0aee5720,0xee830681),
U64(0x10000000,0x00000000), U64(0x172588ad,0x4f5f0981),
U64(0x211e44f7,0xd02c1000), U64(0x2ee56725,0xf06e5c71),
U64(0x41c21cb8,0xe1000000),
};
#endif
#ifdef HAVE_UINT128_T
static const int maxpow128_exp[35] = {
127, 80, 63, 55, 49, 45, 42, 40, 38, 37, 35, 34, 33, 32, 31, 31, 30,
30, 29, 29, 28, 28, 27, 27, 27, 26, 26, 26, 26, 25, 25, 25, 25, 24,
24,
};
static const uint128_t maxpow128_num[35] = {
U128(0x80000000,0x00000000,0x00000000,0x00000000),
U128(0x6f32f1ef,0x8b18a2bc,0x3cea5978,0x9c79d441),
U128(0x40000000,0x00000000,0x00000000,0x00000000),
U128(0xd0cf4b50,0xcfe20765,0xfff4b4e3,0xf741cf6d),
U128(0x6558e2a0,0x921fe069,0x42860000,0x00000000),
U128(0x5080c7b7,0xd0e31ba7,0x5911a67d,0xdd3d35e7),
U128(0x40000000,0x00000000,0x00000000,0x00000000),
U128(0x6f32f1ef,0x8b18a2bc,0x3cea5978,0x9c79d441),
U128(0x4b3b4ca8,0x5a86c47a,0x098a2240,0x00000000),
U128(0xffd1390a,0x0adc2fb8,0xdabbb817,0x4d95c99b),
U128(0x2c6fdb36,0x4c25e6c0,0x00000000,0x00000000),
U128(0x384bacd6,0x42c343b4,0xe90c4272,0x13506d29),
U128(0x31f5db32,0xa34aced6,0x0bf13a0e,0x00000000),
U128(0x20753ada,0xfd1e839f,0x53686d01,0x3143ee01),
U128(0x10000000,0x00000000,0x00000000,0x00000000),
U128(0x68ca11d6,0xb4f6d1d1,0xfaa82667,0x8073c2f1),
U128(0x223e493b,0xb3bb69ff,0xa4b87d6c,0x40000000),
U128(0xad62418d,0x14ea8247,0x01c4b488,0x6cc66f59),
U128(0x2863c1f5,0xcdae42f9,0x54000000,0x00000000),
U128(0xa63fd833,0xb9386b07,0x36039e82,0xbe651b25),
U128(0x1d1f7a9c,0xd087a14d,0x28cdf3d5,0x10000000),
U128(0x651b5095,0xc2ea8fc1,0xb30e2c57,0x77aaf7e1),
U128(0x0ddef20e,0xff760000,0x00000000,0x00000000),
U128(0x29c30f10,0x29939b14,0x6664242d,0x97d9f649),
U128(0x786a435a,0xe9558b0e,0x6aaf6d63,0xa8000000),
U128(0x0c5afe6f,0xf302bcbf,0x94fd9829,0xd87f5079),
U128(0x1fce575c,0xe1692706,0x07100000,0x00000000),
U128(0x4f34497c,0x8597e144,0x36e91802,0x00528229),
U128(0xbf3a8e1d,0x41ef2170,0x7802130d,0x84000000),
U128(0x0e7819e1,0x7f1eb0fb,0x6ee4fb89,0x01d9531f),
U128(0x20000000,0x00000000,0x00000000,0x00000000),
U128(0x4510460d,0xd9e879c0,0x14a82375,0x2f22b321),
U128(0x91abce3c,0x4b4117ad,0xe76d35db,0x22000000),
U128(0x08973ea3,0x55d75bc2,0x2e42c391,0x727d69e1),
U128(0x10e425c5,0x6daffabc,0x35c10000,0x00000000),
};
#endif
static BDIGIT_DBL
maxpow_in_bdigit_dbl(int base, int *exp_ret)
{
BDIGIT_DBL maxpow;
int exponent;
assert(2 <= base && base <= 36);
switch (sizeof(BDIGIT_DBL)) {
case 2:
maxpow = maxpow16_num[base-2];
exponent = maxpow16_exp[base-2];
break;
case 4:
maxpow = maxpow32_num[base-2];
exponent = maxpow32_exp[base-2];
break;
#ifdef HAVE_UINT64_T
case 8:
maxpow = maxpow64_num[base-2];
exponent = maxpow64_exp[base-2];
break;
#endif
#ifdef HAVE_UINT128_T
case 16:
maxpow = maxpow128_num[base-2];
exponent = maxpow128_exp[base-2];
break;
#endif
default:
maxpow = base;
exponent = 1;
while (maxpow <= BDIGIT_DBL_MAX / base) {
maxpow *= base;
exponent++;
}
break;
}
*exp_ret = exponent;
return maxpow;
}
static BDIGIT
maxpow_in_bdigit(int base, int *exp_ret)
{
BDIGIT maxpow;
int exponent;
switch (SIZEOF_BDIGITS) {
case 2:
maxpow = maxpow16_num[base-2];
exponent = maxpow16_exp[base-2];
break;
case 4:
maxpow = maxpow32_num[base-2];
exponent = maxpow32_exp[base-2];
break;
#ifdef HAVE_UINT64_T
case 8:
maxpow = maxpow64_num[base-2];
exponent = maxpow64_exp[base-2];
break;
#endif
#ifdef HAVE_UINT128_T
case 16:
maxpow = maxpow128_num[base-2];
exponent = maxpow128_exp[base-2];
break;
#endif
default:
maxpow = base;
exponent = 1;
while (maxpow <= BDIGMAX / base) {
maxpow *= base;
exponent++;
}
break;
}
*exp_ret = exponent;
return maxpow;
}
static int
bary_zero_p(BDIGIT *xds, size_t nx)
{
if (nx == 0)
return 1;
do {
if (xds[--nx]) return 0;
} while (nx);
return 1;
}
static void
bary_neg(BDIGIT *ds, size_t n)
{
while (n--)
ds[n] = BIGLO(~ds[n]);
}
static int
bary_plus_one(BDIGIT *ds, size_t n)
{
size_t i;
for (i = 0; i < n; i++) {
ds[i] = BIGLO(ds[i]+1);
if (ds[i] != 0)
return 0;
}
return 1;
}
static int
bary_2comp(BDIGIT *ds, size_t n)
{
if (!n) return 1;
bary_neg(ds, n);
return bary_plus_one(ds, n);
}
static void
bary_swap(BDIGIT *ds, size_t num_bdigits)
{
BDIGIT *p1 = ds;
BDIGIT *p2 = ds + num_bdigits - 1;
for (; p1 < p2; p1++, p2--) {
BDIGIT tmp = *p1;
*p1 = *p2;
*p2 = tmp;
}
}
#define INTEGER_PACK_WORDORDER_MASK \
(INTEGER_PACK_MSWORD_FIRST | \
INTEGER_PACK_LSWORD_FIRST)
#define INTEGER_PACK_BYTEORDER_MASK \
(INTEGER_PACK_MSBYTE_FIRST | \
INTEGER_PACK_LSBYTE_FIRST | \
INTEGER_PACK_NATIVE_BYTE_ORDER)
static void
validate_integer_pack_format(size_t numwords, size_t wordsize, size_t nails, int flags, int supported_flags)
{
int wordorder_bits = flags & INTEGER_PACK_WORDORDER_MASK;
int byteorder_bits = flags & INTEGER_PACK_BYTEORDER_MASK;
if (flags & ~supported_flags) {
rb_raise(rb_eArgError, "unsupported flags specified");
}
if (wordorder_bits == 0) {
if (1 < numwords)
rb_raise(rb_eArgError, "word order not specified");
}
else if (wordorder_bits != INTEGER_PACK_MSWORD_FIRST &&
wordorder_bits != INTEGER_PACK_LSWORD_FIRST)
rb_raise(rb_eArgError, "unexpected word order");
if (byteorder_bits == 0) {
rb_raise(rb_eArgError, "byte order not specified");
}
else if (byteorder_bits != INTEGER_PACK_MSBYTE_FIRST &&
byteorder_bits != INTEGER_PACK_LSBYTE_FIRST &&
byteorder_bits != INTEGER_PACK_NATIVE_BYTE_ORDER)
rb_raise(rb_eArgError, "unexpected byte order");
if (wordsize == 0)
rb_raise(rb_eArgError, "invalid wordsize: %"PRI_SIZE_PREFIX"u", wordsize);
if (SSIZE_MAX < wordsize)
rb_raise(rb_eArgError, "too big wordsize: %"PRI_SIZE_PREFIX"u", wordsize);
if (wordsize <= nails / CHAR_BIT)
rb_raise(rb_eArgError, "too big nails: %"PRI_SIZE_PREFIX"u", nails);
if (SIZE_MAX / wordsize < numwords)
rb_raise(rb_eArgError, "too big numwords * wordsize: %"PRI_SIZE_PREFIX"u * %"PRI_SIZE_PREFIX"u", numwords, wordsize);
}
static void
integer_pack_loop_setup(
size_t numwords, size_t wordsize, size_t nails, int flags,
size_t *word_num_fullbytes_ret,
int *word_num_partialbits_ret,
size_t *word_start_ret,
ssize_t *word_step_ret,
size_t *word_last_ret,
size_t *byte_start_ret,
int *byte_step_ret)
{
int wordorder_bits = flags & INTEGER_PACK_WORDORDER_MASK;
int byteorder_bits = flags & INTEGER_PACK_BYTEORDER_MASK;
size_t word_num_fullbytes;
int word_num_partialbits;
size_t word_start;
ssize_t word_step;
size_t word_last;
size_t byte_start;
int byte_step;
word_num_partialbits = CHAR_BIT - (int)(nails % CHAR_BIT);
if (word_num_partialbits == CHAR_BIT)
word_num_partialbits = 0;
word_num_fullbytes = wordsize - (nails / CHAR_BIT);
if (word_num_partialbits != 0) {
word_num_fullbytes--;
}
if (wordorder_bits == INTEGER_PACK_MSWORD_FIRST) {
word_start = wordsize*(numwords-1);
word_step = -(ssize_t)wordsize;
word_last = 0;
}
else {
word_start = 0;
word_step = wordsize;
word_last = wordsize*(numwords-1);
}
if (byteorder_bits == INTEGER_PACK_NATIVE_BYTE_ORDER) {
#ifdef WORDS_BIGENDIAN
byteorder_bits = INTEGER_PACK_MSBYTE_FIRST;
#else
byteorder_bits = INTEGER_PACK_LSBYTE_FIRST;
#endif
}
if (byteorder_bits == INTEGER_PACK_MSBYTE_FIRST) {
byte_start = wordsize-1;
byte_step = -1;
}
else {
byte_start = 0;
byte_step = 1;
}
*word_num_partialbits_ret = word_num_partialbits;
*word_num_fullbytes_ret = word_num_fullbytes;
*word_start_ret = word_start;
*word_step_ret = word_step;
*word_last_ret = word_last;
*byte_start_ret = byte_start;
*byte_step_ret = byte_step;
}
static inline void
integer_pack_fill_dd(BDIGIT **dpp, BDIGIT **dep, BDIGIT_DBL *ddp, int *numbits_in_dd_p)
{
if (*dpp < *dep && BITSPERDIG <= (int)sizeof(*ddp) * CHAR_BIT - *numbits_in_dd_p) {
*ddp |= (BDIGIT_DBL)(*(*dpp)++) << *numbits_in_dd_p;
*numbits_in_dd_p += BITSPERDIG;
}
else if (*dpp == *dep) {
/* higher bits are infinity zeros */
*numbits_in_dd_p = (int)sizeof(*ddp) * CHAR_BIT;
}
}
static inline BDIGIT_DBL
integer_pack_take_lowbits(int n, BDIGIT_DBL *ddp, int *numbits_in_dd_p)
{
BDIGIT_DBL ret;
ret = (*ddp) & (((BDIGIT_DBL)1 << n) - 1);
*ddp >>= n;
*numbits_in_dd_p -= n;
return ret;
}
static int
bytes_2comp(unsigned 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;
}
static int
bary_pack(int sign, BDIGIT *ds, size_t num_bdigits, void *words, size_t numwords, size_t wordsize, size_t nails, int flags)
{
BDIGIT *dp, *de;
unsigned char *buf, *bufend;
dp = ds;
de = ds + num_bdigits;
validate_integer_pack_format(numwords, wordsize, nails, flags,
INTEGER_PACK_MSWORD_FIRST|
INTEGER_PACK_LSWORD_FIRST|
INTEGER_PACK_MSBYTE_FIRST|
INTEGER_PACK_LSBYTE_FIRST|
INTEGER_PACK_NATIVE_BYTE_ORDER|
INTEGER_PACK_2COMP|
INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION);
while (dp < de && de[-1] == 0)
de--;
if (dp == de) {
sign = 0;
}
if (!(flags & INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION)) {
if (sign == 0) {
MEMZERO(words, unsigned char, numwords * wordsize);
return 0;
}
if (nails == 0 && numwords == 1) {
int need_swap = wordsize != 1 &&
(flags & INTEGER_PACK_BYTEORDER_MASK) != INTEGER_PACK_NATIVE_BYTE_ORDER &&
((flags & INTEGER_PACK_MSBYTE_FIRST) ? !HOST_BIGENDIAN_P : HOST_BIGENDIAN_P);
if (0 < sign || !(flags & INTEGER_PACK_2COMP)) {
BDIGIT d;
if (wordsize == 1) {
*((unsigned char *)words) = (unsigned char)(d = dp[0]);
return ((1 < de - dp || CLEAR_LOWBITS(d, 8) != 0) ? 2 : 1) * sign;
}
#if defined(HAVE_UINT16_T) && 2 <= SIZEOF_BDIGITS
if (wordsize == 2 && (uintptr_t)words % ALIGNOF(uint16_t) == 0) {
uint16_t u = (uint16_t)(d = dp[0]);
if (need_swap) u = swap16(u);
*((uint16_t *)words) = u;
return ((1 < de - dp || CLEAR_LOWBITS(d, 16) != 0) ? 2 : 1) * sign;
}
#endif
#if defined(HAVE_UINT32_T) && 4 <= SIZEOF_BDIGITS
if (wordsize == 4 && (uintptr_t)words % ALIGNOF(uint32_t) == 0) {
uint32_t u = (uint32_t)(d = dp[0]);
if (need_swap) u = swap32(u);
*((uint32_t *)words) = u;
return ((1 < de - dp || CLEAR_LOWBITS(d, 32) != 0) ? 2 : 1) * sign;
}
#endif
#if defined(HAVE_UINT64_T) && 8 <= SIZEOF_BDIGITS
if (wordsize == 8 && (uintptr_t)words % ALIGNOF(uint64_t) == 0) {
uint64_t u = (uint64_t)(d = dp[0]);
if (need_swap) u = swap64(u);
*((uint64_t *)words) = u;
return ((1 < de - dp || CLEAR_LOWBITS(d, 64) != 0) ? 2 : 1) * sign;
}
#endif
}
else { /* sign < 0 && (flags & INTEGER_PACK_2COMP) */
BDIGIT_DBL_SIGNED d;
if (wordsize == 1) {
*((unsigned char *)words) = (unsigned char)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
return (1 < de - dp || FILL_LOWBITS(d, 8) != -1) ? -2 : -1;
}
#if defined(HAVE_UINT16_T) && 2 <= SIZEOF_BDIGITS
if (wordsize == 2 && (uintptr_t)words % ALIGNOF(uint16_t) == 0) {
uint16_t u = (uint16_t)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
if (need_swap) u = swap16(u);
*((uint16_t *)words) = u;
return (wordsize == SIZEOF_BDIGITS && de - dp == 2 && dp[1] == 1 && dp[0] == 0) ? -1 :
(1 < de - dp || FILL_LOWBITS(d, 16) != -1) ? -2 : -1;
}
#endif
#if defined(HAVE_UINT32_T) && 4 <= SIZEOF_BDIGITS
if (wordsize == 4 && (uintptr_t)words % ALIGNOF(uint32_t) == 0) {
uint32_t u = (uint32_t)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
if (need_swap) u = swap32(u);
*((uint32_t *)words) = u;
return (wordsize == SIZEOF_BDIGITS && de - dp == 2 && dp[1] == 1 && dp[0] == 0) ? -1 :
(1 < de - dp || FILL_LOWBITS(d, 32) != -1) ? -2 : -1;
}
#endif
#if defined(HAVE_UINT64_T) && 8 <= SIZEOF_BDIGITS
if (wordsize == 8 && (uintptr_t)words % ALIGNOF(uint64_t) == 0) {
uint64_t u = (uint64_t)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
if (need_swap) u = swap64(u);
*((uint64_t *)words) = u;
return (wordsize == SIZEOF_BDIGITS && de - dp == 2 && dp[1] == 1 && dp[0] == 0) ? -1 :
(1 < de - dp || FILL_LOWBITS(d, 64) != -1) ? -2 : -1;
}
#endif
}
}
#if !defined(WORDS_BIGENDIAN)
if (nails == 0 && SIZEOF_BDIGITS == sizeof(BDIGIT) &&
(flags & INTEGER_PACK_WORDORDER_MASK) == INTEGER_PACK_LSWORD_FIRST &&
(flags & INTEGER_PACK_BYTEORDER_MASK) != INTEGER_PACK_MSBYTE_FIRST) {
size_t src_size = (de - dp) * SIZEOF_BDIGITS;
size_t dst_size = numwords * wordsize;
int overflow = 0;
while (0 < src_size && ((unsigned char *)ds)[src_size-1] == 0)
src_size--;
if (src_size <= dst_size) {
MEMCPY(words, dp, char, src_size);
MEMZERO((char*)words + src_size, char, dst_size - src_size);
}
else {
MEMCPY(words, dp, char, dst_size);
overflow = 1;
}
if (sign < 0 && (flags & INTEGER_PACK_2COMP)) {
int zero_p = bytes_2comp(words, dst_size);
if (zero_p && overflow) {
unsigned char *p = (unsigned char *)dp;
if (dst_size == src_size-1 &&
p[dst_size] == 1) {
overflow = 0;
}
}
}
if (overflow)
sign *= 2;
return sign;
}
#endif
if (nails == 0 && SIZEOF_BDIGITS == sizeof(BDIGIT) &&
wordsize % SIZEOF_BDIGITS == 0 && (uintptr_t)words % ALIGNOF(BDIGIT) == 0) {
size_t bdigits_per_word = wordsize / SIZEOF_BDIGITS;
size_t src_num_bdigits = de - dp;
size_t dst_num_bdigits = numwords * bdigits_per_word;
int overflow = 0;
int mswordfirst_p = (flags & INTEGER_PACK_MSWORD_FIRST) != 0;
int msbytefirst_p = (flags & INTEGER_PACK_NATIVE_BYTE_ORDER) ? HOST_BIGENDIAN_P :
(flags & INTEGER_PACK_MSBYTE_FIRST) != 0;
if (src_num_bdigits <= dst_num_bdigits) {
MEMCPY(words, dp, BDIGIT, src_num_bdigits);
MEMZERO((BDIGIT*)words + src_num_bdigits, BDIGIT, dst_num_bdigits - src_num_bdigits);
}
else {
MEMCPY(words, dp, BDIGIT, dst_num_bdigits);
overflow = 1;
}
if (sign < 0 && (flags & INTEGER_PACK_2COMP)) {
int zero_p = bary_2comp(words, dst_num_bdigits);
if (zero_p && overflow &&
dst_num_bdigits == src_num_bdigits-1 &&
dp[dst_num_bdigits] == 1)
overflow = 0;
}
if (msbytefirst_p != HOST_BIGENDIAN_P) {
size_t i;
for (i = 0; i < dst_num_bdigits; i++) {
BDIGIT d = ((BDIGIT*)words)[i];
((BDIGIT*)words)[i] = swap_bdigit(d);
}
}
if (mswordfirst_p ? !msbytefirst_p : msbytefirst_p) {
size_t i;
BDIGIT *p = words;
for (i = 0; i < numwords; i++) {
bary_swap(p, bdigits_per_word);
p += bdigits_per_word;
}
}
if (mswordfirst_p) {
bary_swap(words, dst_num_bdigits);
}
if (overflow)
sign *= 2;
return sign;
}
}
buf = words;
bufend = buf + numwords * wordsize;
if (buf == bufend) {
/* overflow if non-zero*/
if (!(flags & INTEGER_PACK_2COMP) || 0 <= sign)
sign *= 2;
else {
if (de - dp == 1 && dp[0] == 1)
sign = -1; /* val == -1 == -2**(numwords*(wordsize*CHAR_BIT-nails)) */
else
sign = -2; /* val < -1 == -2**(numwords*(wordsize*CHAR_BIT-nails)) */
}
}
else if (dp == de) {
memset(buf, '\0', bufend - buf);
}
else if (dp < de && buf < bufend) {
int word_num_partialbits;
size_t word_num_fullbytes;
ssize_t word_step;
size_t byte_start;
int byte_step;
size_t word_start, word_last;
unsigned char *wordp, *last_wordp;
BDIGIT_DBL dd;
int numbits_in_dd;
integer_pack_loop_setup(numwords, wordsize, nails, flags,
&word_num_fullbytes, &word_num_partialbits,
&word_start, &word_step, &word_last, &byte_start, &byte_step);
wordp = buf + word_start;
last_wordp = buf + word_last;
dd = 0;
numbits_in_dd = 0;
#define FILL_DD \
integer_pack_fill_dd(&dp, &de, &dd, &numbits_in_dd)
#define TAKE_LOWBITS(n) \
integer_pack_take_lowbits(n, &dd, &numbits_in_dd)
while (1) {
size_t index_in_word = 0;
unsigned char *bytep = wordp + byte_start;
while (index_in_word < word_num_fullbytes) {
FILL_DD;
*bytep = TAKE_LOWBITS(CHAR_BIT);
bytep += byte_step;
index_in_word++;
}
if (word_num_partialbits) {
FILL_DD;
*bytep = TAKE_LOWBITS(word_num_partialbits);
bytep += byte_step;
index_in_word++;
}
while (index_in_word < wordsize) {
*bytep = 0;
bytep += byte_step;
index_in_word++;
}
if (wordp == last_wordp)
break;
wordp += word_step;
}
FILL_DD;
/* overflow tests */
if (dp != de || 1 < dd) {
/* 2**(numwords*(wordsize*CHAR_BIT-nails)+1) <= abs(val) */
sign *= 2;
}
else if (dd == 1) {
/* 2**(numwords*(wordsize*CHAR_BIT-nails)) <= abs(val) < 2**(numwords*(wordsize*CHAR_BIT-nails)+1) */
if (!(flags & INTEGER_PACK_2COMP) || 0 <= sign)
sign *= 2;
else { /* overflow_2comp && sign == -1 */
/* test lower bits are all zero. */
dp = ds;
while (dp < de && *dp == 0)
dp++;
if (de - dp == 1 && /* only one non-zero word. */
POW2_P(*dp)) /* *dp contains only one bit set. */
sign = -1; /* val == -2**(numwords*(wordsize*CHAR_BIT-nails)) */
else
sign = -2; /* val < -2**(numwords*(wordsize*CHAR_BIT-nails)) */
}
}
}
if ((flags & INTEGER_PACK_2COMP) && (sign < 0 && numwords != 0)) {
unsigned char *buf;
int word_num_partialbits;
size_t word_num_fullbytes;
ssize_t word_step;
size_t byte_start;
int byte_step;
size_t word_start, word_last;
unsigned char *wordp, *last_wordp;
unsigned int partialbits_mask;
int carry;
integer_pack_loop_setup(numwords, wordsize, nails, flags,
&word_num_fullbytes, &word_num_partialbits,
&word_start, &word_step, &word_last, &byte_start, &byte_step);
partialbits_mask = (1 << word_num_partialbits) - 1;
buf = words;
wordp = buf + word_start;
last_wordp = buf + word_last;
carry = 1;
while (1) {
size_t index_in_word = 0;
unsigned char *bytep = wordp + byte_start;
while (index_in_word < word_num_fullbytes) {
carry += (unsigned char)~*bytep;
*bytep = (unsigned char)carry;
carry >>= CHAR_BIT;
bytep += byte_step;
index_in_word++;
}
if (word_num_partialbits) {
carry += (*bytep & partialbits_mask) ^ partialbits_mask;
*bytep = carry & partialbits_mask;
carry >>= word_num_partialbits;
bytep += byte_step;
index_in_word++;
}
if (wordp == last_wordp)
break;
wordp += word_step;
}
}
return sign;
#undef FILL_DD
#undef TAKE_LOWBITS
}
static size_t
integer_unpack_num_bdigits_small(size_t numwords, size_t wordsize, size_t nails, int *nlp_bits_ret)
{
/* nlp_bits stands for number of leading padding bits */
size_t num_bits = (wordsize * CHAR_BIT - nails) * numwords;
size_t num_bdigits = (num_bits + BITSPERDIG - 1) / BITSPERDIG;
*nlp_bits_ret = (int)(num_bdigits * BITSPERDIG - num_bits);
return num_bdigits;
}
static size_t
integer_unpack_num_bdigits_generic(size_t numwords, size_t wordsize, size_t nails, int *nlp_bits_ret)
{
/* BITSPERDIG = SIZEOF_BDIGITS * CHAR_BIT */
/* num_bits = (wordsize * CHAR_BIT - nails) * numwords */
/* num_bdigits = (num_bits + BITSPERDIG - 1) / BITSPERDIG */
/* num_bits = CHAR_BIT * (wordsize * numwords) - nails * numwords = CHAR_BIT * num_bytes1 - nails * numwords */
size_t num_bytes1 = wordsize * numwords;
/* q1 * CHAR_BIT + r1 = numwords */
size_t q1 = numwords / CHAR_BIT;
size_t r1 = numwords % CHAR_BIT;
/* num_bits = CHAR_BIT * num_bytes1 - nails * (q1 * CHAR_BIT + r1) = CHAR_BIT * num_bytes2 - nails * r1 */
size_t num_bytes2 = num_bytes1 - nails * q1;
/* q2 * CHAR_BIT + r2 = nails */
size_t q2 = nails / CHAR_BIT;
size_t r2 = nails % CHAR_BIT;
/* num_bits = CHAR_BIT * num_bytes2 - (q2 * CHAR_BIT + r2) * r1 = CHAR_BIT * num_bytes3 - r1 * r2 */
size_t num_bytes3 = num_bytes2 - q2 * r1;
/* q3 * BITSPERDIG + r3 = num_bytes3 */
size_t q3 = num_bytes3 / BITSPERDIG;
size_t r3 = num_bytes3 % BITSPERDIG;
/* num_bits = CHAR_BIT * (q3 * BITSPERDIG + r3) - r1 * r2 = BITSPERDIG * num_digits1 + CHAR_BIT * r3 - r1 * r2 */
size_t num_digits1 = CHAR_BIT * q3;
/*
* if CHAR_BIT * r3 >= r1 * r2
* CHAR_BIT * r3 - r1 * r2 = CHAR_BIT * BITSPERDIG - (CHAR_BIT * BITSPERDIG - (CHAR_BIT * r3 - r1 * r2))
* q4 * BITSPERDIG + r4 = CHAR_BIT * BITSPERDIG - (CHAR_BIT * r3 - r1 * r2)
* num_bits = BITSPERDIG * num_digits1 + CHAR_BIT * BITSPERDIG - (q4 * BITSPERDIG + r4) = BITSPERDIG * num_digits2 - r4
* else
* q4 * BITSPERDIG + r4 = -(CHAR_BIT * r3 - r1 * r2)
* num_bits = BITSPERDIG * num_digits1 - (q4 * BITSPERDIG + r4) = BITSPERDIG * num_digits2 - r4
* end
*/
if (CHAR_BIT * r3 >= r1 * r2) {
size_t tmp1 = CHAR_BIT * BITSPERDIG - (CHAR_BIT * r3 - r1 * r2);
size_t q4 = tmp1 / BITSPERDIG;
int r4 = (int)(tmp1 % BITSPERDIG);
size_t num_digits2 = num_digits1 + CHAR_BIT - q4;
*nlp_bits_ret = r4;
return num_digits2;
}
else {
size_t tmp1 = r1 * r2 - CHAR_BIT * r3;
size_t q4 = tmp1 / BITSPERDIG;
int r4 = (int)(tmp1 % BITSPERDIG);
size_t num_digits2 = num_digits1 - q4;
*nlp_bits_ret = r4;
return num_digits2;
}
}
static size_t
integer_unpack_num_bdigits(size_t numwords, size_t wordsize, size_t nails, int *nlp_bits_ret)
{
size_t num_bdigits;
if (numwords <= (SIZE_MAX - (BITSPERDIG-1)) / CHAR_BIT / wordsize) {
num_bdigits = integer_unpack_num_bdigits_small(numwords, wordsize, nails, nlp_bits_ret);
#ifdef DEBUG_INTEGER_PACK
{
int nlp_bits1;
size_t num_bdigits1 = integer_unpack_num_bdigits_generic(numwords, wordsize, nails, &nlp_bits1);
assert(num_bdigits == num_bdigits1);
assert(*nlp_bits_ret == nlp_bits1);
}
#endif
}
else {
num_bdigits = integer_unpack_num_bdigits_generic(numwords, wordsize, nails, nlp_bits_ret);
}
return num_bdigits;
}
static inline void
integer_unpack_push_bits(int data, int numbits, BDIGIT_DBL *ddp, int *numbits_in_dd_p, BDIGIT **dpp)
{
(*ddp) |= ((BDIGIT_DBL)data) << (*numbits_in_dd_p);
*numbits_in_dd_p += numbits;
while (BITSPERDIG <= *numbits_in_dd_p) {
*(*dpp)++ = BIGLO(*ddp);
*ddp = BIGDN(*ddp);
*numbits_in_dd_p -= BITSPERDIG;
}
}
static int
integer_unpack_single_bdigit(BDIGIT u, size_t size, int flags, BDIGIT *dp)
{
int sign;
if (flags & INTEGER_PACK_2COMP) {
sign = (flags & INTEGER_PACK_NEGATIVE) ?
((size == SIZEOF_BDIGITS && u == 0) ? -2 : -1) :
((u >> (size * CHAR_BIT - 1)) ? -1 : 1);
if (sign < 0) {
u |= LSHIFTX(BDIGMAX, size * CHAR_BIT);
u = BIGLO(1 + ~u);
}
}
else
sign = (flags & INTEGER_PACK_NEGATIVE) ? -1 : 1;
*dp = u;
return sign;
}
static int
bary_unpack_internal(BDIGIT *bdigits, size_t num_bdigits, const void *words, size_t numwords, size_t wordsize, size_t nails, int flags, int nlp_bits)
{
int sign;
const unsigned char *buf = words;
BDIGIT *dp;
BDIGIT *de;
dp = bdigits;
de = dp + num_bdigits;
if (!(flags & INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION)) {
if (nails == 0 && numwords == 1) {
int need_swap = wordsize != 1 &&
(flags & INTEGER_PACK_BYTEORDER_MASK) != INTEGER_PACK_NATIVE_BYTE_ORDER &&
((flags & INTEGER_PACK_MSBYTE_FIRST) ? !HOST_BIGENDIAN_P : HOST_BIGENDIAN_P);
if (wordsize == 1) {
return integer_unpack_single_bdigit(*(uint8_t *)buf, sizeof(uint8_t), flags, dp);
}
#if defined(HAVE_UINT16_T) && 2 <= SIZEOF_BDIGITS
if (wordsize == 2 && (uintptr_t)words % ALIGNOF(uint16_t) == 0) {
BDIGIT u = *(uint16_t *)buf;
return integer_unpack_single_bdigit(need_swap ? swap16(u) : u, sizeof(uint16_t), flags, dp);
}
#endif
#if defined(HAVE_UINT32_T) && 4 <= SIZEOF_BDIGITS
if (wordsize == 4 && (uintptr_t)words % ALIGNOF(uint32_t) == 0) {
BDIGIT u = *(uint32_t *)buf;
return integer_unpack_single_bdigit(need_swap ? swap32(u) : u, sizeof(uint32_t), flags, dp);
}
#endif
#if defined(HAVE_UINT64_T) && 8 <= SIZEOF_BDIGITS
if (wordsize == 8 && (uintptr_t)words % ALIGNOF(uint64_t) == 0) {
BDIGIT u = *(uint64_t *)buf;
return integer_unpack_single_bdigit(need_swap ? swap64(u) : u, sizeof(uint64_t), flags, dp);
}
#endif
}
#if !defined(WORDS_BIGENDIAN)
if (nails == 0 && SIZEOF_BDIGITS == sizeof(BDIGIT) &&
(flags & INTEGER_PACK_WORDORDER_MASK) == INTEGER_PACK_LSWORD_FIRST &&
(flags & INTEGER_PACK_BYTEORDER_MASK) != INTEGER_PACK_MSBYTE_FIRST) {
size_t src_size = numwords * wordsize;
size_t dst_size = num_bdigits * SIZEOF_BDIGITS;
MEMCPY(dp, words, char, src_size);
if (flags & INTEGER_PACK_2COMP) {
if (flags & INTEGER_PACK_NEGATIVE) {
int zero_p;
memset((char*)dp + src_size, 0xff, dst_size - src_size);
zero_p = bary_2comp(dp, num_bdigits);
sign = zero_p ? -2 : -1;
}
else if (buf[src_size-1] >> (CHAR_BIT-1)) {
memset((char*)dp + src_size, 0xff, dst_size - src_size);
bary_2comp(dp, num_bdigits);
sign = -1;
}
else {
MEMZERO((char*)dp + src_size, char, dst_size - src_size);
sign = 1;
}
}
else {
MEMZERO((char*)dp + src_size, char, dst_size - src_size);
sign = (flags & INTEGER_PACK_NEGATIVE) ? -1 : 1;
}
return sign;
}
#endif
if (nails == 0 && SIZEOF_BDIGITS == sizeof(BDIGIT) &&
wordsize % SIZEOF_BDIGITS == 0) {
size_t bdigits_per_word = wordsize / SIZEOF_BDIGITS;
int mswordfirst_p = (flags & INTEGER_PACK_MSWORD_FIRST) != 0;
int msbytefirst_p = (flags & INTEGER_PACK_NATIVE_BYTE_ORDER) ? HOST_BIGENDIAN_P :
(flags & INTEGER_PACK_MSBYTE_FIRST) != 0;
MEMCPY(dp, words, BDIGIT, numwords*bdigits_per_word);
if (mswordfirst_p) {
bary_swap(dp, num_bdigits);
}
if (mswordfirst_p ? !msbytefirst_p : msbytefirst_p) {
size_t i;
BDIGIT *p = dp;
for (i = 0; i < numwords; i++) {
bary_swap(p, bdigits_per_word);
p += bdigits_per_word;
}
}
if (msbytefirst_p != HOST_BIGENDIAN_P) {
BDIGIT *p;
for (p = dp; p < de; p++) {
BDIGIT d = *p;
*p = swap_bdigit(d);
}
}
if (flags & INTEGER_PACK_2COMP) {
if (flags & INTEGER_PACK_NEGATIVE) {
int zero_p = bary_2comp(dp, num_bdigits);
sign = zero_p ? -2 : -1;
}
else if (BDIGIT_MSB(de[-1])) {
bary_2comp(dp, num_bdigits);
sign = -1;
}
else {
sign = 1;
}
}
else {
sign = (flags & INTEGER_PACK_NEGATIVE) ? -1 : 1;
}
return sign;
}
}
if (num_bdigits != 0) {
int word_num_partialbits;
size_t word_num_fullbytes;
ssize_t word_step;
size_t byte_start;
int byte_step;
size_t word_start, word_last;
const unsigned char *wordp, *last_wordp;
BDIGIT_DBL dd;
int numbits_in_dd;
integer_pack_loop_setup(numwords, wordsize, nails, flags,
&word_num_fullbytes, &word_num_partialbits,
&word_start, &word_step, &word_last, &byte_start, &byte_step);
wordp = buf + word_start;
last_wordp = buf + word_last;
dd = 0;
numbits_in_dd = 0;
#define PUSH_BITS(data, numbits) \
integer_unpack_push_bits(data, numbits, &dd, &numbits_in_dd, &dp)
while (1) {
size_t index_in_word = 0;
const unsigned char *bytep = wordp + byte_start;
while (index_in_word < word_num_fullbytes) {
PUSH_BITS(*bytep, CHAR_BIT);
bytep += byte_step;
index_in_word++;
}
if (word_num_partialbits) {
PUSH_BITS(*bytep & ((1 << word_num_partialbits) - 1), word_num_partialbits);
bytep += byte_step;
index_in_word++;
}
if (wordp == last_wordp)
break;
wordp += word_step;
}
if (dd)
*dp++ = (BDIGIT)dd;
assert(dp <= de);
while (dp < de)
*dp++ = 0;
#undef PUSH_BITS
}
if (!(flags & INTEGER_PACK_2COMP)) {
sign = (flags & INTEGER_PACK_NEGATIVE) ? -1 : 1;
}
else {
if (nlp_bits) {
if ((flags & INTEGER_PACK_NEGATIVE) ||
(bdigits[num_bdigits-1] >> (BITSPERDIG - nlp_bits - 1))) {
bdigits[num_bdigits-1] |= BIGLO(BDIGMAX << (BITSPERDIG - nlp_bits));
sign = -1;
}
else {
sign = 1;
}
}
else {
if (flags & INTEGER_PACK_NEGATIVE) {
sign = bary_zero_p(bdigits, num_bdigits) ? -2 : -1;
}
else {
if (num_bdigits != 0 && BDIGIT_MSB(bdigits[num_bdigits-1]))
sign = -1;
else
sign = 1;
}
}
if (sign == -1 && num_bdigits != 0) {
bary_2comp(bdigits, num_bdigits);
}
}
return sign;
}
static void
bary_unpack(BDIGIT *bdigits, size_t num_bdigits, const void *words, size_t numwords, size_t wordsize, size_t nails, int flags)
{
size_t num_bdigits0;
int nlp_bits;
int sign;
validate_integer_pack_format(numwords, wordsize, nails, flags,
INTEGER_PACK_MSWORD_FIRST|
INTEGER_PACK_LSWORD_FIRST|
INTEGER_PACK_MSBYTE_FIRST|
INTEGER_PACK_LSBYTE_FIRST|
INTEGER_PACK_NATIVE_BYTE_ORDER|
INTEGER_PACK_2COMP|
INTEGER_PACK_FORCE_BIGNUM|
INTEGER_PACK_NEGATIVE|
INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION);
num_bdigits0 = integer_unpack_num_bdigits(numwords, wordsize, nails, &nlp_bits);
assert(num_bdigits0 <= num_bdigits);
sign = bary_unpack_internal(bdigits, num_bdigits0, words, numwords, wordsize, nails, flags, nlp_bits);
if (num_bdigits0 < num_bdigits) {
MEMZERO(bdigits + num_bdigits0, BDIGIT, num_bdigits - num_bdigits0);
if (sign == -2) {
bdigits[num_bdigits0] = 1;
}
}
}
static int
bary_subb(BDIGIT *zds, size_t zn, BDIGIT *xds, size_t xn, BDIGIT *yds, size_t yn, int borrow)
{
BDIGIT_DBL_SIGNED num;
size_t i;
assert(yn <= xn);
assert(xn <= zn);
num = borrow ? -1 : 0;
for (i = 0; i < yn; i++) {
num += (BDIGIT_DBL_SIGNED)xds[i] - yds[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
for (; i < xn; i++) {
if (num == 0) goto num_is_zero;
num += xds[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
if (num == 0) goto num_is_zero;
for (; i < zn; i++) {
zds[i] = BDIGMAX;
}
return 1;
num_is_zero:
if (xds == zds && xn == zn)
return 0;
for (; i < xn; i++) {
zds[i] = xds[i];
}
for (; i < zn; i++) {
zds[i] = 0;
}
return 0;
}
static int
bary_sub(BDIGIT *zds, size_t zn, BDIGIT *xds, size_t xn, BDIGIT *yds, size_t yn)
{
return bary_subb(zds, zn, xds, xn, yds, yn, 0);
}
static int
bary_sub_one(BDIGIT *zds, size_t zn)
{
return bary_subb(zds, zn, zds, zn, NULL, 0, 1);
}
static int
bary_addc(BDIGIT *zds, size_t zn, BDIGIT *xds, size_t xn, BDIGIT *yds, size_t yn, int carry)
{
BDIGIT_DBL num;
size_t i;
assert(xn <= zn);
assert(yn <= zn);
if (xn > yn) {
BDIGIT *tds;
tds = xds; xds = yds; yds = tds;
i = xn; xn = yn; yn = i;
}
num = carry ? 1 : 0;
for (i = 0; i < xn; i++) {
num += (BDIGIT_DBL)xds[i] + yds[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
for (; i < yn; i++) {
if (num == 0) goto num_is_zero;
num += yds[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
for (; i < zn; i++) {
if (num == 0) goto num_is_zero;
zds[i] = BIGLO(num);
num = BIGDN(num);
}
return num != 0;
num_is_zero:
if (yds == zds && yn == zn)
return 0;
for (; i < yn; i++) {
zds[i] = yds[i];
}
for (; i < zn; i++) {
zds[i] = 0;
}
return 0;
}
static int
bary_add(BDIGIT *zds, size_t zn, BDIGIT *xds, size_t xn, BDIGIT *yds, size_t yn)
{
return bary_addc(zds, zn, xds, xn, yds, yn, 0);
}
static int
bary_add_one(BDIGIT *zds, size_t zn)
{
return bary_addc(zds, zn, NULL, 0, zds, zn, 1);
}
static void
bary_mul_single(BDIGIT *zds, size_t zl, BDIGIT x, BDIGIT y)
{
BDIGIT_DBL n;
assert(2 <= zl);
n = (BDIGIT_DBL)x * y;
zds[0] = BIGLO(n);
zds[1] = (BDIGIT)BIGDN(n);
}
static int
bary_muladd_1xN(BDIGIT *zds, size_t zl, BDIGIT x, BDIGIT *yds, size_t yl)
{
BDIGIT_DBL n;
BDIGIT_DBL dd;
size_t j;
assert(zl > yl);
if (x == 0)
return 0;
dd = x;
n = 0;
for (j = 0; j < yl; j++) {
BDIGIT_DBL ee = n + dd * yds[j];
if (ee) {
n = zds[j] + ee;
zds[j] = BIGLO(n);
n = BIGDN(n);
}
else {
n = 0;
}
}
for (; j < zl; j++) {
if (n == 0)
break;
n += zds[j];
zds[j] = BIGLO(n);
n = BIGDN(n);
}
return n != 0;
}
static void
bary_mul_normal(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl)
{
size_t i;
assert(xl + yl <= zl);
MEMZERO(zds, BDIGIT, zl);
for (i = 0; i < xl; i++) {
bary_muladd_1xN(zds+i, zl-i, xds[i], yds, yl);
}
}
VALUE
rb_big_mul_normal(VALUE x, VALUE y)
{
size_t xn = RBIGNUM_LEN(x), yn = RBIGNUM_LEN(y), zn = xn + yn;
VALUE z = bignew(zn, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
bary_mul_normal(BDIGITS(z), zn, BDIGITS(x), xn, BDIGITS(y), yn);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
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 void
bary_sq_fast(BDIGIT *zds, size_t zn, BDIGIT *xds, size_t xn)
{
size_t i, j;
BDIGIT_DBL c, v, w;
assert(xn * 2 <= zn);
MEMZERO(zds, BDIGIT, zn);
for (i = 0; i < xn; 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 < xn; 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 + xn];
zds[i + xn] = BIGLO(c);
c = BIGDN(c);
assert(c == 0 || i != xn-1);
if (c && i != xn-1)
zds[i + xn + 1] += (BDIGIT)c;
}
}
}
VALUE
rb_big_sq_fast(VALUE x)
{
size_t xn = RBIGNUM_LEN(x), zn = 2 * xn;
VALUE z = bignew(zn, 1);
bary_sq_fast(BDIGITS(z), zn, BDIGITS(x), xn);
RB_GC_GUARD(x);
return z;
}
/* balancing multiplication by slicing larger argument */
static void
bary_mul_balance(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl)
{
VALUE work = 0;
size_t yl0 = yl;
size_t r, n;
assert(xl + yl <= zl);
assert(2 * xl <= yl || 3 * xl <= 2*(yl+2));
MEMZERO(zds, BDIGIT, xl);
n = 0;
while (yl > 0) {
BDIGIT *tds;
size_t tl;
r = xl > yl ? yl : xl;
tl = xl + r;
if (2 * (xl + r) <= zl - n) {
tds = zds + n + xl + r;
bary_mul(tds, tl, xds, xl, yds + n, r, wds, wl);
MEMZERO(zds + n + xl, BDIGIT, r);
bary_add(zds + n, tl,
zds + n, tl,
tds, tl);
}
else {
if (wl < xl) {
wl = xl;
wds = ALLOCV_N(BDIGIT, work, wl);
}
tds = zds + n;
MEMCPY(wds, zds + n, BDIGIT, xl);
bary_mul(tds, tl, xds, xl, yds + n, r, wds-xl, wl-xl);
bary_add(zds + n, tl,
zds + n, tl,
wds, xl);
}
yl -= r;
n += r;
}
MEMZERO(zds+xl+yl0, BDIGIT, zl - (xl+yl0));
if (work)
ALLOCV_END(work);
}
VALUE
rb_big_mul_balance(VALUE x, VALUE y)
{
size_t xn = RBIGNUM_LEN(x), yn = RBIGNUM_LEN(y), zn = xn + yn;
VALUE z = bignew(zn, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
if (!(2 * xn <= yn || 3 * xn <= 2*(yn+2)))
rb_raise(rb_eArgError, "invalid bignum length");
bary_mul_balance(BDIGITS(z), zn, BDIGITS(x), xn, BDIGITS(y), yn, NULL, 0);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
return z;
}
/* multiplication by karatsuba method */
static void
bary_mul_karatsuba(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl)
{
VALUE work = 0;
size_t n;
int sub_p, borrow, carry1, carry2, carry3;
int odd_y = 0;
int odd_xy = 0;
BDIGIT *xds0, *xds1, *yds0, *yds1, *zds0, *zds1, *zds2, *zds3;
assert(xl + yl <= zl);
assert(xl <= yl);
assert(yl < 2 * xl);
if (yl & 1) {
odd_y = 1;
yl--;
if (yl < xl) {
odd_xy = 1;
xl--;
}
}
n = yl / 2;
assert(n < xl);
if (wl < n) {
/* This function itself needs only n BDIGITs for work area.
* However this function calls bary_mul_karatsuba and
* bary_mul_balance recursively.
* 2n BDIGITs are enough to avoid allocations in
* the recursively called functions.
*/
wl = 2*n;
wds = ALLOCV_N(BDIGIT, work, wl);
}
/* Karatsuba algorithm:
*
* x = x0 + r*x1
* y = y0 + r*y1
* z = x*y
* = (x0 + r*x1) * (y0 + r*y1)
* = x0*y0 + r*(x1*y0 + x0*y1) + r*r*x1*y1
* = x0*y0 + r*(x0*y0 + x1*y1 - (x1-x0)*(y1-y0)) + r*r*x1*y1
* = x0*y0 + r*(x0*y0 + x1*y1 - (x0-x1)*(y0-y1)) + r*r*x1*y1
*/
xds0 = xds;
xds1 = xds + n;
yds0 = yds;
yds1 = yds + n;
zds0 = zds;
zds1 = zds + n;
zds2 = zds + 2*n;
zds3 = zds + 3*n;
sub_p = 1;
/* zds0:? zds1:? zds2:? zds3:? wds:? */
if (bary_sub(zds0, n, xds, n, xds+n, xl-n)) {
bary_2comp(zds0, n);
sub_p = !sub_p;
}
/* zds0:|x1-x0| zds1:? zds2:? zds3:? wds:? */
if (bary_sub(wds, n, yds, n, yds+n, n)) {
bary_2comp(wds, n);
sub_p = !sub_p;
}
/* zds0:|x1-x0| zds1:? zds2:? zds3:? wds:|y1-y0| */
bary_mul(zds1, 2*n, zds0, n, wds, n, wds+n, wl-n);
/* zds0:|x1-x0| zds1,zds2:|x1-x0|*|y1-y0| zds3:? wds:|y1-y0| */
borrow = 0;
if (sub_p) {
borrow = !bary_2comp(zds1, 2*n);
}
/* zds0:|x1-x0| zds1,zds2:-?|x1-x0|*|y1-y0| zds3:? wds:|y1-y0| */
MEMCPY(wds, zds1, BDIGIT, n);
/* zds0:|x1-x0| zds1,zds2:-?|x1-x0|*|y1-y0| zds3:? wds:lo(-?|x1-x0|*|y1-y0|) */
bary_mul(zds0, 2*n, xds0, n, yds0, n, wds+n, wl-n);
/* zds0,zds1:x0*y0 zds2:hi(-?|x1-x0|*|y1-y0|) zds3:? wds:lo(-?|x1-x0|*|y1-y0|) */
carry1 = bary_add(wds, n, wds, n, zds0, n);
carry1 = bary_addc(zds2, n, zds2, n, zds1, n, carry1);
/* zds0,zds1:x0*y0 zds2:hi(x0*y0-?|x1-x0|*|y1-y0|) zds3:? wds:lo(x0*y0-?|x1-x0|*|y1-y0|) */
carry2 = bary_add(zds1, n, zds1, n, wds, n);
/* zds0:lo(x0*y0) zds1:hi(x0*y0)+lo(x0*y0-?|x1-x0|*|y1-y0|) zds2:hi(x0*y0-?|x1-x0|*|y1-y0|) zds3:? wds:lo(x0*y0-?|x1-x0|*|y1-y0|) */
MEMCPY(wds, zds2, BDIGIT, n);
/* zds0:lo(x0*y0) zds1:hi(x0*y0)+lo(x0*y0-?|x1-x0|*|y1-y0|) zds2:_ zds3:? wds:hi(x0*y0-?|x1-x0|*|y1-y0|) */
bary_mul(zds2, zl-2*n, xds1, xl-n, yds1, n, wds+n, wl-n);
/* zds0:lo(x0*y0) zds1:hi(x0*y0)+lo(x0*y0-?|x1-x0|*|y1-y0|) zds2,zds3:x1*y1 wds:hi(x0*y0-?|x1-x0|*|y1-y0|) */
carry3 = bary_add(zds1, n, zds1, n, zds2, n);
/* zds0:lo(x0*y0) zds1:hi(x0*y0)+lo(x0*y0-?|x1-x0|*|y1-y0|)+lo(x1*y1) zds2,zds3:x1*y1 wds:hi(x0*y0-?|x1-x0|*|y1-y0|) */
carry3 = bary_addc(zds2, n, zds2, n, zds3, (4*n < zl ? n : zl-3*n), carry3);
/* zds0:lo(x0*y0) zds1:hi(x0*y0)+lo(x0*y0-?|x1-x0|*|y1-y0|)+lo(x1*y1) zds2,zds3:x1*y1+hi(x1*y1) wds:hi(x0*y0-?|x1-x0|*|y1-y0|) */
bary_add(zds2, zl-2*n, zds2, zl-2*n, wds, n);
/* zds0:lo(x0*y0) zds1:hi(x0*y0)+lo(x0*y0-?|x1-x0|*|y1-y0|)+lo(x1*y1) zds2,zds3:x1*y1+hi(x1*y1)+hi(x0*y0-?|x1-x0|*|y1-y0|) wds:_ */
if (carry2)
bary_add_one(zds2, zl-2*n);
if (carry1 + carry3 - borrow < 0)
bary_sub_one(zds3, zl-3*n);
else if (carry1 + carry3 - borrow > 0) {
BDIGIT c = carry1 + carry3 - borrow;
bary_add(zds3, zl-3*n, zds3, zl-3*n, &c, 1);
}
/*
if (SIZEOF_BDIGITS * zl <= 16) {
uint128_t z, x, y;
ssize_t i;
for (x = 0, i = xl-1; 0 <= i; i--) { x <<= SIZEOF_BDIGITS*CHAR_BIT; x |= xds[i]; }
for (y = 0, i = yl-1; 0 <= i; i--) { y <<= SIZEOF_BDIGITS*CHAR_BIT; y |= yds[i]; }
for (z = 0, i = zl-1; 0 <= i; i--) { z <<= SIZEOF_BDIGITS*CHAR_BIT; z |= zds[i]; }
assert(z == x * y);
}
*/
if (odd_xy) {
bary_muladd_1xN(zds+yl, zl-yl, yds[yl], xds, xl);
bary_muladd_1xN(zds+xl, zl-xl, xds[xl], yds, yl+1);
}
else if (odd_y) {
bary_muladd_1xN(zds+yl, zl-yl, yds[yl], xds, xl);
}
if (work)
ALLOCV_END(work);
}
VALUE
rb_big_mul_karatsuba(VALUE x, VALUE y)
{
size_t xn = RBIGNUM_LEN(x), yn = RBIGNUM_LEN(y), zn = xn + yn;
VALUE z = bignew(zn, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
if (!(xn <= yn && yn < 2 * xn))
rb_raise(rb_eArgError, "invalid bignum length");
bary_mul_karatsuba(BDIGITS(z), zn, BDIGITS(x), xn, BDIGITS(y), yn, NULL, 0);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
return z;
}
static void
bary_mul1(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl)
{
size_t l;
assert(xl + yl <= zl);
if (xl == 1 && yl == 1) {
l = 2;
bary_mul_single(zds, zl, xds[0], yds[0]);
}
else {
l = xl + yl;
bary_mul_normal(zds, zl, xds, xl, yds, yl);
rb_thread_check_ints();
}
MEMZERO(zds + l, BDIGIT, zl - l);
}
/* determine whether a bignum is sparse or not by random sampling */
static inline int
bary_sparse_p(BDIGIT *ds, size_t n)
{
long c = 0;
if ( ds[rb_genrand_ulong_limited(n / 2) + n / 4]) c++;
if (c <= 1 && ds[rb_genrand_ulong_limited(n / 2) + n / 4]) c++;
if (c <= 1 && ds[rb_genrand_ulong_limited(n / 2) + n / 4]) c++;
return (c <= 1) ? 1 : 0;
}
static void
bary_mul(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl)
{
size_t nlsz; /* number of least significant zero BDIGITs */
assert(xl + yl <= zl);
while (0 < xl && xds[xl-1] == 0)
xl--;
while (0 < yl && yds[yl-1] == 0)
yl--;
nlsz = 0;
while (0 < xl && xds[0] == 0) {
xds++;
xl--;
nlsz++;
}
while (0 < yl && yds[0] == 0) {
yds++;
yl--;
nlsz++;
}
if (nlsz) {
MEMZERO(zds, BDIGIT, nlsz);
zds += nlsz;
zl -= nlsz;
}
/* make sure that y is longer than x */
if (xl > yl) {
BDIGIT *tds;
size_t tl;
tds = xds; xds = yds; yds = tds;
tl = xl; xl = yl; yl = tl;
}
assert(xl <= yl);
if (xl == 0) {
MEMZERO(zds, BDIGIT, zl);
return;
}
/* normal multiplication when x is small */
if (xl < KARATSUBA_MUL_DIGITS) {
normal:
if (xds == yds && xl == yl)
bary_sq_fast(zds, zl, xds, xl);
else
bary_mul1(zds, zl, xds, xl, yds, yl);
return;
}
/* normal multiplication when x or y is a sparse bignum */
if (bary_sparse_p(xds, xl)) goto normal;
if (bary_sparse_p(yds, yl)) {
bary_mul1(zds, zl, yds, yl, xds, xl);
return;
}
/* balance multiplication by slicing y when x is much smaller than y */
if (2 * xl <= yl) {
bary_mul_balance(zds, zl, xds, xl, yds, yl, wds, wl);
return;
}
if (xl < TOOM3_MUL_DIGITS) {
/* multiplication by karatsuba method */
bary_mul_karatsuba(zds, zl, xds, xl, yds, yl, wds, wl);
return;
}
if (3*xl <= 2*(yl + 2)) {
bary_mul_balance(zds, zl, xds, xl, yds, yl, wds, wl);
return;
}
{
VALUE x, y, z;
x = bignew(xl, 1);
MEMCPY(BDIGITS(x), xds, BDIGIT, xl);
y = bignew(yl, 1);
MEMCPY(BDIGITS(y), yds, BDIGIT, yl);
z = bigtrunc(bigmul1_toom3(x, y));
MEMCPY(zds, BDIGITS(z), BDIGIT, RBIGNUM_LEN(z));
MEMZERO(zds + RBIGNUM_LEN(z), BDIGIT, zl - RBIGNUM_LEN(z));
RB_GC_GUARD(z);
}
}
#define BIGNUM_DEBUG 0
#if BIGNUM_DEBUG
#define ON_DEBUG(x) do { x; } while (0)
static void
dump_bignum(VALUE x)
{
long i;
printf("%c0x0", RBIGNUM_SIGN(x) ? '+' : '-');
for (i = RBIGNUM_LEN(x); i--; ) {
printf("_%0*"PRIxBDIGIT, SIZEOF_BDIGITS*2, BDIGITS(x)[i]);
}
printf(", len=%lu", RBIGNUM_LEN(x));
puts("");
}
static VALUE
rb_big_dump(VALUE x)
{
dump_bignum(x);
return x;
}
#else
#define ON_DEBUG(x)
#endif
static int
bigzero_p(VALUE x)
{
return bary_zero_p(BDIGITS(x), RBIGNUM_LEN(x));
}
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 (RB_TYPE_P(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_OF(big, struct RBignum, klass, T_BIGNUM | (RGENGC_WB_PROTECTED_BIGNUM ? FL_WB_PROTECTED : 0));
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;
}
OBJ_FREEZE(big);
return (VALUE)big;
}
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;
}
static void
big_extend_carry(VALUE x)
{
rb_big_resize(x, RBIGNUM_LEN(x)+1);
BDIGITS(x)[RBIGNUM_LEN(x)-1] = 1;
}
/* modify a bignum by 2's complement */
static void
get2comp(VALUE x)
{
long i = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
if (bary_2comp(ds, i)) {
big_extend_carry(x);
}
}
void
rb_big_2comp(VALUE x) /* get 2's complement */
{
get2comp(x);
}
static BDIGIT
abs2twocomp(VALUE *xp, long *n_ret)
{
VALUE x = *xp;
long n = RBIGNUM_LEN(x);
BDIGIT *ds = BDIGITS(x);
BDIGIT hibits = 0;
while (0 < n && ds[n-1] == 0)
n--;
if (n != 0 && RBIGNUM_NEGATIVE_P(x)) {
VALUE z = bignew_1(CLASS_OF(x), n, 0);
MEMCPY(BDIGITS(z), ds, BDIGIT, n);
bary_2comp(BDIGITS(z), n);
hibits = BDIGMAX;
*xp = z;
}
*n_ret = n;
return hibits;
}
static void
twocomp2abs_bang(VALUE x, int hibits)
{
RBIGNUM_SET_SIGN(x, !hibits);
if (hibits) {
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 (BIGSIZE(x) <= sizeof(long)) {
long num = 0;
#if 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 (RB_TYPE_P(x, T_BIGNUM)) {
x = bigfixize(x);
if (!FIXNUM_P(x))
bigtrunc(x);
}
return x;
}
VALUE
rb_big_norm(VALUE x)
{
return bignorm(x);
}
VALUE
rb_uint2big(VALUE n)
{
long i;
VALUE big = bignew(bdigit_roomof(SIZEOF_VALUE), 1);
BDIGIT *digits = BDIGITS(big);
#if SIZEOF_BDIGITS >= SIZEOF_VALUE
digits[0] = n;
#else
for (i = 0; i < bdigit_roomof(SIZEOF_VALUE); i++) {
digits[i] = BIGLO(n);
n = BIGDN(n);
}
#endif
i = bdigit_roomof(SIZEOF_VALUE);
while (--i && !digits[i]) ;
RBIGNUM_SET_LEN(big, i+1);
return big;
}
VALUE
rb_int2big(SIGNED_VALUE n)
{
long neg = 0;
VALUE u;
VALUE big;
if (n < 0) {
u = 1 + (VALUE)(-(n + 1)); /* u = -n avoiding overflow */
neg = 1;
}
else {
u = n;
}
big = rb_uint2big(u);
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);
}
void
rb_big_pack(VALUE val, unsigned long *buf, long num_longs)
{
rb_integer_pack(val, buf, num_longs, sizeof(long), 0,
INTEGER_PACK_LSWORD_FIRST|INTEGER_PACK_NATIVE_BYTE_ORDER|
INTEGER_PACK_2COMP);
}
VALUE
rb_big_unpack(unsigned long *buf, long num_longs)
{
return rb_integer_unpack(buf, num_longs, sizeof(long), 0,
INTEGER_PACK_LSWORD_FIRST|INTEGER_PACK_NATIVE_BYTE_ORDER|
INTEGER_PACK_2COMP);
}
/*
* Calculate the number of bytes to be required to represent
* the absolute value of the integer given as _val_.
*
* [val] an integer.
* [nlz_bits_ret] number of leading zero bits in the most significant byte is returned if not NULL.
*
* This function returns ((val_numbits * CHAR_BIT + CHAR_BIT - 1) / CHAR_BIT)
* where val_numbits is the number of bits of abs(val).
* This function should not overflow.
*
* If nlz_bits_ret is not NULL,
* (return_value * CHAR_BIT - val_numbits) is stored in *nlz_bits_ret.
* In this case, 0 <= *nlz_bits_ret < CHAR_BIT.
*
*/
size_t
rb_absint_size(VALUE val, int *nlz_bits_ret)
{
BDIGIT *dp;
BDIGIT *de;
BDIGIT fixbuf[bdigit_roomof(sizeof(long))];
int num_leading_zeros;
val = rb_to_int(val);
if (FIXNUM_P(val)) {
long v = FIX2LONG(val);
if (v < 0) {
v = -v;
}
#if SIZEOF_BDIGITS >= SIZEOF_LONG
fixbuf[0] = v;
#else
{
int i;
for (i = 0; i < numberof(fixbuf); i++) {
fixbuf[i] = BIGLO(v);
v = BIGDN(v);
}
}
#endif
dp = fixbuf;
de = fixbuf + numberof(fixbuf);
}
else {
dp = BDIGITS(val);
de = dp + RBIGNUM_LEN(val);
}
while (dp < de && de[-1] == 0)
de--;
if (dp == de) {
if (nlz_bits_ret)
*nlz_bits_ret = 0;
return 0;
}
num_leading_zeros = nlz(de[-1]);
if (nlz_bits_ret)
*nlz_bits_ret = num_leading_zeros % CHAR_BIT;
return (de - dp) * SIZEOF_BDIGITS - num_leading_zeros / CHAR_BIT;
}
static size_t
absint_numwords_small(size_t numbytes, int nlz_bits_in_msbyte, size_t word_numbits, size_t *nlz_bits_ret)
{
size_t val_numbits = numbytes * CHAR_BIT - nlz_bits_in_msbyte;
size_t div = val_numbits / word_numbits;
size_t mod = val_numbits % word_numbits;
size_t numwords;
size_t nlz_bits;
numwords = mod == 0 ? div : div + 1;
nlz_bits = mod == 0 ? 0 : word_numbits - mod;
*nlz_bits_ret = nlz_bits;
return numwords;
}
static size_t
absint_numwords_generic(size_t numbytes, int nlz_bits_in_msbyte, size_t word_numbits, size_t *nlz_bits_ret)
{
BDIGIT numbytes_bary[bdigit_roomof(sizeof(numbytes))];
BDIGIT char_bit[1] = { CHAR_BIT };
BDIGIT val_numbits_bary[bdigit_roomof(sizeof(numbytes) + 1)];
BDIGIT nlz_bits_in_msbyte_bary[1] = { nlz_bits_in_msbyte };
BDIGIT word_numbits_bary[bdigit_roomof(sizeof(word_numbits))];
BDIGIT div_bary[numberof(val_numbits_bary) + BIGDIVREM_EXTRA_WORDS];
BDIGIT mod_bary[numberof(word_numbits_bary)];
BDIGIT one[1] = { 1 };
size_t nlz_bits;
size_t mod;
int sign;
size_t numwords;
/*
* val_numbits = numbytes * CHAR_BIT - nlz_bits_in_msbyte
* div, mod = val_numbits.divmod(word_numbits)
* numwords = mod == 0 ? div : div + 1
* nlz_bits = mod == 0 ? 0 : word_numbits - mod
*/
bary_unpack(BARY_ARGS(numbytes_bary), &numbytes, 1, sizeof(numbytes), 0,
INTEGER_PACK_NATIVE_BYTE_ORDER);
BARY_MUL1(val_numbits_bary, numbytes_bary, char_bit);
if (nlz_bits_in_msbyte)
BARY_SUB(val_numbits_bary, val_numbits_bary, nlz_bits_in_msbyte_bary);
bary_unpack(BARY_ARGS(word_numbits_bary), &word_numbits, 1, sizeof(word_numbits), 0,
INTEGER_PACK_NATIVE_BYTE_ORDER);
BARY_DIVMOD(div_bary, mod_bary, val_numbits_bary, word_numbits_bary);
if (BARY_ZERO_P(mod_bary)) {
nlz_bits = 0;
}
else {
BARY_ADD(div_bary, div_bary, one);
bary_pack(+1, BARY_ARGS(mod_bary), &mod, 1, sizeof(mod), 0,
INTEGER_PACK_NATIVE_BYTE_ORDER);
nlz_bits = word_numbits - mod;
}
sign = bary_pack(+1, BARY_ARGS(div_bary), &numwords, 1, sizeof(numwords), 0,
INTEGER_PACK_NATIVE_BYTE_ORDER);
if (sign == 2)
return (size_t)-1;
*nlz_bits_ret = nlz_bits;
return numwords;
}
/*
* Calculate the number of words to be required to represent
* the absolute value of the integer given as _val_.
*
* [val] an integer.
* [word_numbits] number of bits in a word.
* [nlz_bits_ret] number of leading zero bits in the most significant word is returned if not NULL.
*
* This function returns ((val_numbits * CHAR_BIT + word_numbits - 1) / word_numbits)
* where val_numbits is the number of bits of abs(val).
*
* This function can overflow.
* When overflow occur, (size_t)-1 is returned.
*
* If nlz_bits_ret is not NULL and overflow is not occur,
* (return_value * word_numbits - val_numbits) is stored in *nlz_bits_ret.
* In this case, 0 <= *nlz_bits_ret < word_numbits.
*
*/
size_t
rb_absint_numwords(VALUE val, size_t word_numbits, size_t *nlz_bits_ret)
{
size_t numbytes;
int nlz_bits_in_msbyte;
size_t numwords;
size_t nlz_bits;
if (word_numbits == 0)
return (size_t)-1;
numbytes = rb_absint_size(val, &nlz_bits_in_msbyte);
if (numbytes <= SIZE_MAX / CHAR_BIT) {
numwords = absint_numwords_small(numbytes, nlz_bits_in_msbyte, word_numbits, &nlz_bits);
#ifdef DEBUG_INTEGER_PACK
{
size_t numwords0, nlz_bits0;
numwords0 = absint_numwords_generic(numbytes, nlz_bits_in_msbyte, word_numbits, &nlz_bits0);
assert(numwords0 == numwords);
assert(nlz_bits0 == nlz_bits);
}
#endif
}
else {
numwords = absint_numwords_generic(numbytes, nlz_bits_in_msbyte, word_numbits, &nlz_bits);
}
if (numwords == (size_t)-1)
return numwords;
if (nlz_bits_ret)
*nlz_bits_ret = nlz_bits;
return numwords;
}
int
rb_absint_singlebit_p(VALUE val)
{
BDIGIT *dp;
BDIGIT *de;
BDIGIT fixbuf[bdigit_roomof(sizeof(long))];
BDIGIT d;
val = rb_to_int(val);
if (FIXNUM_P(val)) {
long v = FIX2LONG(val);
if (v < 0) {
v = -v;
}
#if SIZEOF_BDIGITS >= SIZEOF_LONG
fixbuf[0] = v;
#else
{
int i;
for (i = 0; i < numberof(fixbuf); i++) {
fixbuf[i] = BIGLO(v);
v = BIGDN(v);
}
}
#endif
dp = fixbuf;
de = fixbuf + numberof(fixbuf);
}
else {
dp = BDIGITS(val);
de = dp + RBIGNUM_LEN(val);
}
while (dp < de && de[-1] == 0)
de--;
while (dp < de && dp[0] == 0)
dp++;
if (dp == de) /* no bit set. */
return 0;
if (dp != de-1) /* two non-zero words. two bits set, at least. */
return 0;
d = *dp;
return POW2_P(d);
}
/*
* Export an integer into a buffer.
*
* This function fills the buffer specified by _words_ and _numwords_ as
* val in the format specified by _wordsize_, _nails_ and _flags_.
*
* [val] Fixnum, Bignum or another integer like object which has to_int method.
* [words] buffer to export abs(val).
* [numwords] the size of given buffer as number of words.
* [wordsize] the size of word as number of bytes.
* [nails] number of padding bits in a word.
* Most significant nails bits of each word are filled by zero.
* [flags] bitwise or of constants which name starts "INTEGER_PACK_".
*
* flags:
* [INTEGER_PACK_MSWORD_FIRST] Store the most significant word as the first word.
* [INTEGER_PACK_LSWORD_FIRST] Store the least significant word as the first word.
* [INTEGER_PACK_MSBYTE_FIRST] Store the most significant byte in a word as the first byte in the word.
* [INTEGER_PACK_LSBYTE_FIRST] Store the least significant byte in a word as the first byte in the word.
* [INTEGER_PACK_NATIVE_BYTE_ORDER] INTEGER_PACK_MSBYTE_FIRST or INTEGER_PACK_LSBYTE_FIRST corresponding to the host's endian.
* [INTEGER_PACK_2COMP] Use 2's complement representation.
* [INTEGER_PACK_LITTLE_ENDIAN] Same as INTEGER_PACK_LSWORD_FIRST|INTEGER_PACK_LSBYTE_FIRST
* [INTEGER_PACK_BIG_ENDIAN] Same as INTEGER_PACK_MSWORD_FIRST|INTEGER_PACK_MSBYTE_FIRST
* [INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION] Use generic implementation (for test and debug).
*
* This function fills the buffer specified by _words_
* as abs(val) if INTEGER_PACK_2COMP is not specified in _flags_.
* If INTEGER_PACK_2COMP is specified, 2's complement representation of val is
* filled in the buffer.
*
* This function returns the signedness and overflow condition.
* The overflow condition depends on INTEGER_PACK_2COMP.
*
* INTEGER_PACK_2COMP is not specified:
* -2 : negative overflow. val <= -2**(numwords*(wordsize*CHAR_BIT-nails))
* -1 : negative without overflow. -2**(numwords*(wordsize*CHAR_BIT-nails)) < val < 0
* 0 : zero. val == 0
* 1 : positive without overflow. 0 < val < 2**(numwords*(wordsize*CHAR_BIT-nails))
* 2 : positive overflow. 2**(numwords*(wordsize*CHAR_BIT-nails)) <= val
*
* INTEGER_PACK_2COMP is specified:
* -2 : negative overflow. val < -2**(numwords*(wordsize*CHAR_BIT-nails))
* -1 : negative without overflow. -2**(numwords*(wordsize*CHAR_BIT-nails)) <= val < 0
* 0 : zero. val == 0
* 1 : positive without overflow. 0 < val < 2**(numwords*(wordsize*CHAR_BIT-nails))
* 2 : positive overflow. 2**(numwords*(wordsize*CHAR_BIT-nails)) <= val
*
* The value, -2**(numwords*(wordsize*CHAR_BIT-nails)), is representable
* in 2's complement representation but not representable in absolute value.
* So -1 is returned for the value if INTEGER_PACK_2COMP is specified
* but returns -2 if INTEGER_PACK_2COMP is not specified.
*
* The least significant words are filled in the buffer when overflow occur.
*/
int
rb_integer_pack(VALUE val, void *words, size_t numwords, size_t wordsize, size_t nails, int flags)
{
int sign;
BDIGIT *ds;
size_t num_bdigits;
BDIGIT fixbuf[bdigit_roomof(sizeof(long))];
RB_GC_GUARD(val) = rb_to_int(val);
if (FIXNUM_P(val)) {
long v = FIX2LONG(val);
if (v < 0) {
sign = -1;
v = -v;
}
else {
sign = 1;
}
#if SIZEOF_BDIGITS >= SIZEOF_LONG
fixbuf[0] = v;
#else
{
int i;
for (i = 0; i < numberof(fixbuf); i++) {
fixbuf[i] = BIGLO(v);
v = BIGDN(v);
}
}
#endif
ds = fixbuf;
num_bdigits = numberof(fixbuf);
}
else {
sign = RBIGNUM_POSITIVE_P(val) ? 1 : -1;
ds = BDIGITS(val);
num_bdigits = RBIGNUM_LEN(val);
}
return bary_pack(sign, ds, num_bdigits, words, numwords, wordsize, nails, flags);
}
/*
* Import an integer into a buffer.
*
* [words] buffer to import.
* [numwords] the size of given buffer as number of words.
* [wordsize] the size of word as number of bytes.
* [nails] number of padding bits in a word.
* Most significant nails bits of each word are ignored.
* [flags] bitwise or of constants which name starts "INTEGER_PACK_".
*
* flags:
* [INTEGER_PACK_MSWORD_FIRST] Interpret the first word as the most significant word.
* [INTEGER_PACK_LSWORD_FIRST] Interpret the first word as the least significant word.
* [INTEGER_PACK_MSBYTE_FIRST] Interpret the first byte in a word as the most significant byte in the word.
* [INTEGER_PACK_LSBYTE_FIRST] Interpret the first byte in a word as the least significant byte in the word.
* [INTEGER_PACK_NATIVE_BYTE_ORDER] INTEGER_PACK_MSBYTE_FIRST or INTEGER_PACK_LSBYTE_FIRST corresponding to the host's endian.
* [INTEGER_PACK_2COMP] Use 2's complement representation.
* [INTEGER_PACK_LITTLE_ENDIAN] Same as INTEGER_PACK_LSWORD_FIRST|INTEGER_PACK_LSBYTE_FIRST
* [INTEGER_PACK_BIG_ENDIAN] Same as INTEGER_PACK_MSWORD_FIRST|INTEGER_PACK_MSBYTE_FIRST
* [INTEGER_PACK_FORCE_BIGNUM] the result will be a Bignum
* even if it is representable as a Fixnum.
* [INTEGER_PACK_NEGATIVE] Returns non-positive value.
* (Returns non-negative value if not specified.)
* [INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION] Use generic implementation (for test and debug).
*
* This function returns the imported integer as Fixnum or Bignum.
*
* The range of the result value depends on INTEGER_PACK_2COMP and INTEGER_PACK_NEGATIVE.
*
* INTEGER_PACK_2COMP is not set:
* 0 <= val < 2**(numwords*(wordsize*CHAR_BIT-nails)) if !INTEGER_PACK_NEGATIVE
* -2**(numwords*(wordsize*CHAR_BIT-nails)) < val <= 0 if INTEGER_PACK_NEGATIVE
*
* INTEGER_PACK_2COMP is set:
* -2**(numwords*(wordsize*CHAR_BIT-nails)-1) <= val <= 2**(numwords*(wordsize*CHAR_BIT-nails)-1)-1 if !INTEGER_PACK_NEGATIVE
* -2**(numwords*(wordsize*CHAR_BIT-nails)) <= val <= -1 if INTEGER_PACK_NEGATIVE
*
* INTEGER_PACK_2COMP without INTEGER_PACK_NEGATIVE means sign extension.
* INTEGER_PACK_2COMP with INTEGER_PACK_NEGATIVE mean assuming the higher bits are 1.
*
* Note that this function returns 0 when numwords is zero and
* INTEGER_PACK_2COMP is set but INTEGER_PACK_NEGATIVE is not set.
*/
VALUE
rb_integer_unpack(const void *words, size_t numwords, size_t wordsize, size_t nails, int flags)
{
VALUE val;
size_t num_bdigits;
int sign;
int nlp_bits;
BDIGIT *ds;
BDIGIT fixbuf[2] = { 0, 0 };
validate_integer_pack_format(numwords, wordsize, nails, flags,
INTEGER_PACK_MSWORD_FIRST|
INTEGER_PACK_LSWORD_FIRST|
INTEGER_PACK_MSBYTE_FIRST|
INTEGER_PACK_LSBYTE_FIRST|
INTEGER_PACK_NATIVE_BYTE_ORDER|
INTEGER_PACK_2COMP|
INTEGER_PACK_FORCE_BIGNUM|
INTEGER_PACK_NEGATIVE|
INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION);
num_bdigits = integer_unpack_num_bdigits(numwords, wordsize, nails, &nlp_bits);
if (LONG_MAX-1 < num_bdigits)
rb_raise(rb_eArgError, "too big to unpack as an integer");
if (num_bdigits <= numberof(fixbuf) && !(flags & INTEGER_PACK_FORCE_BIGNUM)) {
val = Qfalse;
ds = fixbuf;
}
else {
val = bignew((long)num_bdigits, 0);
ds = BDIGITS(val);
}
sign = bary_unpack_internal(ds, num_bdigits, words, numwords, wordsize, nails, flags, nlp_bits);
if (sign == -2) {
if (val) {
big_extend_carry(val);
}
else if (num_bdigits == numberof(fixbuf)) {
val = bignew((long)num_bdigits+1, 0);
MEMCPY(BDIGITS(val), fixbuf, BDIGIT, num_bdigits);
BDIGITS(val)[num_bdigits++] = 1;
}
else {
ds[num_bdigits++] = 1;
}
}
if (!val) {
BDIGIT_DBL u = fixbuf[0] + BIGUP(fixbuf[1]);
if (u == 0)
return LONG2FIX(0);
if (0 < sign && POSFIXABLE(u))
return LONG2FIX(u);
if (sign < 0 && BDIGIT_MSB(fixbuf[1]) == 0 &&
NEGFIXABLE(-(BDIGIT_DBL_SIGNED)u))
return LONG2FIX(-(BDIGIT_DBL_SIGNED)u);
val = bignew((long)num_bdigits, 0 <= sign);
MEMCPY(BDIGITS(val), fixbuf, BDIGIT, num_bdigits);
}
if ((flags & INTEGER_PACK_FORCE_BIGNUM) && sign != 0 &&
bary_zero_p(BDIGITS(val), RBIGNUM_LEN(val)))
sign = 0;
RBIGNUM_SET_SIGN(val, 0 <= sign);
if (flags & INTEGER_PACK_FORCE_BIGNUM)
return bigtrunc(val);
return bignorm(val);
}
#define QUAD_SIZE 8
void
rb_quad_pack(char *buf, VALUE val)
{
rb_integer_pack(val, buf, 1, QUAD_SIZE, 0,
INTEGER_PACK_NATIVE_BYTE_ORDER|
INTEGER_PACK_2COMP);
}
VALUE
rb_quad_unpack(const char *buf, int signed_p)
{
return rb_integer_unpack(buf, 1, QUAD_SIZE, 0,
INTEGER_PACK_NATIVE_BYTE_ORDER|
(signed_p ? INTEGER_PACK_2COMP : 0));
}
VALUE
rb_cstr_to_inum(const char *str, int base, int badcheck)
{
const char *s = str;
char sign = 1, nondigit = 0;
int c;
VALUE z;
int bits_per_digit;
size_t i;
const char *digits_start, *digits_end, *p;
size_t num_digits;
size_t num_bdigits;
#undef ISDIGIT
#define ISDIGIT(c) ('0' <= (c) && (c) <= '9')
#define conv_digit(c) (ruby_digit36_to_number_table[(unsigned char)(c)])
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;
str += 2;
break;
case 'b': case 'B':
base = 2;
str += 2;
break;
case 'o': case 'O':
base = 8;
str += 2;
break;
case 'd': case 'D':
base = 10;
str += 2;
break;
default:
base = 8;
}
}
else if (base < -1) {
base = -base;
}
else {
base = 10;
}
}
else if (base == 2) {
if (str[0] == '0' && (str[1] == 'b'||str[1] == 'B')) {
str += 2;
}
}
else if (base == 8) {
if (str[0] == '0' && (str[1] == 'o'||str[1] == 'O')) {
str += 2;
}
}
else if (base == 10) {
if (str[0] == '0' && (str[1] == 'd'||str[1] == 'D')) {
str += 2;
}
}
else if (base == 16) {
if (str[0] == '0' && (str[1] == 'x'||str[1] == 'X')) {
str += 2;
}
}
if (base < 2 || 36 < base) {
rb_raise(rb_eArgError, "invalid radix %d", base);
}
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);
}
bits_per_digit = bitsize(base-1);
if (bits_per_digit * strlen(str) <= sizeof(long) * CHAR_BIT) {
char *end;
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:
if (badcheck && *str == '_') goto bad;
num_digits = 0;
digits_start = digits_end = str;
while ((c = *str++) != 0) {
if (c == '_') {
if (nondigit) {
if (badcheck) goto bad;
break;
}
nondigit = (char) c;
continue;
}
else if ((c = conv_digit(c)) < 0) {
break;
}
if (c >= base) break;
nondigit = 0;
num_digits++;
digits_end = str;
}
if (badcheck) {
str--;
if (s+1 < str && str[-1] == '_') goto bad;
while (*str && ISSPACE(*str)) str++;
if (*str) {
bad:
rb_invalid_str(s, "Integer()");
}
}
if (POW2_P(base)) {
BDIGIT *dp;
BDIGIT_DBL dd;
int numbits;
num_bdigits = (num_digits / BITSPERDIG) * bits_per_digit + roomof((num_digits % BITSPERDIG) * bits_per_digit, BITSPERDIG);
z = bignew(num_bdigits, sign);
dp = BDIGITS(z);
dd = 0;
numbits = 0;
for (p = digits_end; digits_start < p; p--) {
if ((c = conv_digit(p[-1])) < 0)
continue;
dd |= (BDIGIT_DBL)c << numbits;
numbits += bits_per_digit;
if (BITSPERDIG <= numbits) {
*dp++ = BIGLO(dd);
dd = BIGDN(dd);
numbits -= BITSPERDIG;
}
}
if (numbits) {
*dp++ = BIGLO(dd);
}
assert((size_t)(dp - BDIGITS(z)) == num_bdigits);
}
else {
int digits_per_bdigits_dbl;
BDIGIT_DBL power;
power = maxpow_in_bdigit_dbl(base, &digits_per_bdigits_dbl);
num_bdigits = roomof(num_digits, digits_per_bdigits_dbl)*2;
if (num_bdigits < KARATSUBA_MUL_DIGITS) {
size_t blen = 1;
BDIGIT *zds;
BDIGIT_DBL num;
z = bignew(num_bdigits, sign);
zds = BDIGITS(z);
MEMZERO(zds, BDIGIT, num_bdigits);
for (p = digits_start; p < digits_end; p++) {
if ((c = conv_digit(*p)) < 0)
continue;
num = c;
i = 0;
for (;;) {
while (i<blen) {
num += (BDIGIT_DBL)zds[i]*base;
zds[i++] = BIGLO(num);
num = BIGDN(num);
}
if (num) {
blen++;
continue;
}
break;
}
assert(blen <= num_bdigits);
}
}
else {
VALUE powerv;
size_t unit;
VALUE tmpuv = 0;
BDIGIT *uds, *vds, *tds;
BDIGIT_DBL dd;
BDIGIT_DBL current_base;
int m;
uds = ALLOCV_N(BDIGIT, tmpuv, 2*num_bdigits);
vds = uds + num_bdigits;
powerv = bignew(2, 1);
BDIGITS(powerv)[0] = BIGLO(power);
BDIGITS(powerv)[1] = (BDIGIT)BIGDN(power);
i = 0;
dd = 0;
current_base = 1;
m = digits_per_bdigits_dbl;
if (num_digits < (size_t)m)
m = (int)num_digits;
for (p = digits_end; digits_start < p; p--) {
if ((c = conv_digit(p[-1])) < 0)
continue;
dd = dd + c * current_base;
current_base *= base;
num_digits--;
m--;
if (m == 0) {
uds[i++] = BIGLO(dd);
uds[i++] = (BDIGIT)BIGDN(dd);
dd = 0;
m = digits_per_bdigits_dbl;
if (num_digits < (size_t)m)
m = (int)num_digits;
current_base = 1;
}
}
assert(i == num_bdigits);
for (unit = 2; unit < num_bdigits; unit *= 2) {
for (i = 0; i < num_bdigits; i += unit*2) {
if (2*unit <= num_bdigits - i) {
bary_mul(vds+i, unit*2, BDIGITS(powerv), RBIGNUM_LEN(powerv), uds+i+unit, unit, NULL, 0);
bary_add(vds+i, unit*2, vds+i, unit*2, uds+i, unit);
}
else if (unit <= num_bdigits - i) {
bary_mul(vds+i, num_bdigits-i, BDIGITS(powerv), RBIGNUM_LEN(powerv), uds+i+unit, num_bdigits-(i+unit), NULL, 0);
bary_add(vds+i, num_bdigits-i, vds+i, num_bdigits-i, uds+i, unit);
}
else {
MEMCPY(vds+i, uds+i, BDIGIT, num_bdigits-i);
}
}
powerv = bigtrunc(bigmul0(powerv, powerv));
tds = vds;
vds = uds;
uds = tds;
}
while (0 < num_bdigits && uds[num_bdigits-1] == 0)
num_bdigits--;
z = bignew(num_bdigits, sign);
MEMCPY(BDIGITS(z), uds, BDIGIT, num_bdigits);
if (tmpuv)
ALLOCV_END(tmpuv);
}
}
return bignorm(z);
}
VALUE
rb_str_to_inum(VALUE str, int base, int badcheck)
{
char *s;
long len;
VALUE v = 0;
VALUE ret;
StringValue(str);
rb_must_asciicompat(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 = ALLOCV(v, len+1);
MEMCPY(p, s, char, len);
p[len] = '\0';
s = p;
}
}
ret = rb_cstr_to_inum(s, base, badcheck);
if (v)
ALLOCV_END(v);
return ret;
}
#if HAVE_LONG_LONG
static VALUE
rb_ull2big(unsigned LONG_LONG n)
{
long i;
VALUE big = bignew(bdigit_roomof(SIZEOF_LONG_LONG), 1);
BDIGIT *digits = BDIGITS(big);
#if SIZEOF_BDIGITS >= SIZEOF_LONG_LONG
digits[0] = n;
#else
for (i = 0; i < bdigit_roomof(SIZEOF_LONG_LONG); i++) {
digits[i] = BIGLO(n);
n = BIGDN(n);
}
#endif
i = bdigit_roomof(SIZEOF_LONG_LONG);
while (i-- && !digits[i]) ;
RBIGNUM_SET_LEN(big, i+1);
return big;
}
static VALUE
rb_ll2big(LONG_LONG n)
{
long neg = 0;
unsigned LONG_LONG u;
VALUE big;
if (n < 0) {
u = 1 + (unsigned LONG_LONG)(-(n + 1)); /* u = -n avoiding overflow */
neg = 1;
}
else {
u = n;
}
big = rb_ull2big(u);
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);
}
static inline int
ones(register unsigned long x)
{
#if GCC_VERSION_SINCE(3, 4, 0)
return __builtin_popcountl(x);
#else
# 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
#endif
}
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);
}
/* @shyouhei note: vvvvvvvvvvvvv this cast is suspicious. But I believe it is OK, because if that cast loses data, this x value is too big, and should have raised RangeError. */
return (long)ceil(((double)bits)/log_2[base - 2]);
}
static long
big2str_orig(VALUE x, int base, char* ptr, long len, BDIGIT hbase, int hbase_numdigits, 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 = hbase_numdigits;
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, BDIGIT hbase, int hbase_numdigits, 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, hbase_numdigits, trim);
}
b = power_cache_get_power(base, n1, &m1);
bigdivmod(x, b, &q, &r);
rb_obj_hide(q);
rb_obj_hide(r);
lh = big2str_karatsuba(q, base, ptr, (len - m1)/2,
len - m1, hbase, hbase_numdigits, trim);
rb_big_resize(q, 0);
ll = big2str_karatsuba(r, base, ptr + lh, m1/2,
m1, hbase, hbase_numdigits, !lh && trim);
rb_big_resize(r, 0);
return lh + ll;
}
static VALUE
big2str_base_powerof2(VALUE x, size_t len, int base, int trim)
{
int word_numbits = ffs(base) - 1;
size_t numwords;
VALUE result;
char *ptr;
numwords = trim ? rb_absint_numwords(x, word_numbits, NULL) : len;
if (RBIGNUM_NEGATIVE_P(x) || !trim) {
if (LONG_MAX-1 < numwords)
rb_raise(rb_eArgError, "too big number");
result = rb_usascii_str_new(0, 1+numwords);
ptr = RSTRING_PTR(result);
*ptr++ = RBIGNUM_POSITIVE_P(x) ? '+' : '-';
}
else {
if (LONG_MAX < numwords)
rb_raise(rb_eArgError, "too big number");
result = rb_usascii_str_new(0, numwords);
ptr = RSTRING_PTR(result);
}
rb_integer_pack(x, ptr, numwords, 1, CHAR_BIT-word_numbits,
INTEGER_PACK_BIG_ENDIAN);
while (0 < numwords) {
*ptr = ruby_digitmap[*(unsigned char *)ptr];
ptr++;
numwords--;
}
return result;
}
VALUE
rb_big2str0(VALUE x, int base, int trim)
{
int off;
VALUE ss, xx;
long n1, n2, len;
BDIGIT hbase;
int hbase_numdigits;
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);
if (POW2_P(base)) {
/* base == 2 || base == 4 || base == 8 || base == 16 || base == 32 */
return big2str_base_powerof2(x, (size_t)n2, base, trim);
}
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 = maxpow_in_bdigit(base, &hbase_numdigits);
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, hbase_numdigits, trim);
}
else {
len = off + big2str_karatsuba(xx, base, ptr + off, n1,
n2, hbase, hbase_numdigits, 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 unsigned long
big2ulong(VALUE x, const char *type)
{
long len = RBIGNUM_LEN(x);
unsigned long num;
BDIGIT *ds;
if (len == 0)
return 0;
if (BIGSIZE(x) > sizeof(long)) {
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
}
ds = BDIGITS(x);
#if SIZEOF_LONG <= SIZEOF_BDIGITS
num = (unsigned long)ds[0];
#else
num = 0;
while (len--) {
num <<= BITSPERDIG;
num += (unsigned long)ds[len]; /* overflow is already checked */
}
#endif
return num;
}
VALUE
rb_big2ulong_pack(VALUE x)
{
unsigned long num;
rb_integer_pack(x, &num, 1, sizeof(num), 0,
INTEGER_PACK_NATIVE_BYTE_ORDER|INTEGER_PACK_2COMP);
return num;
}
VALUE
rb_big2ulong(VALUE x)
{
unsigned long num = big2ulong(x, "unsigned long");
if (RBIGNUM_POSITIVE_P(x)) {
return num;
}
else {
if (num <= LONG_MAX)
return -(long)num;
if (num == 1+(unsigned long)(-(LONG_MIN+1)))
return LONG_MIN;
}
rb_raise(rb_eRangeError, "bignum out of range of unsigned long");
}
SIGNED_VALUE
rb_big2long(VALUE x)
{
unsigned long num = big2ulong(x, "long");
if (RBIGNUM_POSITIVE_P(x)) {
if (num <= LONG_MAX)
return num;
}
else {
if (num <= LONG_MAX)
return -(long)num;
if (num == 1+(unsigned long)(-(LONG_MIN+1)))
return LONG_MIN;
}
rb_raise(rb_eRangeError, "bignum too big to convert into `long'");
}
#if HAVE_LONG_LONG
static unsigned LONG_LONG
big2ull(VALUE x, const char *type)
{
long len = RBIGNUM_LEN(x);
unsigned LONG_LONG num;
BDIGIT *ds = BDIGITS(x);
if (len == 0)
return 0;
if (BIGSIZE(x) > SIZEOF_LONG_LONG)
rb_raise(rb_eRangeError, "bignum too big to convert into `%s'", type);
#if SIZEOF_LONG_LONG <= SIZEOF_BDIGITS
num = (unsigned LONG_LONG)ds[0];
#else
num = 0;
while (len--) {
num = BIGUP(num);
num += ds[len];
}
#endif
return num;
}
unsigned LONG_LONG
rb_big2ull(VALUE x)
{
unsigned LONG_LONG num = big2ull(x, "unsigned long long");
if (RBIGNUM_POSITIVE_P(x)) {
return num;
}
else {
if (num <= LLONG_MAX)
return -(LONG_LONG)num;
if (num == 1+(unsigned LONG_LONG)(-(LLONG_MIN+1)))
return LLONG_MIN;
}
rb_raise(rb_eRangeError, "bignum out of range of unsigned long long");
}
LONG_LONG
rb_big2ll(VALUE x)
{
unsigned LONG_LONG num = big2ull(x, "long long");
if (RBIGNUM_POSITIVE_P(x)) {
if (num <= LLONG_MAX)
return num;
}
else {
if (num <= LLONG_MAX)
return -(LONG_LONG)num;
if (num == 1+(unsigned LONG_LONG)(-(LLONG_MIN+1)))
return LLONG_MIN;
}
rb_raise(rb_eRangeError, "bignum too big to convert into `long long'");
}
#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 = (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 & ((BDIGIT)1 << (bits %= BITSPERDIG)))) {
int carry = (dl & ~(BDIGMAX << bits)) != 0;
if (!carry) {
while (i-- > 0) {
carry = ds[i] != 0;
if (carry) break;
}
}
if (carry) {
dl &= BDIGMAX << bits;
dl = BIGLO(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));
}
VALUE
rb_integer_float_cmp(VALUE x, VALUE y)
{
double yd = RFLOAT_VALUE(y);
double yi, yf;
VALUE rel;
if (isnan(yd))
return Qnil;
if (isinf(yd)) {
if (yd > 0.0) return INT2FIX(-1);
else return INT2FIX(1);
}
yf = modf(yd, &yi);
if (FIXNUM_P(x)) {
#if SIZEOF_LONG * CHAR_BIT < DBL_MANT_DIG /* assume FLT_RADIX == 2 */
double xd = (double)FIX2LONG(x);
if (xd < yd)
return INT2FIX(-1);
if (xd > yd)
return INT2FIX(1);
return INT2FIX(0);
#else
long xl, yl;
if (yi < FIXNUM_MIN)
return INT2FIX(1);
if (FIXNUM_MAX+1 <= yi)
return INT2FIX(-1);
xl = FIX2LONG(x);
yl = (long)yi;
if (xl < yl)
return INT2FIX(-1);
if (xl > yl)
return INT2FIX(1);
if (yf < 0.0)
return INT2FIX(1);
if (0.0 < yf)
return INT2FIX(-1);
return INT2FIX(0);
#endif
}
y = rb_dbl2big(yi);
rel = rb_big_cmp(x, y);
if (yf == 0.0 || rel != INT2FIX(0))
return rel;
if (yf < 0.0)
return INT2FIX(1);
return INT2FIX(-1);
}
VALUE
rb_integer_float_eq(VALUE x, VALUE y)
{
double yd = RFLOAT_VALUE(y);
double yi, yf;
if (isnan(yd) || isinf(yd))
return Qfalse;
yf = modf(yd, &yi);
if (yf != 0)
return Qfalse;
if (FIXNUM_P(x)) {
#if SIZEOF_LONG * CHAR_BIT < DBL_MANT_DIG /* assume FLT_RADIX == 2 */
double xd = (double)FIX2LONG(x);
if (xd != yd)
return Qfalse;
return Qtrue;
#else
long xl, yl;
if (yi < LONG_MIN || LONG_MAX < yi)
return Qfalse;
xl = FIX2LONG(x);
yl = (long)yi;
if (xl != yl)
return Qfalse;
return Qtrue;
#endif
}
y = rb_dbl2big(yi);
return rb_big_eq(x, y);
}
/*
* call-seq:
* big <=> numeric -> -1, 0, +1 or nil
*
* Comparison---Returns -1, 0, or +1 depending on whether +big+ is
* less than, equal to, or greater than +numeric+. This is the
* basis for the tests in Comparable.
*
* +nil+ is returned if the two values are incomparable.
*
*/
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:
return rb_integer_float_cmp(x, y);
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));
}
enum big_op_t {
big_op_gt,
big_op_ge,
big_op_lt,
big_op_le
};
static VALUE
big_op(VALUE x, VALUE y, enum big_op_t op)
{
VALUE rel;
int n;
switch (TYPE(y)) {
case T_FIXNUM:
case T_BIGNUM:
rel = rb_big_cmp(x, y);
break;
case T_FLOAT:
rel = rb_integer_float_cmp(x, y);
break;
default:
{
ID id = 0;
switch (op) {
case big_op_gt: id = '>'; break;
case big_op_ge: id = rb_intern(">="); break;
case big_op_lt: id = '<'; break;
case big_op_le: id = rb_intern("<="); break;
}
return rb_num_coerce_relop(x, y, id);
}
}
if (NIL_P(rel)) return Qfalse;
n = FIX2INT(rel);
switch (op) {
case big_op_gt: return n > 0 ? Qtrue : Qfalse;
case big_op_ge: return n >= 0 ? Qtrue : Qfalse;
case big_op_lt: return n < 0 ? Qtrue : Qfalse;
case big_op_le: 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, big_op_gt);
}
/*
* 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, big_op_ge);
}
/*
* 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, big_op_lt);
}
/*
* 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, big_op_le);
}
/*
* 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:
if (bignorm(x) == y) return Qtrue;
y = rb_int2big(FIX2LONG(y));
break;
case T_BIGNUM:
break;
case T_FLOAT:
return rb_integer_float_eq(x, y);
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
*/
VALUE
rb_big_eql(VALUE x, VALUE y)
{
if (!RB_TYPE_P(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)
*/
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 = BDIGITS(z);
long n = RBIGNUM_LEN(z);
if (!n) return INT2FIX(-1);
if (RBIGNUM_POSITIVE_P(z)) {
if (bary_plus_one(ds, n)) {
big_extend_carry(z);
}
RBIGNUM_SET_NEGATIVE_SIGN(z);
}
else {
bary_neg(ds, n);
if (bary_plus_one(ds, n))
return INT2FIX(-1);
bary_neg(ds, n);
RBIGNUM_SET_POSITIVE_SIGN(z);
}
return bignorm(z);
}
static void
bigsub_core(BDIGIT *xds, long xn, BDIGIT *yds, long yn, BDIGIT *zds, long zn)
{
bary_sub(zds, zn, xds, xn, yds, yn);
}
static VALUE
bigsub(VALUE x, VALUE y)
{
VALUE z = 0;
long i = RBIGNUM_LEN(x);
BDIGIT *xds, *yds;
/* if x is smaller 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, zn;
BDIGIT_DBL_SIGNED num;
long i, y;
y = y0;
xds = BDIGITS(x);
xn = RBIGNUM_LEN(x);
if (xn == 0)
return LONG2NUM(-y0);
zn = xn;
#if SIZEOF_BDIGITS < SIZEOF_LONG
if (zn < bdigit_roomof(SIZEOF_LONG))
zn = bdigit_roomof(SIZEOF_LONG);
#endif
z = bignew(zn, RBIGNUM_SIGN(x));
zds = BDIGITS(z);
#if SIZEOF_BDIGITS >= SIZEOF_LONG
assert(xn == zn);
num = (BDIGIT_DBL_SIGNED)xds[0] - y;
if (xn == 1 && num < 0) {
RBIGNUM_SET_SIGN(z, !RBIGNUM_SIGN(x));
zds[0] = (BDIGIT)-num;
RB_GC_GUARD(x);
return bignorm(z);
}
zds[0] = BIGLO(num);
num = BIGDN(num);
i = 1;
if (i < xn)
goto y_is_zero_x;
goto finish;
#else
num = 0;
for (i=0; i < xn; i++) {
if (y == 0) goto y_is_zero_x;
num += (BDIGIT_DBL_SIGNED)xds[i] - BIGLO(y);
zds[i] = BIGLO(num);
num = BIGDN(num);
y = BIGDN(y);
}
for (; i < zn; i++) {
if (y == 0) goto y_is_zero_z;
num -= BIGLO(y);
zds[i] = BIGLO(num);
num = BIGDN(num);
y = BIGDN(y);
}
goto finish;
#endif
for (; i < xn; i++) {
y_is_zero_x:
if (num == 0) goto num_is_zero_x;
num += xds[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
#if SIZEOF_BDIGITS < SIZEOF_LONG
for (; i < zn; i++) {
y_is_zero_z:
if (num == 0) goto num_is_zero_z;
zds[i] = BIGLO(num);
num = BIGDN(num);
}
#endif
goto finish;
for (; i < xn; i++) {
num_is_zero_x:
zds[i] = xds[i];
}
#if SIZEOF_BDIGITS < SIZEOF_LONG
for (; i < zn; i++) {
num_is_zero_z:
zds[i] = 0;
}
#endif
goto finish;
finish:
assert(num == 0 || num == -1);
if (num < 0) {
get2comp(z);
RBIGNUM_SET_SIGN(z, !RBIGNUM_SIGN(x));
}
RB_GC_GUARD(x);
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 == 0)
return LONG2NUM(y);
zn = xn;
#if SIZEOF_BDIGITS < SIZEOF_LONG
if (zn < bdigit_roomof(SIZEOF_LONG))
zn = bdigit_roomof(SIZEOF_LONG);
#endif
zn++;
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;
if (i < xn)
goto y_is_zero_x;
goto y_is_zero_z;
#else
num = 0;
for (i=0; i < xn; i++) {
if (y == 0) goto y_is_zero_x;
num += (BDIGIT_DBL)xds[i] + BIGLO(y);
zds[i] = BIGLO(num);
num = BIGDN(num);
y = BIGDN(y);
}
for (; i < zn; i++) {
if (y == 0) goto y_is_zero_z;
num += BIGLO(y);
zds[i] = BIGLO(num);
num = BIGDN(num);
y = BIGDN(y);
}
goto finish;
#endif
for (;i < xn; i++) {
y_is_zero_x:
if (num == 0) goto num_is_zero_x;
num += (BDIGIT_DBL)xds[i];
zds[i] = BIGLO(num);
num = BIGDN(num);
}
for (; i < zn; i++) {
y_is_zero_z:
if (num == 0) goto num_is_zero_z;
zds[i] = BIGLO(num);
num = BIGDN(num);
}
goto finish;
for (;i < xn; i++) {
num_is_zero_x:
zds[i] = xds[i];
}
for (; i < zn; i++) {
num_is_zero_z:
zds[i] = 0;
}
goto finish;
finish:
RB_GC_GUARD(x);
return bignorm(z);
}
static void
bigadd_core(BDIGIT *xds, long xn, BDIGIT *yds, long yn, BDIGIT *zds, long zn)
{
bary_add(zds, zn, xds, xn, yds, yn);
}
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;
}
/* 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;
}
if (!hn) {
h = rb_uint2big(0);
}
else {
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;
}
static void
biglsh_bang(BDIGIT *xds, long xn, unsigned long shift)
{
long const s1 = shift/BITSPERDIG;
int const s2 = (int)(shift%BITSPERDIG);
int const s3 = BITSPERDIG-s2;
BDIGIT* zds;
BDIGIT num;
if (s1 >= xn) {
MEMZERO(xds, BDIGIT, xn);
return;
}
if (s2 == 0) {
MEMMOVE(xds + s1, xds, BDIGIT, xn - s1);
}
else {
zds = xds + xn - 1;
xn -= s1 + 1;
num = BIGLO(xds[xn]<<s2);
while (0 < xn) {
*zds-- = num | xds[--xn]>>s3;
num = BIGLO(xds[xn]<<s2);
}
assert(xds <= zds);
*zds = num;
}
MEMZERO(xds, BDIGIT, s1);
}
static void
bigrsh_bang(BDIGIT* xds, long xn, unsigned long shift)
{
long s1 = shift/BITSPERDIG;
int s2 = (int)(shift%BITSPERDIG);
int s3 = BITSPERDIG - s2;
int i;
BDIGIT num;
BDIGIT* zds;
if (s1 >= xn) {
MEMZERO(xds, BDIGIT, xn);
return;
}
if (s2 == 0) {
MEMMOVE(xds, xds + s1, BDIGIT, xn - s1);
}
else {
i = 0;
zds = xds + s1;
num = *zds++>>s2;
while (i < xn - s1 - 1) {
xds[i++] = BIGLO(*zds<<s3) | num;
num = *zds++>>s2;
}
assert(i < xn);
xds[i] = num;
}
MEMZERO(xds + xn - s1, BDIGIT, s1);
}
static void
big_split3(VALUE v, long n, volatile VALUE* p0, volatile VALUE* p1, volatile VALUE* p2)
{
VALUE v0, v12, v1, v2;
big_split(v, n, &v12, &v0);
big_split(v12, n, &v2, &v1);
*p0 = bigtrunc(v0);
*p1 = bigtrunc(v1);
*p2 = bigtrunc(v2);
}
static VALUE big_lshift(VALUE, unsigned long);
static VALUE big_rshift(VALUE, unsigned long);
static VALUE bigdivrem(VALUE, VALUE, volatile VALUE*, volatile VALUE*);
static VALUE
bigmul1_toom3(VALUE x, VALUE y)
{
long n, xn, yn, zn;
VALUE x0, x1, x2, y0, y1, y2;
VALUE u0, u1, u2, u3, u4, v1, v2, v3;
VALUE z0, z1, z2, z3, z4, z, t;
BDIGIT* zds;
xn = RBIGNUM_LEN(x);
yn = RBIGNUM_LEN(y);
assert(xn <= yn); /* assume y >= x */
n = (yn + 2) / 3;
big_split3(x, n, &x0, &x1, &x2);
if (x == y) {
y0 = x0; y1 = x1; y2 = x2;
}
else big_split3(y, n, &y0, &y1, &y2);
/*
* ref. http://en.wikipedia.org/wiki/Toom%E2%80%93Cook_multiplication
*
* x(b) = x0 * b^0 + x1 * b^1 + x2 * b^2
* y(b) = y0 * b^0 + y1 * b^1 + y2 * b^2
*
* z(b) = x(b) * y(b)
* z(b) = z0 * b^0 + z1 * b^1 + z2 * b^2 + z3 * b^3 + z4 * b^4
* where:
* z0 = x0 * y0
* z1 = x0 * y1 + x1 * y0
* z2 = x0 * y2 + x1 * y1 + x2 * y0
* z3 = x1 * y2 + x2 * y1
* z4 = x2 * y2
*
* Toom3 method (a.k.a. Toom-Cook method):
* (Step1) calculating 5 points z(b0), z(b1), z(b2), z(b3), z(b4),
* where:
* b0 = 0, b1 = 1, b2 = -1, b3 = -2, b4 = inf,
* z(0) = x(0) * y(0) = x0 * y0
* z(1) = x(1) * y(1) = (x0 + x1 + x2) * (y0 + y1 + y2)
* z(-1) = x(-1) * y(-1) = (x0 - x1 + x2) * (y0 - y1 + y2)
* z(-2) = x(-2) * y(-2) = (x0 - 2 * (x1 - 2 * x2)) * (y0 - 2 * (y1 - 2 * y2))
* z(inf) = x(inf) * y(inf) = x2 * y2
*
* (Step2) interpolating z0, z1, z2, z3, z4, and z5.
*
* (Step3) Substituting base value into b of the polynomial z(b),
*/
/*
* [Step1] calculating 5 points z(b0), z(b1), z(b2), z(b3), z(b4)
*/
/* u1 <- x0 + x2 */
u1 = bigtrunc(bigadd(x0, x2, 1));
/* x(-1) : u2 <- u1 - x1 = x0 - x1 + x2 */
u2 = bigtrunc(bigsub(u1, x1));
/* x(1) : u1 <- u1 + x1 = x0 + x1 + x2 */
u1 = bigtrunc(bigadd(u1, x1, 1));
/* x(-2) : u3 <- 2 * (u2 + x2) - x0 = x0 - 2 * (x1 - 2 * x2) */
u3 = bigadd(u2, x2, 1);
if (BDIGITS(u3)[RBIGNUM_LEN(u3)-1] & BIGRAD_HALF) {
rb_big_resize(u3, RBIGNUM_LEN(u3) + 1);
BDIGITS(u3)[RBIGNUM_LEN(u3)-1] = 0;
}
biglsh_bang(BDIGITS(u3), RBIGNUM_LEN(u3), 1);
u3 = bigtrunc(bigadd(bigtrunc(u3), x0, 0));
if (x == y) {
v1 = u1; v2 = u2; v3 = u3;
}
else {
/* v1 <- y0 + y2 */
v1 = bigtrunc(bigadd(y0, y2, 1));
/* y(-1) : v2 <- v1 - y1 = y0 - y1 + y2 */
v2 = bigtrunc(bigsub(v1, y1));
/* y(1) : v1 <- v1 + y1 = y0 + y1 + y2 */
v1 = bigtrunc(bigadd(v1, y1, 1));
/* y(-2) : v3 <- 2 * (v2 + y2) - y0 = y0 - 2 * (y1 - 2 * y2) */
v3 = bigadd(v2, y2, 1);
if (BDIGITS(v3)[RBIGNUM_LEN(v3)-1] & BIGRAD_HALF) {
rb_big_resize(v3, RBIGNUM_LEN(v3) + 1);
BDIGITS(v3)[RBIGNUM_LEN(v3)-1] = 0;
}
biglsh_bang(BDIGITS(v3), RBIGNUM_LEN(v3), 1);
v3 = bigtrunc(bigadd(bigtrunc(v3), y0, 0));
}
/* z(0) : u0 <- x0 * y0 */
u0 = bigtrunc(bigmul0(x0, y0));
/* z(1) : u1 <- u1 * v1 */
u1 = bigtrunc(bigmul0(u1, v1));
/* z(-1) : u2 <- u2 * v2 */
u2 = bigtrunc(bigmul0(u2, v2));
/* z(-2) : u3 <- u3 * v3 */
u3 = bigtrunc(bigmul0(u3, v3));
/* z(inf) : u4 <- x2 * y2 */
u4 = bigtrunc(bigmul0(x2, y2));
/* for GC */
v1 = v2 = v3 = Qnil;
/*
* [Step2] interpolating z0, z1, z2, z3, z4, and z5.
*/
/* z0 <- z(0) == u0 */
z0 = u0;
/* z4 <- z(inf) == u4 */
z4 = u4;
/* z3 <- (z(-2) - z(1)) / 3 == (u3 - u1) / 3 */
z3 = bigadd(u3, u1, 0);
bigdivrem(z3, big_three, &z3, NULL); /* TODO: optimize */
bigtrunc(z3);
/* z1 <- (z(1) - z(-1)) / 2 == (u1 - u2) / 2 */
z1 = bigtrunc(bigadd(u1, u2, 0));
bigrsh_bang(BDIGITS(z1), RBIGNUM_LEN(z1), 1);
/* z2 <- z(-1) - z(0) == u2 - u0 */
z2 = bigtrunc(bigadd(u2, u0, 0));
/* z3 <- (z2 - z3) / 2 + 2 * z(inf) == (z2 - z3) / 2 + 2 * u4 */
z3 = bigtrunc(bigadd(z2, z3, 0));
bigrsh_bang(BDIGITS(z3), RBIGNUM_LEN(z3), 1);
t = big_lshift(u4, 1); /* TODO: combining with next addition */
z3 = bigtrunc(bigadd(z3, t, 1));
/* z2 <- z2 + z1 - z(inf) == z2 + z1 - u4 */
z2 = bigtrunc(bigadd(z2, z1, 1));
z2 = bigtrunc(bigadd(z2, u4, 0));
/* z1 <- z1 - z3 */
z1 = bigtrunc(bigadd(z1, z3, 0));
/*
* [Step3] Substituting base value into b of the polynomial z(b),
*/
zn = 6*n + 1;
z = bignew(zn, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
zds = BDIGITS(z);
MEMCPY(zds, BDIGITS(z0), BDIGIT, RBIGNUM_LEN(z0));
MEMZERO(zds + RBIGNUM_LEN(z0), BDIGIT, zn - RBIGNUM_LEN(z0));
bigadd_core(zds + n, zn - n, BDIGITS(z1), big_real_len(z1), zds + n, zn - n);
bigadd_core(zds + 2*n, zn - 2*n, BDIGITS(z2), big_real_len(z2), zds + 2*n, zn - 2*n);
bigadd_core(zds + 3*n, zn - 3*n, BDIGITS(z3), big_real_len(z3), zds + 3*n, zn - 3*n);
bigadd_core(zds + 4*n, zn - 4*n, BDIGITS(z4), big_real_len(z4), zds + 4*n, zn - 4*n);
return bignorm(z);
}
VALUE
rb_big_mul_toom3(VALUE x, VALUE y)
{
return bigmul1_toom3(x, y);
}
static VALUE
bigmul0(VALUE x, VALUE y)
{
long xn, yn, zn;
VALUE z;
BDIGIT *xds, *yds, *zds;
xn = RBIGNUM_LEN(x);
yn = RBIGNUM_LEN(y);
zn = xn + yn;
z = bignew(zn, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
xds = BDIGITS(x);
yds = BDIGITS(y);
zds = BDIGITS(z);
bary_mul(zds, zn, xds, xn, yds, yn, NULL, 0);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
return z;
}
/*
* 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, j, nyzero;
BDIGIT *yds, *zds;
volatile VALUE stop;
};
static void *
bigdivrem1(void *ptr)
{
struct big_div_struct *bds = (struct big_div_struct*)ptr;
long ny = bds->ny;
long i, j;
BDIGIT *yds = bds->yds, *zds = bds->zds;
BDIGIT_DBL t2;
BDIGIT_DBL_SIGNED num;
BDIGIT q;
j = bds->j;
do {
if (bds->stop) {
bds->j = j;
return 0;
}
if (zds[j] == yds[ny-1]) q = BDIGMAX;
else q = (BDIGIT)((BIGUP(zds[j]) + zds[j-1])/yds[ny-1]);
if (q) {
i = bds->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 0;
}
static void
rb_big_stop(void *ptr)
{
struct big_div_struct *bds = ptr;
bds->stop = Qtrue;
}
static inline int
bigdivrem_num_extra_words(long nx, long ny)
{
int ret = nx==ny ? 2 : 1;
assert(ret <= BIGDIVREM_EXTRA_WORDS);
return ret;
}
static BDIGIT
bigdivrem_single(BDIGIT *qds, BDIGIT *xds, long nx, BDIGIT y)
{
long i;
BDIGIT_DBL t2;
t2 = 0;
i = nx;
while (i--) {
t2 = BIGUP(t2) + xds[i];
qds[i] = (BDIGIT)(t2 / y);
t2 %= y;
}
return (BDIGIT)t2;
}
static void
bigdivrem_normal(BDIGIT *zds, long nz, BDIGIT *xds, long nx, BDIGIT *yds, long ny, int needs_mod)
{
struct big_div_struct bds;
BDIGIT q;
int shift;
q = yds[ny-1];
shift = nlz(q);
if (shift) {
bary_small_lshift(yds, yds, ny, shift);
zds[nx] = bary_small_lshift(zds, xds, nx, shift);
}
else {
MEMCPY(zds, xds, BDIGIT, nx);
zds[nx] = 0;
}
if (nx+1 < nz) zds[nx+1] = 0;
bds.nx = nx;
bds.ny = ny;
bds.zds = zds;
bds.yds = yds;
bds.stop = Qfalse;
bds.j = nz - 1;
for (bds.nyzero = 0; !yds[bds.nyzero]; bds.nyzero++);
if (nx > 10000 || ny > 10000) {
retry:
bds.stop = Qfalse;
rb_thread_call_without_gvl(bigdivrem1, &bds, rb_big_stop, &bds);
if (bds.stop == Qtrue) {
/* execute trap handler, but exception was not raised. */
goto retry;
}
}
else {
bigdivrem1(&bds);
}
if (needs_mod && shift) {
bary_small_rshift(zds, zds, ny, shift, 0);
}
}
static void
bary_divmod(BDIGIT *qds, size_t nq, BDIGIT *rds, size_t nr, BDIGIT *xds, size_t nx, BDIGIT *yds, size_t ny)
{
assert(nx <= nq);
assert(ny <= nr);
while (0 < ny && !yds[ny-1]) ny--;
if (ny == 0)
rb_num_zerodiv();
while (0 < nx && !xds[nx-1]) nx--;
if (nx == 0) {
MEMZERO(qds, BDIGIT, nq);
MEMZERO(rds, BDIGIT, nr);
return;
}
if (ny == 1) {
MEMCPY(qds, xds, BDIGIT, nx);
MEMZERO(qds+nx, BDIGIT, nq-nx);
rds[0] = bigdivrem_single(qds, xds, nx, yds[0]);
MEMZERO(rds+1, BDIGIT, nr-1);
}
else {
int extra_words;
long j;
long nz;
BDIGIT *zds;
VALUE tmpz = 0;
BDIGIT *tds;
extra_words = bigdivrem_num_extra_words(nx, ny);
nz = nx + extra_words;
if (nx + extra_words <= nq)
zds = qds;
else
zds = ALLOCV_N(BDIGIT, tmpz, nx + extra_words);
MEMCPY(zds, xds, BDIGIT, nx);
MEMZERO(zds+nx, BDIGIT, nz-nx);
if (BDIGIT_MSB(yds[ny-1])) {
/* bigdivrem_normal will not modify y.
* So use yds directly. */
tds = yds;
}
else {
/* bigdivrem_normal will modify y.
* So use rds as a temporary buffer. */
MEMCPY(rds, yds, BDIGIT, ny);
tds = rds;
}
bigdivrem_normal(zds, nz, xds, nx, tds, ny, 1);
/* copy remainder */
MEMCPY(rds, zds, BDIGIT, ny);
MEMZERO(rds+ny, BDIGIT, nr-ny);
/* move quotient */
j = nz - ny;
MEMMOVE(qds, zds+ny, BDIGIT, j);
MEMZERO(qds+j, BDIGIT, nq-j);
if (tmpz)
ALLOCV_END(tmpz);
}
}
static VALUE
bigdivrem(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp)
{
long nx = RBIGNUM_LEN(x), ny = RBIGNUM_LEN(y), nz;
long j;
VALUE z, zz;
VALUE tmpy = 0, tmpz = 0;
BDIGIT *xds, *yds, *zds, *tds;
BDIGIT dd;
yds = BDIGITS(y);
while (0 < ny && !yds[ny-1]) ny--;
if (ny == 0)
rb_num_zerodiv();
xds = BDIGITS(x);
while (0 < nx && !xds[nx-1]) nx--;
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 = bignew(nx, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
zds = BDIGITS(z);
dd = bigdivrem_single(zds, xds, nx, dd);
if (modp) {
*modp = rb_uint2big((VALUE)dd);
RBIGNUM_SET_SIGN(*modp, RBIGNUM_SIGN(x));
}
if (divp) *divp = z;
return Qnil;
}
if (BDIGIT_MSB(yds[ny-1]) == 0) {
/* Make yds modifiable. */
tds = ALLOCV_N(BDIGIT, tmpy, ny);
MEMCPY(tds, yds, BDIGIT, ny);
yds = tds;
}
nz = nx + bigdivrem_num_extra_words(nx, ny);
zds = ALLOCV_N(BDIGIT, tmpz, nz);
bigdivrem_normal(zds, nz, xds, nx, yds, ny, modp != NULL);
if (divp) { /* move quotient down in z */
j = nz - ny;
while (0 < j && !zds[j-1+ny])
j--;
*divp = zz = bignew(j, RBIGNUM_SIGN(x)==RBIGNUM_SIGN(y));
MEMCPY(BDIGITS(zz), zds+ny, BDIGIT, j);
}
if (modp) { /* normalize remainder */
while (ny > 0 && !zds[ny-1]) --ny;
*modp = zz = bignew(ny, RBIGNUM_SIGN(x));
MEMCPY(BDIGITS(zz), zds, BDIGIT, ny);
}
if (tmpy)
ALLOCV_END(tmpy);
if (tmpz)
ALLOCV_END(tmpz);
return Qnil;
}
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:
{
if (op == '/') {
return DBL2NUM(rb_big2dbl(x) / RFLOAT_VALUE(y));
}
else {
double dy = RFLOAT_VALUE(y);
if (dy == 0.0) rb_num_zerodiv();
return rb_dbl2big(rb_big2dbl(x) / dy);
}
}
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 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);
ex = l * BITSPERDIG - nlz(BDIGITS(x)[l-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:
bigtrunc(y);
l = RBIGNUM_LEN(y);
ey = l * BITSPERDIG - nlz(BDIGITS(y)[l-1]);
ey -= DBL_BIGDIG * BITSPERDIG;
if (ey) y = big_shift(y, ey);
break;
case T_FLOAT:
y = dbl2big(ldexp(frexp(RFLOAT_VALUE(y), &i), DBL_MANT_DIG));
ey = i - DBL_MANT_DIG;
break;
default:
rb_bug("big_fdiv");
}
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));
}
/*
* 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;
again:
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:
y = bignorm(y);
if (FIXNUM_P(y))
goto again;
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 size_t xbits = rb_absint_numwords(x, 1, NULL);
const size_t BIGLEN_LIMIT = 32*1024*1024;
if (xbits == (size_t)-1 ||
(xbits > BIGLEN_LIMIT) ||
(xbits * yy > BIGLEN_LIMIT)) {
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 VALUE
bigand_int(VALUE x, long xn, BDIGIT hibitsx, long y)
{
VALUE z;
BDIGIT *xds, *zds;
long zn;
long i;
BDIGIT hibitsy;
if (y == 0) return INT2FIX(0);
if (xn == 0) return hibitsx ? LONG2NUM(y) : 0;
hibitsy = 0 <= y ? 0 : BDIGMAX;
xds = BDIGITS(x);
#if SIZEOF_BDIGITS >= SIZEOF_LONG
if (!hibitsy) {
y &= xds[0];
return LONG2NUM(y);
}
#endif
zn = xn;
#if SIZEOF_BDIGITS < SIZEOF_LONG
if (hibitsx && zn < bdigit_roomof(SIZEOF_LONG))
zn = bdigit_roomof(SIZEOF_LONG);
#endif
z = bignew(zn, 0);
zds = BDIGITS(z);
#if SIZEOF_BDIGITS >= SIZEOF_LONG
i = 1;
zds[0] = xds[0] & y;
#else
for (i=0; i < xn; i++) {
if (y == 0 || y == -1) break;
zds[i] = xds[i] & BIGLO(y);
y = BIGDN(y);
}
for (; i < zn; i++) {
if (y == 0 || y == -1) break;
zds[i] = hibitsx & BIGLO(y);
y = BIGDN(y);
}
#endif
for (;i < xn; i++) {
zds[i] = xds[i] & hibitsy;
}
for (;i < zn; i++) {
zds[i] = hibitsx & hibitsy;
}
twocomp2abs_bang(z, hibitsx && hibitsy);
RB_GC_GUARD(x);
return bignorm(z);
}
/*
* call-seq:
* big & numeric -> integer
*
* Performs bitwise +and+ between _big_ and _numeric_.
*/
VALUE
rb_big_and(VALUE x, VALUE y)
{
VALUE z;
BDIGIT *ds1, *ds2, *zds;
long i, xl, yl, l1, l2;
BDIGIT hibitsx, hibitsy;
BDIGIT hibits1, hibits2;
VALUE tmpv;
BDIGIT tmph;
long tmpl;
if (!FIXNUM_P(y) && !RB_TYPE_P(y, T_BIGNUM)) {
return rb_num_coerce_bit(x, y, '&');
}
hibitsx = abs2twocomp(&x, &xl);
if (FIXNUM_P(y)) {
return bigand_int(x, xl, hibitsx, FIX2LONG(y));
}
hibitsy = abs2twocomp(&y, &yl);
if (xl > yl) {
tmpv = x; x = y; y = tmpv;
tmpl = xl; xl = yl; yl = tmpl;
tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
}
l1 = xl;
l2 = yl;
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
hibits1 = hibitsx;
hibits2 = hibitsy;
if (!hibits1)
l2 = l1;
z = bignew(l2, 0);
zds = BDIGITS(z);
for (i=0; i<l1; i++) {
zds[i] = ds1[i] & ds2[i];
}
for (; i<l2; i++) {
zds[i] = hibits1 & ds2[i];
}
twocomp2abs_bang(z, hibits1 && hibits2);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
return bignorm(z);
}
static VALUE
bigor_int(VALUE x, long xn, BDIGIT hibitsx, long y)
{
VALUE z;
BDIGIT *xds, *zds;
long zn;
long i;
BDIGIT hibitsy;
if (y == -1) return INT2FIX(-1);
if (xn == 0) return hibitsx ? INT2FIX(-1) : LONG2FIX(y);
hibitsy = 0 <= y ? 0 : BDIGMAX;
xds = BDIGITS(x);
zn = RBIGNUM_LEN(x);
#if SIZEOF_BDIGITS < SIZEOF_LONG
if (zn < bdigit_roomof(SIZEOF_LONG))
zn = bdigit_roomof(SIZEOF_LONG);
#endif
z = bignew(zn, 0);
zds = BDIGITS(z);
#if SIZEOF_BDIGITS >= SIZEOF_LONG
i = 1;
zds[0] = xds[0] | y;
if (i < zn)
goto y_is_fixed_point;
goto finish;
#else
for (i=0; i < xn; i++) {
if (y == 0 || y == -1) goto y_is_fixed_point;
zds[i] = xds[i] | BIGLO(y);
y = BIGDN(y);
}
if (hibitsx)
goto fill_hibits;
for (; i < zn; i++) {
if (y == 0 || y == -1) goto y_is_fixed_point;
zds[i] = BIGLO(y);
y = BIGDN(y);
}
goto finish;
#endif
y_is_fixed_point:
if (hibitsy)
goto fill_hibits;
for (; i < xn; i++) {
zds[i] = xds[i];
}
if (hibitsx)
goto fill_hibits;
for (; i < zn; i++) {
zds[i] = 0;
}
goto finish;
fill_hibits:
for (; i < zn; i++) {
zds[i] = BDIGMAX;
}
finish:
twocomp2abs_bang(z, hibitsx || hibitsy);
RB_GC_GUARD(x);
return bignorm(z);
}
/*
* call-seq:
* big | numeric -> integer
*
* Performs bitwise +or+ between _big_ and _numeric_.
*/
VALUE
rb_big_or(VALUE x, VALUE y)
{
VALUE z;
BDIGIT *ds1, *ds2, *zds;
long i, xl, yl, l1, l2;
BDIGIT hibitsx, hibitsy;
BDIGIT hibits1, hibits2;
VALUE tmpv;
BDIGIT tmph;
long tmpl;
if (!FIXNUM_P(y) && !RB_TYPE_P(y, T_BIGNUM)) {
return rb_num_coerce_bit(x, y, '|');
}
hibitsx = abs2twocomp(&x, &xl);
if (FIXNUM_P(y)) {
return bigor_int(x, xl, hibitsx, FIX2LONG(y));
}
hibitsy = abs2twocomp(&y, &yl);
if (xl > yl) {
tmpv = x; x = y; y = tmpv;
tmpl = xl; xl = yl; yl = tmpl;
tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
}
l1 = xl;
l2 = yl;
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
hibits1 = hibitsx;
hibits2 = hibitsy;
if (hibits1)
l2 = l1;
z = bignew(l2, 0);
zds = BDIGITS(z);
for (i=0; i<l1; i++) {
zds[i] = ds1[i] | ds2[i];
}
for (; i<l2; i++) {
zds[i] = hibits1 | ds2[i];
}
twocomp2abs_bang(z, hibits1 || hibits2);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
return bignorm(z);
}
static VALUE
bigxor_int(VALUE x, long xn, BDIGIT hibitsx, long y)
{
VALUE z;
BDIGIT *xds, *zds;
long zn;
long i;
BDIGIT hibitsy;
hibitsy = 0 <= y ? 0 : BDIGMAX;
xds = BDIGITS(x);
zn = RBIGNUM_LEN(x);
#if SIZEOF_BDIGITS < SIZEOF_LONG
if (zn < bdigit_roomof(SIZEOF_LONG))
zn = bdigit_roomof(SIZEOF_LONG);
#endif
z = bignew(zn, 0);
zds = BDIGITS(z);
#if SIZEOF_BDIGITS >= SIZEOF_LONG
i = 1;
zds[0] = xds[0] ^ y;
#else
for (i = 0; i < xn; i++) {
zds[i] = xds[i] ^ BIGLO(y);
y = BIGDN(y);
}
for (; i < zn; i++) {
zds[i] = hibitsx ^ BIGLO(y);
y = BIGDN(y);
}
#endif
for (; i < xn; i++) {
zds[i] = xds[i] ^ hibitsy;
}
for (; i < zn; i++) {
zds[i] = hibitsx ^ hibitsy;
}
twocomp2abs_bang(z, (hibitsx ^ hibitsy) != 0);
RB_GC_GUARD(x);
return bignorm(z);
}
/*
* call-seq:
* big ^ numeric -> integer
*
* Performs bitwise +exclusive or+ between _big_ and _numeric_.
*/
VALUE
rb_big_xor(VALUE x, VALUE y)
{
VALUE z;
BDIGIT *ds1, *ds2, *zds;
long i, xl, yl, l1, l2;
BDIGIT hibitsx, hibitsy;
BDIGIT hibits1, hibits2;
VALUE tmpv;
BDIGIT tmph;
long tmpl;
if (!FIXNUM_P(y) && !RB_TYPE_P(y, T_BIGNUM)) {
return rb_num_coerce_bit(x, y, '^');
}
hibitsx = abs2twocomp(&x, &xl);
if (FIXNUM_P(y)) {
return bigxor_int(x, xl, hibitsx, FIX2LONG(y));
}
hibitsy = abs2twocomp(&y, &yl);
if (xl > yl) {
tmpv = x; x = y; y = tmpv;
tmpl = xl; xl = yl; yl = tmpl;
tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
}
l1 = xl;
l2 = yl;
ds1 = BDIGITS(x);
ds2 = BDIGITS(y);
hibits1 = hibitsx;
hibits2 = hibitsy;
z = bignew(l2, 0);
zds = BDIGITS(z);
for (i=0; i<l1; i++) {
zds[i] = ds1[i] ^ ds2[i];
}
for (; i<l2; i++) {
zds[i] = hibitsx ^ ds2[i];
}
twocomp2abs_bang(z, (hibits1 ^ hibits2) != 0);
RB_GC_GUARD(x);
RB_GC_GUARD(y);
return bignorm(z);
}
static VALUE
check_shiftdown(VALUE y, VALUE x)
{
if (!RBIGNUM_LEN(x)) return INT2FIX(0);
if (BIGSIZE(y) > SIZEOF_LONG) {
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)
{
unsigned long shift;
int neg = 0;
for (;;) {
if (FIXNUM_P(y)) {
long l = FIX2LONG(y);
if (0 <= l) {
shift = l;
}
else {
neg = 1;
shift = 1+(unsigned long)(-(l+1));
}
break;
}
else if (RB_TYPE_P(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");
break;
}
y = rb_to_int(y);
}
x = neg ? big_rshift(x, shift) : big_lshift(x, shift);
return bignorm(x);
}
static BDIGIT
bary_small_lshift(BDIGIT *zds, BDIGIT *xds, long n, int shift)
{
long i;
BDIGIT_DBL num = 0;
for (i=0; i<n; i++) {
num = num | (BDIGIT_DBL)*xds++ << shift;
*zds++ = BIGLO(num);
num = BIGDN(num);
}
return BIGLO(num);
}
static VALUE
big_lshift(VALUE x, unsigned long shift)
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = (int)(shift%BITSPERDIG);
VALUE z;
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);
zds[len] = bary_small_lshift(zds, xds, len, s2);
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)
{
unsigned long shift;
int neg = 0;
for (;;) {
if (FIXNUM_P(y)) {
long l = FIX2LONG(y);
if (0 <= l) {
shift = l;
}
else {
neg = 1;
shift = 1+(unsigned long)(-(l+1));
}
break;
}
else if (RB_TYPE_P(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");
break;
}
y = rb_to_int(y);
}
x = neg ? big_lshift(x, shift) : big_rshift(x, shift);
return bignorm(x);
}
static void
bary_small_rshift(BDIGIT *zds, BDIGIT *xds, long n, int shift, int sign_bit)
{
BDIGIT_DBL num = 0;
BDIGIT x;
if (sign_bit) {
num = (~(BDIGIT_DBL)0) << BITSPERDIG;
}
while (n--) {
num = (num | xds[n]) >> shift;
x = xds[n];
zds[n] = BIGLO(num);
num = BIGUP(x);
}
}
static VALUE
big_rshift(VALUE x, unsigned long shift)
{
BDIGIT *xds, *zds;
long s1 = shift/BITSPERDIG;
int s2 = (int)(shift%BITSPERDIG);
VALUE z;
long j;
long xl;
BDIGIT hibitsx;
if (s1 > RBIGNUM_LEN(x)) {
if (RBIGNUM_POSITIVE_P(x) || bary_zero_p(BDIGITS(x), RBIGNUM_LEN(x)))
return INT2FIX(0);
else
return INT2FIX(-1);
}
hibitsx = abs2twocomp(&x, &xl);
xds = BDIGITS(x);
j = xl - s1;
if (j <= 0) {
if (!hibitsx) return INT2FIX(0);
else return INT2FIX(-1);
}
z = bignew(j, 0);
zds = BDIGITS(z);
bary_small_rshift(zds, xds+s1, j, s2, hibitsx != 0);
twocomp2abs_bang(z, hibitsx != 0);
RB_GC_GUARD(x);
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;
unsigned long shift;
long i, s1, s2;
if (RB_TYPE_P(y, T_BIGNUM)) {
if (!RBIGNUM_SIGN(y))
return INT2FIX(0);
bigtrunc(y);
if (BIGSIZE(y) > sizeof(long)) {
out_of_range:
return RBIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
}
shift = big2ulong(y, "long");
}
else {
i = NUM2LONG(y);
if (i < 0) return INT2FIX(0);
shift = 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 += BIGLO(~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)) {
y = rb_int2big(FIX2LONG(y));
}
else if (!RB_TYPE_P(y, T_BIGNUM)) {
rb_raise(rb_eTypeError, "can't coerce %s to Bignum",
rb_obj_classname(y));
}
return rb_assoc_new(y, x);
}
/*
* call-seq:
* big.abs -> aBignum
* big.magnitude -> 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_alias(rb_cBignum, "inspect", "to_s");
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();
big_three = rb_uint2big(3);
rb_gc_register_mark_object(big_three);
}
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