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bignum.c
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/**********************************************************************
bignum.c -
$Author: nagachika $
created at: Fri Jun 10 00:48:55 JST 1994
Copyright (C) 1993-2007 Yukihiro Matsumoto
**********************************************************************/
#include "internal.h"
#include "ruby/thread.h"
#include "ruby/util.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 "ruby_assert.h"
#if defined(HAVE_LIBGMP) && defined(HAVE_GMP_H)
#define USE_GMP
#include <gmp.h>
#endif
#define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM)
#ifndef RUBY_INTEGER_UNIFICATION
VALUE rb_cBignum;
#endif
const char ruby_digitmap[] = "0123456789abcdefghijklmnopqrstuvwxyz";
#ifndef SIZEOF_BDIGIT_DBL
# if SIZEOF_INT*2 <= SIZEOF_LONG_LONG
# define SIZEOF_BDIGIT_DBL SIZEOF_LONG_LONG
# else
# define SIZEOF_BDIGIT_DBL SIZEOF_LONG
# endif
#endif
STATIC_ASSERT(sizeof_bdigit_dbl, sizeof(BDIGIT_DBL) == SIZEOF_BDIGIT_DBL);
STATIC_ASSERT(sizeof_bdigit_dbl_signed, sizeof(BDIGIT_DBL_SIGNED) == SIZEOF_BDIGIT_DBL);
STATIC_ASSERT(sizeof_bdigit, SIZEOF_BDIGIT <= sizeof(BDIGIT));
STATIC_ASSERT(sizeof_bdigit_and_dbl, SIZEOF_BDIGIT*2 <= SIZEOF_BDIGIT_DBL);
STATIC_ASSERT(bdigit_signedness, 0 < (BDIGIT)-1);
STATIC_ASSERT(bdigit_dbl_signedness, 0 < (BDIGIT_DBL)-1);
STATIC_ASSERT(bdigit_dbl_signed_signedness, 0 > (BDIGIT_DBL_SIGNED)-1);
STATIC_ASSERT(rbignum_embed_len_max, BIGNUM_EMBED_LEN_MAX <= (BIGNUM_EMBED_LEN_MASK >> BIGNUM_EMBED_LEN_SHIFT));
#if SIZEOF_BDIGIT < SIZEOF_LONG
STATIC_ASSERT(sizeof_long_and_sizeof_bdigit, SIZEOF_LONG % SIZEOF_BDIGIT == 0);
#else
STATIC_ASSERT(sizeof_long_and_sizeof_bdigit, SIZEOF_BDIGIT % SIZEOF_LONG == 0);
#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))
/* (!LSHIFTABLE(d, 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) (BIGNUM_DIGITS(x))
#define BITSPERDIG (SIZEOF_BDIGIT*CHAR_BIT)
#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
#define BIGRAD_HALF ((BDIGIT)(BIGRAD >> 1))
#define BDIGIT_MSB(d) (((d) & BIGRAD_HALF) != 0)
#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_BDIGIT == 2
# define swap_bdigit(x) swap16(x)
#elif SIZEOF_BDIGIT == 4
# define swap_bdigit(x) swap32(x)
#elif SIZEOF_BDIGIT == 8
# define swap_bdigit(x) swap64(x)
#endif
#define BIGZEROP(x) (BIGNUM_LEN(x) == 0 || \
(BDIGITS(x)[0] == 0 && \
(BIGNUM_LEN(x) == 1 || bigzero_p(x))))
#define BIGSIZE(x) (BIGNUM_LEN(x) == 0 ? (size_t)0 : \
BDIGITS(x)[BIGNUM_LEN(x)-1] ? \
(size_t)(BIGNUM_LEN(x)*SIZEOF_BDIGIT - nlz(BDIGITS(x)[BIGNUM_LEN(x)-1])/CHAR_BIT) : \
rb_absint_size(x, NULL))
#define BIGDIVREM_EXTRA_WORDS 1
#define bdigit_roomof(n) roomof(n, SIZEOF_BDIGIT)
#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_SHORT_MUL(z, x, y) bary_short_mul(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 BIGNUM_SET_NEGATIVE_SIGN(b) BIGNUM_SET_SIGN(b, 0)
#define BIGNUM_SET_POSITIVE_SIGN(b) BIGNUM_SET_SIGN(b, 1)
#define bignew(len,sign) bignew_1(rb_cInteger,(len),(sign))
#define BDIGITS_ZERO(ptr, n) do { \
BDIGIT *bdigitz_zero_ptr = (ptr); \
size_t bdigitz_zero_n = (n); \
while (bdigitz_zero_n) { \
*bdigitz_zero_ptr++ = 0; \
bdigitz_zero_n--; \
} \
} while (0)
#define BARY_TRUNC(ds, n) do { \
while (0 < (n) && (ds)[(n)-1] == 0) \
(n)--; \
} while (0)
#define KARATSUBA_BALANCED(xn, yn) ((yn)/2 < (xn))
#define TOOM3_BALANCED(xn, yn) (((yn)+2)/3 * 2 < (xn))
#define GMP_MUL_DIGITS 20
#define KARATSUBA_MUL_DIGITS 70
#define TOOM3_MUL_DIGITS 150
#define GMP_DIV_DIGITS 20
#define GMP_BIG2STR_DIGITS 20
#define GMP_STR2BIG_DIGITS 20
typedef void (mulfunc_t)(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn);
static mulfunc_t bary_mul_toom3_start;
static mulfunc_t bary_mul_karatsuba_start;
static BDIGIT bigdivrem_single(BDIGIT *qds, const BDIGIT *xds, size_t xn, BDIGIT y);
static void bary_divmod(BDIGIT *qds, size_t qn, BDIGIT *rds, size_t rn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn);
static VALUE bigmul0(VALUE x, VALUE y);
static void bary_mul_toom3(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn);
static VALUE bignew_1(VALUE klass, size_t len, int sign);
static inline VALUE bigtrunc(VALUE x);
static VALUE bigsq(VALUE x);
static void bigdivmod(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp);
static inline VALUE power_cache_get_power(int base, int power_level, size_t *numdigits_ret);
#if SIZEOF_BDIGIT <= SIZEOF_INT
static int nlz(BDIGIT x) { return nlz_int((unsigned int)x) - (SIZEOF_INT-SIZEOF_BDIGIT) * CHAR_BIT; }
#elif SIZEOF_BDIGIT <= SIZEOF_LONG
static int nlz(BDIGIT x) { return nlz_long((unsigned long)x) - (SIZEOF_LONG-SIZEOF_BDIGIT) * CHAR_BIT; }
#elif SIZEOF_BDIGIT <= SIZEOF_LONG_LONG
static int nlz(BDIGIT x) { return nlz_long_long((unsigned LONG_LONG)x) - (SIZEOF_LONG_LONG-SIZEOF_BDIGIT) * CHAR_BIT; }
#elif SIZEOF_BDIGIT <= SIZEOF_INT128_T
static int nlz(BDIGIT x) { return nlz_int128((uint128_t)x) - (SIZEOF_INT128_T-SIZEOF_BDIGIT) * CHAR_BIT; }
#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 script, 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"
}
*/
#if SIZEOF_BDIGIT_DBL == 2
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),
};
#elif SIZEOF_BDIGIT_DBL == 4
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),
};
#elif SIZEOF_BDIGIT_DBL == 8 && defined 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),
};
#elif SIZEOF_BDIGIT_DBL == 16 && defined 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);
{
#if SIZEOF_BDIGIT_DBL == 2
maxpow = maxpow16_num[base-2];
exponent = maxpow16_exp[base-2];
#elif SIZEOF_BDIGIT_DBL == 4
maxpow = maxpow32_num[base-2];
exponent = maxpow32_exp[base-2];
#elif SIZEOF_BDIGIT_DBL == 8 && defined HAVE_UINT64_T
maxpow = maxpow64_num[base-2];
exponent = maxpow64_exp[base-2];
#elif SIZEOF_BDIGIT_DBL == 16 && defined HAVE_UINT128_T
maxpow = maxpow128_num[base-2];
exponent = maxpow128_exp[base-2];
#else
maxpow = base;
exponent = 1;
while (maxpow <= BDIGIT_DBL_MAX / base) {
maxpow *= base;
exponent++;
}
#endif
}
*exp_ret = exponent;
return maxpow;
}
static inline BDIGIT_DBL
bary2bdigitdbl(const BDIGIT *ds, size_t n)
{
assert(n <= 2);
if (n == 2)
return ds[0] | BIGUP(ds[1]);
if (n == 1)
return ds[0];
return 0;
}
static inline void
bdigitdbl2bary(BDIGIT *ds, size_t n, BDIGIT_DBL num)
{
assert(n == 2);
ds[0] = BIGLO(num);
ds[1] = (BDIGIT)BIGDN(num);
}
static int
bary_cmp(const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
{
BARY_TRUNC(xds, xn);
BARY_TRUNC(yds, yn);
if (xn < yn)
return -1;
if (xn > yn)
return 1;
while (xn-- && xds[xn] == yds[xn])
;
if (xn == (size_t)-1)
return 0;
return xds[xn] < yds[xn] ? -1 : 1;
}
static BDIGIT
bary_small_lshift(BDIGIT *zds, const BDIGIT *xds, size_t n, int shift)
{
size_t i;
BDIGIT_DBL num = 0;
assert(0 <= shift && shift < BITSPERDIG);
for (i=0; i<n; i++) {
num = num | (BDIGIT_DBL)*xds++ << shift;
*zds++ = BIGLO(num);
num = BIGDN(num);
}
return BIGLO(num);
}
static void
bary_small_rshift(BDIGIT *zds, const BDIGIT *xds, size_t n, int shift, BDIGIT higher_bdigit)
{
BDIGIT_DBL num = 0;
BDIGIT x;
assert(0 <= shift && shift < BITSPERDIG);
num = BIGUP(higher_bdigit);
while (n--) {
num = (num | xds[n]) >> shift;
x = xds[n];
zds[n] = BIGLO(num);
num = BIGUP(x);
}
}
static int
bary_zero_p(BDIGIT *xds, size_t xn)
{
if (xn == 0)
return 1;
do {
if (xds[--xn]) return 0;
} while (xn);
return 1;
}
static void
bary_neg(BDIGIT *ds, size_t n)
{
while (n--)
ds[n] = BIGLO(~ds[n]);
}
static int
bary_2comp(BDIGIT *ds, size_t n)
{
size_t i;
i = 0;
for (i = 0; i < n; i++) {
if (ds[i] != 0) {
goto non_zero;
}
}
return 1;
non_zero:
ds[i] = BIGLO(~ds[i] + 1);
i++;
for (; i < n; i++) {
ds[i] = BIGLO(~ds[i]);
}
return 0;
}
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;
}
#if !defined(WORDS_BIGENDIAN)
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;
}
#endif
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_BDIGIT
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_BDIGIT
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_BDIGIT
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_BDIGIT
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_BDIGIT && 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_BDIGIT
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_BDIGIT && 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_BDIGIT
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_BDIGIT && 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_BDIGIT == 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_BDIGIT;
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_BDIGIT == sizeof(BDIGIT) &&
wordsize % SIZEOF_BDIGIT == 0 && (uintptr_t)words % ALIGNOF(BDIGIT) == 0) {
size_t bdigits_per_word = wordsize / SIZEOF_BDIGIT;
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);
BDIGITS_ZERO((BDIGIT*)words + src_num_bdigits, 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_BDIGIT * 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))