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[ruby-core:55578] [Feature #8553] This is accepted by matz on DevelopersMeeting20130727Japan. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@42204 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
6385 lines
162 KiB
C
6385 lines
162 KiB
C
/**********************************************************************
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bignum.c -
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$Author$
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created at: Fri Jun 10 00:48:55 JST 1994
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Copyright (C) 1993-2007 Yukihiro Matsumoto
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**********************************************************************/
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#include "ruby/ruby.h"
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#include "ruby/thread.h"
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#include "ruby/util.h"
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#include "internal.h"
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#ifdef HAVE_STRINGS_H
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#include <strings.h>
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#endif
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#include <math.h>
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#include <float.h>
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#include <ctype.h>
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#ifdef HAVE_IEEEFP_H
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#include <ieeefp.h>
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#endif
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#include <assert.h>
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VALUE rb_cBignum;
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const char ruby_digitmap[] = "0123456789abcdefghijklmnopqrstuvwxyz";
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#ifndef SIZEOF_BDIGIT_DBL
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# if defined(HAVE_INT64_T) && defined(HAVE_INT128_T)
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# define SIZEOF_BDIGIT_DBL SIZEOF_INT128_T
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# elif SIZEOF_INT*2 <= SIZEOF_LONG_LONG
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# define SIZEOF_BDIGIT_DBL SIZEOF_LONG_LONG
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# else
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# define SIZEOF_BDIGIT_DBL SIZEOF_LONG
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# endif
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#endif
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STATIC_ASSERT(sizeof_bdigit_dbl, sizeof(BDIGIT_DBL) == SIZEOF_BDIGIT_DBL);
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STATIC_ASSERT(sizeof_bdigit_dbl_signed, sizeof(BDIGIT_DBL_SIGNED) == SIZEOF_BDIGIT_DBL);
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STATIC_ASSERT(sizeof_bdigit, SIZEOF_BDIGITS <= sizeof(BDIGIT));
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STATIC_ASSERT(sizeof_bdigit_and_dbl, SIZEOF_BDIGITS*2 <= SIZEOF_BDIGIT_DBL);
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STATIC_ASSERT(bdigit_signedness, 0 < (BDIGIT)-1);
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STATIC_ASSERT(bdigit_dbl_signedness, 0 < (BDIGIT_DBL)-1);
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STATIC_ASSERT(bdigit_dbl_signed_signedness, 0 > (BDIGIT_DBL_SIGNED)-1);
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STATIC_ASSERT(rbignum_embed_len_max, RBIGNUM_EMBED_LEN_MAX <= (RBIGNUM_EMBED_LEN_MASK >> RBIGNUM_EMBED_LEN_SHIFT));
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#if SIZEOF_BDIGITS < SIZEOF_LONG
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STATIC_ASSERT(sizeof_long_and_sizeof_bdigit, SIZEOF_LONG % SIZEOF_BDIGITS == 0);
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#else
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STATIC_ASSERT(sizeof_long_and_sizeof_bdigit, SIZEOF_BDIGITS % SIZEOF_LONG == 0);
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#endif
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#ifdef WORDS_BIGENDIAN
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# define HOST_BIGENDIAN_P 1
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#else
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# define HOST_BIGENDIAN_P 0
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#endif
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#define ALIGNOF(type) ((int)offsetof(struct { char f1; type f2; }, f2))
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/* (sizeof(d) * CHAR_BIT <= (n) ? 0 : (n)) is same as n but suppress a warning, C4293, by Visual Studio. */
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#define LSHIFTABLE(d, n) ((n) < sizeof(d) * CHAR_BIT)
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#define LSHIFTX(d, n) (!LSHIFTABLE(d, n) ? 0 : ((d) << (!LSHIFTABLE(d, n) ? 0 : (n))))
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#define CLEAR_LOWBITS(d, numbits) ((d) & LSHIFTX(~((d)*0), (numbits)))
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#define FILL_LOWBITS(d, numbits) ((d) | (LSHIFTX(((d)*0+1), (numbits))-1))
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#define POW2_P(x) (((x)&((x)-1))==0)
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#define BDIGITS(x) (RBIGNUM_DIGITS(x))
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#define BITSPERDIG (SIZEOF_BDIGITS*CHAR_BIT)
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#if BITSPERDIG >= INT_MAX
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# error incredible BDIGIT
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#endif
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#define BIGRAD ((BDIGIT_DBL)1 << BITSPERDIG)
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#define BIGRAD_HALF ((BDIGIT)(BIGRAD >> 1))
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#define BDIGIT_MSB(d) (((d) & BIGRAD_HALF) != 0)
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#define BIGUP(x) LSHIFTX(((x) + (BDIGIT_DBL)0), BITSPERDIG)
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#define BIGDN(x) RSHIFT((x),BITSPERDIG)
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#define BIGLO(x) ((BDIGIT)((x) & BDIGMAX))
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#define BDIGMAX ((BDIGIT)(BIGRAD-1))
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#define BDIGIT_DBL_MAX (~(BDIGIT_DBL)0)
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#if SIZEOF_BDIGITS == 2
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# define swap_bdigit(x) swap16(x)
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#elif SIZEOF_BDIGITS == 4
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# define swap_bdigit(x) swap32(x)
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#elif SIZEOF_BDIGITS == 8
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# define swap_bdigit(x) swap64(x)
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#endif
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#define BIGZEROP(x) (RBIGNUM_LEN(x) == 0 || \
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(BDIGITS(x)[0] == 0 && \
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(RBIGNUM_LEN(x) == 1 || bigzero_p(x))))
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#define BIGSIZE(x) (RBIGNUM_LEN(x) == 0 ? (size_t)0 : \
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BDIGITS(x)[RBIGNUM_LEN(x)-1] ? \
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(size_t)(RBIGNUM_LEN(x)*SIZEOF_BDIGITS - nlz(BDIGITS(x)[RBIGNUM_LEN(x)-1])/CHAR_BIT) : \
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rb_absint_size(x, NULL))
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#define BIGDIVREM_EXTRA_WORDS 2
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#define roomof(n, m) ((long)(((n)+(m)-1) / (m)))
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#define bdigit_roomof(n) roomof(n, SIZEOF_BDIGITS)
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#define BARY_ARGS(ary) ary, numberof(ary)
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#define BARY_ADD(z, x, y) bary_add(BARY_ARGS(z), BARY_ARGS(x), BARY_ARGS(y))
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#define BARY_SUB(z, x, y) bary_sub(BARY_ARGS(z), BARY_ARGS(x), BARY_ARGS(y))
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#define BARY_MUL1(z, x, y) bary_mul1(BARY_ARGS(z), BARY_ARGS(x), BARY_ARGS(y))
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#define BARY_DIVMOD(q, r, x, y) bary_divmod(BARY_ARGS(q), BARY_ARGS(r), BARY_ARGS(x), BARY_ARGS(y))
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#define BARY_ZERO_P(x) bary_zero_p(BARY_ARGS(x))
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#define RBIGNUM_SET_NEGATIVE_SIGN(b) RBIGNUM_SET_SIGN(b, 0)
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#define RBIGNUM_SET_POSITIVE_SIGN(b) RBIGNUM_SET_SIGN(b, 1)
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#define bignew(len,sign) bignew_1(rb_cBignum,(len),(sign))
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#define BDIGITS_ZERO(ptr, n) do { \
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BDIGIT *bdigitz_zero_ptr = (ptr); \
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size_t bdigitz_zero_n = (n); \
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while (bdigitz_zero_n) { \
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*bdigitz_zero_ptr++ = 0; \
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bdigitz_zero_n--; \
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} \
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} while (0)
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#define KARATSUBA_BALANCED(xn, yn) ((yn)/2 < (xn))
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#define TOOM3_BALANCED(xn, yn) (((yn)+2)/3 * 2 < (xn))
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#define KARATSUBA_MUL_DIGITS 70
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#define TOOM3_MUL_DIGITS 150
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typedef void (mulfunc_t)(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl);
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static mulfunc_t bary_mul_toom3_start;
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static mulfunc_t bary_mul_karatsuba_start;
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static BDIGIT bigdivrem_single(BDIGIT *qds, BDIGIT *xds, long nx, BDIGIT y);
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static void bary_divmod(BDIGIT *qds, size_t nq, BDIGIT *rds, size_t nr, BDIGIT *xds, size_t nx, BDIGIT *yds, size_t ny);
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static VALUE bigmul0(VALUE x, VALUE y);
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static void bary_mul_toom3(BDIGIT *zds, size_t zn, BDIGIT *xds, size_t xn, BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn);
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static VALUE bignew_1(VALUE klass, long len, int sign);
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static inline VALUE bigtrunc(VALUE x);
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static VALUE bigsq(VALUE x);
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static void bigdivmod(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp);
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static int
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nlz16(uint16_t x)
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{
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#if defined(HAVE_BUILTIN___BUILTIN_CLZ) && 2 <= SIZEOF_INT
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if (x == 0) return 16;
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return __builtin_clz(x) - (SIZEOF_INT-2)*CHAR_BIT;
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#else
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uint16_t y;
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int n = 16;
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y = x >> 8; if (y) {n -= 8; x = y;}
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y = x >> 4; if (y) {n -= 4; x = y;}
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y = x >> 2; if (y) {n -= 2; x = y;}
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y = x >> 1; if (y) {return n - 2;}
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return (int)(n - x);
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#endif
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}
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static int
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nlz32(uint32_t x)
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{
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#if defined(HAVE_BUILTIN___BUILTIN_CLZ) && 4 <= SIZEOF_INT
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if (x == 0) return 32;
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return __builtin_clz(x) - (SIZEOF_INT-4)*CHAR_BIT;
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#elif defined(HAVE_BUILTIN___BUILTIN_CLZL) && 4 <= SIZEOF_LONG
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if (x == 0) return 32;
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return __builtin_clzl(x) - (SIZEOF_LONG-4)*CHAR_BIT;
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#else
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uint32_t y;
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int n = 32;
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y = x >> 16; if (y) {n -= 16; x = y;}
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y = x >> 8; if (y) {n -= 8; x = y;}
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y = x >> 4; if (y) {n -= 4; x = y;}
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y = x >> 2; if (y) {n -= 2; x = y;}
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y = x >> 1; if (y) {return n - 2;}
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return (int)(n - x);
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#endif
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}
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#if defined(HAVE_UINT64_T)
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static int
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nlz64(uint64_t x)
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{
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#if defined(HAVE_BUILTIN___BUILTIN_CLZL) && 8 <= SIZEOF_LONG
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if (x == 0) return 64;
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return __builtin_clzl(x) - (SIZEOF_LONG-8)*CHAR_BIT;
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#elif defined(HAVE_BUILTIN___BUILTIN_CLZLL) && 8 <= SIZEOF_LONG_LONG
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if (x == 0) return 64;
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return __builtin_clzll(x) - (SIZEOF_LONG_LONG-8)*CHAR_BIT;
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#else
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uint64_t y;
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int n = 64;
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y = x >> 32; if (y) {n -= 32; x = y;}
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y = x >> 16; if (y) {n -= 16; x = y;}
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y = x >> 8; if (y) {n -= 8; x = y;}
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y = x >> 4; if (y) {n -= 4; x = y;}
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y = x >> 2; if (y) {n -= 2; x = y;}
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y = x >> 1; if (y) {return n - 2;}
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return (int)(n - x);
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#endif
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}
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#endif
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#if defined(HAVE_UINT128_T)
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static int
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nlz128(uint128_t x)
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{
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#if defined(HAVE_BUILTIN___BUILTIN_CLZLL) && 16 <= SIZEOF_LONG_LONG
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if (x == 0) return 128;
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return __builtin_clzll(x) - (SIZEOF_LONG_LONG-16)*CHAR_BIT;
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#else
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uint128_t y;
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int n = 128;
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y = x >> 64; if (y) {n -= 64; x = y;}
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y = x >> 32; if (y) {n -= 32; x = y;}
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y = x >> 16; if (y) {n -= 16; x = y;}
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y = x >> 8; if (y) {n -= 8; x = y;}
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y = x >> 4; if (y) {n -= 4; x = y;}
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y = x >> 2; if (y) {n -= 2; x = y;}
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y = x >> 1; if (y) {return n - 2;}
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return (int)(n - x);
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#endif
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}
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#endif
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#if SIZEOF_BDIGITS == 2
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static int nlz(BDIGIT x) { return nlz16((uint16_t)x); }
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#elif SIZEOF_BDIGITS == 4
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static int nlz(BDIGIT x) { return nlz32((uint32_t)x); }
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#elif SIZEOF_BDIGITS == 8
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static int nlz(BDIGIT x) { return nlz64((uint64_t)x); }
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#elif SIZEOF_BDIGITS == 16
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static int nlz(BDIGIT x) { return nlz128((uint128_t)x); }
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#endif
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#if defined(HAVE_UINT128_T)
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# define bitsize(x) \
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(sizeof(x) <= 2 ? 16 - nlz16(x) : \
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sizeof(x) <= 4 ? 32 - nlz32(x) : \
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sizeof(x) <= 8 ? 64 - nlz64(x) : \
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128 - nlz128(x))
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#elif defined(HAVE_UINT64_T)
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# define bitsize(x) \
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(sizeof(x) <= 2 ? 16 - nlz16(x) : \
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sizeof(x) <= 4 ? 32 - nlz32(x) : \
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64 - nlz64(x))
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#else
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# define bitsize(x) \
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(sizeof(x) <= 2 ? 16 - nlz16(x) : \
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32 - nlz32(x))
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#endif
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#define U16(a) ((uint16_t)(a))
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#define U32(a) ((uint32_t)(a))
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#ifdef HAVE_UINT64_T
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#define U64(a,b) (((uint64_t)(a) << 32) | (b))
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#endif
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#ifdef HAVE_UINT128_T
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#define U128(a,b,c,d) (((uint128_t)U64(a,b) << 64) | U64(c,d))
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#endif
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/* The following scirpt, maxpow.rb, generates the tables follows.
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def big(n, bits)
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ns = []
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((bits+31)/32).times {
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ns << sprintf("0x%08x", n & 0xffff_ffff)
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n >>= 32
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}
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"U#{bits}(" + ns.reverse.join(",") + ")"
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end
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def values(ary, width, indent)
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lines = [""]
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ary.each {|e|
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lines << "" if !ary.last.empty? && width < (lines.last + e + ", ").length
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lines.last << e + ", "
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}
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lines.map {|line| " " * indent + line.chomp(" ") + "\n" }.join
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end
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[16,32,64,128].each {|bits|
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max = 2**bits-1
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exps = []
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nums = []
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2.upto(36) {|base|
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exp = 0
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n = 1
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while n * base <= max
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exp += 1
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n *= base
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end
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exps << exp.to_s
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nums << big(n, bits)
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}
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puts "#ifdef HAVE_UINT#{bits}_T"
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puts "static const int maxpow#{bits}_exp[35] = {"
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print values(exps, 70, 4)
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puts "};"
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puts "static const uint#{bits}_t maxpow#{bits}_num[35] = {"
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print values(nums, 70, 4)
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puts "};"
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puts "#endif"
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}
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*/
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#ifdef HAVE_UINT16_T
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static const int maxpow16_exp[35] = {
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15, 10, 7, 6, 6, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3,
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3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
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};
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static const uint16_t maxpow16_num[35] = {
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U16(0x00008000), U16(0x0000e6a9), U16(0x00004000), U16(0x00003d09),
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U16(0x0000b640), U16(0x000041a7), U16(0x00008000), U16(0x0000e6a9),
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U16(0x00002710), U16(0x00003931), U16(0x00005100), U16(0x00006f91),
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U16(0x00009610), U16(0x0000c5c1), U16(0x00001000), U16(0x00001331),
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U16(0x000016c8), U16(0x00001acb), U16(0x00001f40), U16(0x0000242d),
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U16(0x00002998), U16(0x00002f87), U16(0x00003600), U16(0x00003d09),
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U16(0x000044a8), U16(0x00004ce3), U16(0x000055c0), U16(0x00005f45),
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U16(0x00006978), U16(0x0000745f), U16(0x00008000), U16(0x00008c61),
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U16(0x00009988), U16(0x0000a77b), U16(0x0000b640),
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};
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#endif
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#ifdef HAVE_UINT32_T
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static const int maxpow32_exp[35] = {
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31, 20, 15, 13, 12, 11, 10, 10, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 7, 7,
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7, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
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};
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static const uint32_t maxpow32_num[35] = {
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U32(0x80000000), U32(0xcfd41b91), U32(0x40000000), U32(0x48c27395),
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U32(0x81bf1000), U32(0x75db9c97), U32(0x40000000), U32(0xcfd41b91),
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U32(0x3b9aca00), U32(0x8c8b6d2b), U32(0x19a10000), U32(0x309f1021),
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U32(0x57f6c100), U32(0x98c29b81), U32(0x10000000), U32(0x18754571),
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U32(0x247dbc80), U32(0x3547667b), U32(0x4c4b4000), U32(0x6b5a6e1d),
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U32(0x94ace180), U32(0xcaf18367), U32(0x0b640000), U32(0x0e8d4a51),
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U32(0x1269ae40), U32(0x17179149), U32(0x1cb91000), U32(0x23744899),
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U32(0x2b73a840), U32(0x34e63b41), U32(0x40000000), U32(0x4cfa3cc1),
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U32(0x5c13d840), U32(0x6d91b519), U32(0x81bf1000),
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};
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#endif
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#ifdef HAVE_UINT64_T
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static const int maxpow64_exp[35] = {
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63, 40, 31, 27, 24, 22, 21, 20, 19, 18, 17, 17, 16, 16, 15, 15, 15,
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15, 14, 14, 14, 14, 13, 13, 13, 13, 13, 13, 13, 12, 12, 12, 12, 12,
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12,
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};
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static const uint64_t maxpow64_num[35] = {
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U64(0x80000000,0x00000000), U64(0xa8b8b452,0x291fe821),
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U64(0x40000000,0x00000000), U64(0x6765c793,0xfa10079d),
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U64(0x41c21cb8,0xe1000000), U64(0x36427987,0x50226111),
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U64(0x80000000,0x00000000), U64(0xa8b8b452,0x291fe821),
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U64(0x8ac72304,0x89e80000), U64(0x4d28cb56,0xc33fa539),
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U64(0x1eca170c,0x00000000), U64(0x780c7372,0x621bd74d),
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U64(0x1e39a505,0x7d810000), U64(0x5b27ac99,0x3df97701),
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U64(0x10000000,0x00000000), U64(0x27b95e99,0x7e21d9f1),
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U64(0x5da0e1e5,0x3c5c8000), U64(0xd2ae3299,0xc1c4aedb),
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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);
|
|
|
|
{
|
|
#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 BDIGIT
|
|
maxpow_in_bdigit(int base, int *exp_ret)
|
|
{
|
|
BDIGIT maxpow;
|
|
int exponent;
|
|
|
|
{
|
|
#if SIZEOF_BDIGITS == 0
|
|
#elif SIZEOF_BDIGITS == 2
|
|
maxpow = maxpow16_num[base-2];
|
|
exponent = maxpow16_exp[base-2];
|
|
#elif SIZEOF_BDIGITS == 4
|
|
maxpow = maxpow32_num[base-2];
|
|
exponent = maxpow32_exp[base-2];
|
|
#elif SIZEOF_BDIGITS == 8 && defined HAVE_UINT64_T
|
|
maxpow = maxpow64_num[base-2];
|
|
exponent = maxpow64_exp[base-2];
|
|
#elif SIZEOF_BDIGITS == 16 && defined HAVE_UINT128_T
|
|
maxpow = maxpow128_num[base-2];
|
|
exponent = maxpow128_exp[base-2];
|
|
#else
|
|
maxpow = base;
|
|
exponent = 1;
|
|
while (maxpow <= BDIGMAX / base) {
|
|
maxpow *= base;
|
|
exponent++;
|
|
}
|
|
#endif
|
|
}
|
|
|
|
*exp_ret = exponent;
|
|
return maxpow;
|
|
}
|
|
|
|
static BDIGIT
|
|
bary_small_lshift(BDIGIT *zds, 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, BDIGIT *xds, size_t n, int shift, int sign_bit)
|
|
{
|
|
BDIGIT_DBL num = 0;
|
|
BDIGIT x;
|
|
|
|
assert(0 <= shift && shift < BITSPERDIG);
|
|
|
|
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 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_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;
|
|
}
|
|
|
|
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);
|
|
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_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) {
|
|
uint16_t 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) {
|
|
uint32_t 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) {
|
|
uint64_t 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) {
|
|
BDIGITS_ZERO(bdigits + num_bdigits0, 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;
|
|
size_t sn;
|
|
|
|
assert(xn <= zn);
|
|
assert(yn <= zn);
|
|
|
|
sn = xn < yn ? xn : yn;
|
|
|
|
num = borrow ? -1 : 0;
|
|
for (i = 0; i < sn; i++) {
|
|
num += (BDIGIT_DBL_SIGNED)xds[i] - yds[i];
|
|
zds[i] = BIGLO(num);
|
|
num = BIGDN(num);
|
|
}
|
|
if (yn <= xn) {
|
|
for (; i < xn; i++) {
|
|
if (num == 0) goto num_is_zero;
|
|
num += xds[i];
|
|
zds[i] = BIGLO(num);
|
|
num = BIGDN(num);
|
|
}
|
|
}
|
|
else {
|
|
for (; i < yn; i++) {
|
|
num -= yds[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 *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 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);
|
|
|
|
BDIGITS_ZERO(zds + 2, zl - 2);
|
|
}
|
|
|
|
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 BDIGIT_DBL_SIGNED
|
|
bigdivrem_mulsub(BDIGIT *zds, size_t zn, BDIGIT x, BDIGIT *yds, size_t yn)
|
|
{
|
|
size_t i;
|
|
BDIGIT_DBL t2;
|
|
BDIGIT_DBL_SIGNED num;
|
|
|
|
assert(zn == yn + 1);
|
|
|
|
num = 0;
|
|
t2 = 0;
|
|
i = 0;
|
|
|
|
do {
|
|
BDIGIT_DBL ee;
|
|
t2 += (BDIGIT_DBL)yds[i] * x;
|
|
ee = num - BIGLO(t2);
|
|
num = (BDIGIT_DBL)zds[i] + ee;
|
|
if (ee) zds[i] = BIGLO(num);
|
|
num = BIGDN(num);
|
|
t2 = BIGDN(t2);
|
|
} while (++i < yn);
|
|
num += zds[i] - t2; /* borrow from high digit; don't update */
|
|
return num;
|
|
}
|
|
|
|
static int
|
|
bary_mulsub_1xN(BDIGIT *zds, size_t zn, BDIGIT x, BDIGIT *yds, size_t yn)
|
|
{
|
|
BDIGIT_DBL_SIGNED num;
|
|
|
|
assert(zn == yn + 1);
|
|
|
|
num = bigdivrem_mulsub(zds, zn, x, yds, yn);
|
|
zds[yn] = BIGLO(num);
|
|
if (BIGDN(num))
|
|
return 1;
|
|
return 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);
|
|
|
|
BDIGITS_ZERO(zds, 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;
|
|
BDIGIT vl;
|
|
int vh;
|
|
|
|
assert(xn * 2 <= zn);
|
|
|
|
BDIGITS_ZERO(zds, zn);
|
|
|
|
if (xn == 0)
|
|
return;
|
|
|
|
for (i = 0; i < xn-1; 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;
|
|
vl = BIGLO(v);
|
|
vh = (int)BIGDN(v);
|
|
for (j = i + 1; j < xn; j++) {
|
|
w = (BDIGIT_DBL)xds[j];
|
|
c += (BDIGIT_DBL)zds[i + j] + vl * w;
|
|
zds[i + j] = BIGLO(c);
|
|
c = BIGDN(c);
|
|
if (vh)
|
|
c += w;
|
|
}
|
|
if (c) {
|
|
c += (BDIGIT_DBL)zds[i + xn];
|
|
zds[i + xn] = BIGLO(c);
|
|
c = BIGDN(c);
|
|
if (c)
|
|
zds[i + xn + 1] += (BDIGIT)c;
|
|
}
|
|
}
|
|
|
|
/* i == xn-1 */
|
|
v = (BDIGIT_DBL)xds[i];
|
|
if (!v)
|
|
return;
|
|
c = (BDIGIT_DBL)zds[i + i] + v * v;
|
|
zds[i + i] = BIGLO(c);
|
|
c = BIGDN(c);
|
|
if (c) {
|
|
zds[i + xn] += BIGLO(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_with_mulfunc(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl, mulfunc_t *mulfunc)
|
|
{
|
|
VALUE work = 0;
|
|
size_t yl0 = yl;
|
|
size_t r, n;
|
|
|
|
assert(xl + yl <= zl);
|
|
assert(xl <= yl);
|
|
assert(!KARATSUBA_BALANCED(xl, yl) || !TOOM3_BALANCED(xl, yl));
|
|
|
|
BDIGITS_ZERO(zds, 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;
|
|
mulfunc(tds, tl, xds, xl, yds + n, r, wds, wl);
|
|
BDIGITS_ZERO(zds + n + xl, 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);
|
|
mulfunc(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;
|
|
}
|
|
BDIGITS_ZERO(zds+xl+yl0, 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));
|
|
bary_mul_balance_with_mulfunc(BDIGITS(z), zn, BDIGITS(x), xn, BDIGITS(y), yn, NULL, 0, bary_mul_toom3_start);
|
|
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;
|
|
int sq;
|
|
|
|
BDIGIT *xds0, *xds1, *yds0, *yds1, *zds0, *zds1, *zds2, *zds3;
|
|
|
|
assert(xl + yl <= zl);
|
|
assert(xl <= yl);
|
|
assert(yl < 2 * xl);
|
|
|
|
sq = xds == yds && xl == yl;
|
|
|
|
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 (sq) {
|
|
sub_p = 1;
|
|
bary_mul_karatsuba_start(zds1, 2*n, zds0, n, zds0, n, wds, wl);
|
|
}
|
|
else {
|
|
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_karatsuba_start(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_karatsuba_start(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_karatsuba_start(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 || KARATSUBA_BALANCED(xn, yn)))
|
|
rb_raise(rb_eArgError, "unexpected bignum length for karatsuba");
|
|
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_mul_toom3(BDIGIT *zds, size_t zn, BDIGIT *xds, size_t xn, BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn)
|
|
{
|
|
size_t n;
|
|
size_t wnc;
|
|
VALUE work = 0;
|
|
|
|
/* "p" means "positive". Actually "non-negative", though. */
|
|
size_t x0n; BDIGIT *x0ds;
|
|
size_t x1n; BDIGIT *x1ds;
|
|
size_t x2n; BDIGIT *x2ds;
|
|
size_t y0n; BDIGIT *y0ds;
|
|
size_t y1n; BDIGIT *y1ds;
|
|
size_t y2n; BDIGIT *y2ds;
|
|
|
|
size_t u1n; BDIGIT *u1ds; int u1p;
|
|
size_t u2n; BDIGIT *u2ds; int u2p;
|
|
size_t u3n; BDIGIT *u3ds; int u3p;
|
|
|
|
size_t v1n; BDIGIT *v1ds; int v1p;
|
|
size_t v2n; BDIGIT *v2ds; int v2p;
|
|
size_t v3n; BDIGIT *v3ds; int v3p;
|
|
|
|
size_t t0n; BDIGIT *t0ds; int t0p;
|
|
size_t t1n; BDIGIT *t1ds; int t1p;
|
|
size_t t2n; BDIGIT *t2ds; int t2p;
|
|
size_t t3n; BDIGIT *t3ds; int t3p;
|
|
size_t t4n; BDIGIT *t4ds; int t4p;
|
|
|
|
size_t z0n; BDIGIT *z0ds;
|
|
size_t z1n; BDIGIT *z1ds; int z1p;
|
|
size_t z2n; BDIGIT *z2ds; int z2p;
|
|
size_t z3n; BDIGIT *z3ds; int z3p;
|
|
size_t z4n; BDIGIT *z4ds; int z4p;
|
|
|
|
size_t zzn; BDIGIT *zzds;
|
|
|
|
int sq = xds == yds && xn == yn;
|
|
|
|
assert(xn <= yn); /* assume y >= x */
|
|
assert(xn + yn <= zn);
|
|
|
|
n = (yn + 2) / 3;
|
|
assert(2*n < xn);
|
|
|
|
wnc = 0;
|
|
|
|
wnc += (u1n = n+1); /* BITSPERDIG*n+2 bits */
|
|
wnc += (u2n = n+1); /* BITSPERDIG*n+1 bits */
|
|
wnc += (u3n = n+1); /* BITSPERDIG*n+3 bits */
|
|
wnc += (v1n = n+1); /* BITSPERDIG*n+2 bits */
|
|
wnc += (v2n = n+1); /* BITSPERDIG*n+1 bits */
|
|
wnc += (v3n = n+1); /* BITSPERDIG*n+3 bits */
|
|
|
|
wnc += (t0n = 2*n); /* BITSPERDIG*2*n bits */
|
|
wnc += (t1n = 2*n+2); /* BITSPERDIG*2*n+4 bits but bary_mul needs u1n+v1n */
|
|
wnc += (t2n = 2*n+2); /* BITSPERDIG*2*n+2 bits but bary_mul needs u2n+v2n */
|
|
wnc += (t3n = 2*n+2); /* BITSPERDIG*2*n+6 bits but bary_mul needs u3n+v3n */
|
|
wnc += (t4n = 2*n); /* BITSPERDIG*2*n bits */
|
|
|
|
wnc += (z1n = 2*n+1); /* BITSPERDIG*2*n+5 bits */
|
|
wnc += (z2n = 2*n+1); /* BITSPERDIG*2*n+6 bits */
|
|
wnc += (z3n = 2*n+1); /* BITSPERDIG*2*n+8 bits */
|
|
|
|
if (wn < wnc) {
|
|
wn = wnc * 3 / 2; /* Allocate working memory for whole recursion at once. */
|
|
wds = ALLOCV_N(BDIGIT, work, wn);
|
|
}
|
|
|
|
u1ds = wds; wds += u1n;
|
|
u2ds = wds; wds += u2n;
|
|
u3ds = wds; wds += u3n;
|
|
|
|
v1ds = wds; wds += v1n;
|
|
v2ds = wds; wds += v2n;
|
|
v3ds = wds; wds += v3n;
|
|
|
|
t0ds = wds; wds += t0n;
|
|
t1ds = wds; wds += t1n;
|
|
t2ds = wds; wds += t2n;
|
|
t3ds = wds; wds += t3n;
|
|
t4ds = wds; wds += t4n;
|
|
|
|
z1ds = wds; wds += z1n;
|
|
z2ds = wds; wds += z2n;
|
|
z3ds = wds; wds += z3n;
|
|
|
|
wn -= wnc;
|
|
|
|
zzds = u1ds;
|
|
zzn = 6*n+1;
|
|
|
|
x0n = n;
|
|
x1n = n;
|
|
x2n = xn - 2*n;
|
|
x0ds = xds;
|
|
x1ds = xds + n;
|
|
x2ds = xds + 2*n;
|
|
|
|
if (sq) {
|
|
y0n = x0n;
|
|
y1n = x1n;
|
|
y2n = x2n;
|
|
y0ds = x0ds;
|
|
y1ds = x1ds;
|
|
y2ds = x2ds;
|
|
}
|
|
else {
|
|
y0n = n;
|
|
y1n = n;
|
|
y2n = yn - 2*n;
|
|
y0ds = yds;
|
|
y1ds = yds + n;
|
|
y2ds = yds + 2*n;
|
|
}
|
|
|
|
/*
|
|
* 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 and z4.
|
|
*
|
|
* (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 */
|
|
bary_add(u1ds, u1n, x0ds, x0n, x2ds, x2n);
|
|
u1p = 1;
|
|
|
|
/* x(-1) : u2 <- u1 - x1 = x0 - x1 + x2 */
|
|
if (bary_sub(u2ds, u2n, u1ds, u1n, x1ds, x1n)) {
|
|
bary_2comp(u2ds, u2n);
|
|
u2p = 0;
|
|
}
|
|
else {
|
|
u2p = 1;
|
|
}
|
|
|
|
/* x(1) : u1 <- u1 + x1 = x0 + x1 + x2 */
|
|
bary_add(u1ds, u1n, u1ds, u1n, x1ds, x1n);
|
|
|
|
/* x(-2) : u3 <- 2 * (u2 + x2) - x0 = x0 - 2 * (x1 - 2 * x2) */
|
|
u3p = 1;
|
|
if (u2p) {
|
|
bary_add(u3ds, u3n, u2ds, u2n, x2ds, x2n);
|
|
}
|
|
else if (bary_sub(u3ds, u3n, x2ds, x2n, u2ds, u2n)) {
|
|
bary_2comp(u3ds, u3n);
|
|
u3p = 0;
|
|
}
|
|
bary_small_lshift(u3ds, u3ds, u3n, 1);
|
|
if (!u3p) {
|
|
bary_add(u3ds, u3n, u3ds, u3n, x0ds, x0n);
|
|
}
|
|
else if (bary_sub(u3ds, u3n, u3ds, u3n, x0ds, x0n)) {
|
|
bary_2comp(u3ds, u3n);
|
|
u3p = 0;
|
|
}
|
|
|
|
if (sq) {
|
|
v1n = u1n; v1ds = u1ds; v1p = u1p;
|
|
v2n = u2n; v2ds = u2ds; v2p = u2p;
|
|
v3n = u3n; v3ds = u3ds; v3p = u3p;
|
|
}
|
|
else {
|
|
/* v1 <- y0 + y2 */
|
|
bary_add(v1ds, v1n, y0ds, y0n, y2ds, y2n);
|
|
v1p = 1;
|
|
|
|
/* y(-1) : v2 <- v1 - y1 = y0 - y1 + y2 */
|
|
v2p = 1;
|
|
if (bary_sub(v2ds, v2n, v1ds, v1n, y1ds, y1n)) {
|
|
bary_2comp(v2ds, v2n);
|
|
v2p = 0;
|
|
}
|
|
|
|
/* y(1) : v1 <- v1 + y1 = y0 + y1 + y2 */
|
|
bary_add(v1ds, v1n, v1ds, v1n, y1ds, y1n);
|
|
|
|
/* y(-2) : v3 <- 2 * (v2 + y2) - y0 = y0 - 2 * (y1 - 2 * y2) */
|
|
v3p = 1;
|
|
if (v2p) {
|
|
bary_add(v3ds, v3n, v2ds, v2n, y2ds, y2n);
|
|
}
|
|
else if (bary_sub(v3ds, v3n, y2ds, y2n, v2ds, v2n)) {
|
|
bary_2comp(v3ds, v3n);
|
|
v3p = 0;
|
|
}
|
|
bary_small_lshift(v3ds, v3ds, v3n, 1);
|
|
if (!v3p) {
|
|
bary_add(v3ds, v3n, v3ds, v3n, y0ds, y0n);
|
|
}
|
|
else if (bary_sub(v3ds, v3n, v3ds, v3n, y0ds, y0n)) {
|
|
bary_2comp(v3ds, v3n);
|
|
v3p = 0;
|
|
}
|
|
}
|
|
|
|
/* z(0) : t0 <- x0 * y0 */
|
|
bary_mul_toom3_start(t0ds, t0n, x0ds, x0n, y0ds, y0n, wds, wn);
|
|
t0p = 1;
|
|
|
|
/* z(1) : t1 <- u1 * v1 */
|
|
bary_mul_toom3_start(t1ds, t1n, u1ds, u1n, v1ds, v1n, wds, wn);
|
|
t1p = u1p == v1p;
|
|
assert(t1ds[t1n-1] == 0);
|
|
t1n--;
|
|
|
|
/* z(-1) : t2 <- u2 * v2 */
|
|
bary_mul_toom3_start(t2ds, t2n, u2ds, u2n, v2ds, v2n, wds, wn);
|
|
t2p = u2p == v2p;
|
|
assert(t2ds[t2n-1] == 0);
|
|
t2n--;
|
|
|
|
/* z(-2) : t3 <- u3 * v3 */
|
|
bary_mul_toom3_start(t3ds, t3n, u3ds, u3n, v3ds, v3n, wds, wn);
|
|
t3p = u3p == v3p;
|
|
assert(t3ds[t3n-1] == 0);
|
|
t3n--;
|
|
|
|
/* z(inf) : t4 <- x2 * y2 */
|
|
bary_mul_toom3_start(t4ds, t4n, x2ds, x2n, y2ds, y2n, wds, wn);
|
|
t4p = 1;
|
|
|
|
/*
|
|
* [Step2] interpolating z0, z1, z2, z3 and z4.
|
|
*/
|
|
|
|
/* z0 <- z(0) == t0 */
|
|
z0n = t0n; z0ds = t0ds;
|
|
|
|
/* z4 <- z(inf) == t4 */
|
|
z4n = t4n; z4ds = t4ds; z4p = t4p;
|
|
|
|
/* z3 <- (z(-2) - z(1)) / 3 == (t3 - t1) / 3 */
|
|
if (t3p == t1p) {
|
|
z3p = t3p;
|
|
if (bary_sub(z3ds, z3n, t3ds, t3n, t1ds, t1n)) {
|
|
bary_2comp(z3ds, z3n);
|
|
z3p = !z3p;
|
|
}
|
|
}
|
|
else {
|
|
z3p = t3p;
|
|
bary_add(z3ds, z3n, t3ds, t3n, t1ds, t1n);
|
|
}
|
|
bigdivrem_single(z3ds, z3ds, z3n, 3);
|
|
|
|
/* z1 <- (z(1) - z(-1)) / 2 == (t1 - t2) / 2 */
|
|
if (t1p == t2p) {
|
|
z1p = t1p;
|
|
if (bary_sub(z1ds, z1n, t1ds, t1n, t2ds, t2n)) {
|
|
bary_2comp(z1ds, z1n);
|
|
z1p = !z1p;
|
|
}
|
|
}
|
|
else {
|
|
z1p = t1p;
|
|
bary_add(z1ds, z1n, t1ds, t1n, t2ds, t2n);
|
|
}
|
|
bary_small_rshift(z1ds, z1ds, z1n, 1, 0);
|
|
|
|
/* z2 <- z(-1) - z(0) == t2 - t0 */
|
|
if (t2p == t0p) {
|
|
z2p = t2p;
|
|
if (bary_sub(z2ds, z2n, t2ds, t2n, t0ds, t0n)) {
|
|
bary_2comp(z2ds, z2n);
|
|
z2p = !z2p;
|
|
}
|
|
}
|
|
else {
|
|
z2p = t2p;
|
|
bary_add(z2ds, z2n, t2ds, t2n, t0ds, t0n);
|
|
}
|
|
|
|
/* z3 <- (z2 - z3) / 2 + 2 * z(inf) == (z2 - z3) / 2 + 2 * t4 */
|
|
if (z2p == z3p) {
|
|
z3p = z2p;
|
|
if (bary_sub(z3ds, z3n, z2ds, z2n, z3ds, z3n)) {
|
|
bary_2comp(z3ds, z3n);
|
|
z3p = !z3p;
|
|
}
|
|
}
|
|
else {
|
|
z3p = z2p;
|
|
bary_add(z3ds, z3n, z2ds, z2n, z3ds, z3n);
|
|
}
|
|
bary_small_rshift(z3ds, z3ds, z3n, 1, 0);
|
|
if (z3p == t4p) {
|
|
bary_muladd_1xN(z3ds, z3n, 2, t4ds, t4n);
|
|
}
|
|
else {
|
|
if (bary_mulsub_1xN(z3ds, z3n, 2, t4ds, t4n)) {
|
|
bary_2comp(z3ds, z3n);
|
|
z3p = !z3p;
|
|
}
|
|
}
|
|
|
|
/* z2 <- z2 + z1 - z(inf) == z2 + z1 - t4 */
|
|
if (z2p == z1p) {
|
|
bary_add(z2ds, z2n, z2ds, z2n, z1ds, z1n);
|
|
}
|
|
else {
|
|
if (bary_sub(z2ds, z2n, z2ds, z2n, z1ds, z1n)) {
|
|
bary_2comp(z2ds, z2n);
|
|
z2p = !z2p;
|
|
}
|
|
}
|
|
|
|
if (z2p == t4p) {
|
|
if (bary_sub(z2ds, z2n, z2ds, z2n, t4ds, t4n)) {
|
|
bary_2comp(z2ds, z2n);
|
|
z2p = !z2p;
|
|
}
|
|
}
|
|
else {
|
|
bary_add(z2ds, z2n, z2ds, z2n, t4ds, t4n);
|
|
}
|
|
|
|
/* z1 <- z1 - z3 */
|
|
if (z1p == z3p) {
|
|
if (bary_sub(z1ds, z1n, z1ds, z1n, z3ds, z3n)) {
|
|
bary_2comp(z1ds, z1n);
|
|
z1p = !z1p;
|
|
}
|
|
}
|
|
else {
|
|
bary_add(z1ds, z1n, z1ds, z1n, z3ds, z3n);
|
|
}
|
|
|
|
/*
|
|
* [Step3] Substituting base value into b of the polynomial z(b),
|
|
*/
|
|
|
|
MEMCPY(zzds, z0ds, BDIGIT, z0n);
|
|
BDIGITS_ZERO(zzds + z0n, zzn - z0n);
|
|
if (z1p)
|
|
bary_add(zzds + n, zzn - n, zzds + n, zzn - n, z1ds, z1n);
|
|
else
|
|
bary_sub(zzds + n, zzn - n, zzds + n, zzn - n, z1ds, z1n);
|
|
if (z2p)
|
|
bary_add(zzds + 2*n, zzn - 2*n, zzds + 2*n, zzn - 2*n, z2ds, z2n);
|
|
else
|
|
bary_sub(zzds + 2*n, zzn - 2*n, zzds + 2*n, zzn - 2*n, z2ds, z2n);
|
|
if (z3p)
|
|
bary_add(zzds + 3*n, zzn - 3*n, zzds + 3*n, zzn - 3*n, z3ds, z3n);
|
|
else
|
|
bary_sub(zzds + 3*n, zzn - 3*n, zzds + 3*n, zzn - 3*n, z3ds, z3n);
|
|
if (z4p)
|
|
bary_add(zzds + 4*n, zzn - 4*n, zzds + 4*n, zzn - 4*n, z4ds, z4n);
|
|
else
|
|
bary_sub(zzds + 4*n, zzn - 4*n, zzds + 4*n, zzn - 4*n, z4ds, z4n);
|
|
|
|
while (0 < zzn && zzds[zzn-1] == 0)
|
|
zzn--;
|
|
MEMCPY(zds, zzds, BDIGIT, zzn);
|
|
BDIGITS_ZERO(zds + zzn, zn - zzn);
|
|
|
|
if (work)
|
|
ALLOCV_END(work);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_mul_toom3(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 < 3 || !TOOM3_BALANCED(xn,yn))
|
|
rb_raise(rb_eArgError, "unexpected bignum length for toom3");
|
|
bary_mul_toom3(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)
|
|
{
|
|
assert(xl + yl <= zl);
|
|
|
|
if (xl == 1 && yl == 1) {
|
|
bary_mul_single(zds, zl, xds[0], yds[0]);
|
|
}
|
|
else {
|
|
bary_mul_normal(zds, zl, xds, xl, yds, yl);
|
|
rb_thread_check_ints();
|
|
}
|
|
}
|
|
|
|
/* 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 int
|
|
bary_mul_precheck(BDIGIT **zdsp, size_t *zlp, BDIGIT **xdsp, size_t *xlp, BDIGIT **ydsp, size_t *ylp)
|
|
{
|
|
size_t nlsz; /* number of least significant zero BDIGITs */
|
|
|
|
BDIGIT *zds = *zdsp;
|
|
size_t zl = *zlp;
|
|
BDIGIT *xds = *xdsp;
|
|
size_t xl = *xlp;
|
|
BDIGIT *yds = *ydsp;
|
|
size_t yl = *ylp;
|
|
|
|
assert(xl + yl <= zl);
|
|
|
|
nlsz = 0;
|
|
|
|
while (0 < xl) {
|
|
if (xds[xl-1] == 0) {
|
|
xl--;
|
|
}
|
|
else {
|
|
do {
|
|
if (xds[0] != 0)
|
|
break;
|
|
xds++;
|
|
xl--;
|
|
nlsz++;
|
|
} while (0 < xl);
|
|
break;
|
|
}
|
|
}
|
|
|
|
while (0 < yl) {
|
|
if (yds[yl-1] == 0) {
|
|
yl--;
|
|
}
|
|
else {
|
|
do {
|
|
if (xds[0] != 0)
|
|
break;
|
|
yds++;
|
|
yl--;
|
|
nlsz++;
|
|
} while (0 < yl);
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (nlsz) {
|
|
BDIGITS_ZERO(zds, 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 <= 1) {
|
|
if (xl == 0) {
|
|
BDIGITS_ZERO(zds, zl);
|
|
return 1;
|
|
}
|
|
|
|
if (xds[0] == 1) {
|
|
MEMCPY(zds, yds, BDIGIT, yl);
|
|
BDIGITS_ZERO(zds+yl, zl-yl);
|
|
return 1;
|
|
}
|
|
if (POW2_P(xds[0])) {
|
|
zds[yl] = bary_small_lshift(zds, yds, yl, bitsize(xds[0])-1);
|
|
BDIGITS_ZERO(zds+yl+1, zl-yl-1);
|
|
return 1;
|
|
}
|
|
if (yl == 1 && yds[0] == 1) {
|
|
zds[0] = xds[0];
|
|
BDIGITS_ZERO(zds+1, zl-1);
|
|
return 1;
|
|
}
|
|
bary_mul_normal(zds, zl, xds, xl, yds, yl);
|
|
return 1;
|
|
}
|
|
|
|
*zdsp = zds;
|
|
*zlp = zl;
|
|
*xdsp = xds;
|
|
*xlp = xl;
|
|
*ydsp = yds;
|
|
*ylp = yl;
|
|
|
|
return 0;
|
|
}
|
|
|
|
static void
|
|
bary_mul_karatsuba_branch(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl)
|
|
{
|
|
/* 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 (!KARATSUBA_BALANCED(xl, yl)) {
|
|
bary_mul_balance_with_mulfunc(zds, zl, xds, xl, yds, yl, wds, wl, bary_mul_karatsuba_start);
|
|
return;
|
|
}
|
|
|
|
/* multiplication by karatsuba method */
|
|
bary_mul_karatsuba(zds, zl, xds, xl, yds, yl, wds, wl);
|
|
}
|
|
|
|
static void
|
|
bary_mul_karatsuba_start(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl)
|
|
{
|
|
if (bary_mul_precheck(&zds, &zl, &xds, &xl, &yds, &yl))
|
|
return;
|
|
|
|
bary_mul_karatsuba_branch(zds, zl, xds, xl, yds, yl, wds, wl);
|
|
}
|
|
|
|
static void
|
|
bary_mul_toom3_branch(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl)
|
|
{
|
|
if (yl < TOOM3_MUL_DIGITS) {
|
|
bary_mul_karatsuba_branch(zds, zl, xds, xl, yds, yl, wds, wl);
|
|
return;
|
|
}
|
|
|
|
if (!TOOM3_BALANCED(xl, yl)) {
|
|
bary_mul_balance_with_mulfunc(zds, zl, xds, xl, yds, yl, wds, wl, bary_mul_toom3_start);
|
|
return;
|
|
}
|
|
|
|
bary_mul_toom3(zds, zl, xds, xl, yds, yl, wds, wl);
|
|
}
|
|
|
|
static void
|
|
bary_mul_toom3_start(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl, BDIGIT *wds, size_t wl)
|
|
{
|
|
if (bary_mul_precheck(&zds, &zl, &xds, &xl, &yds, &yl))
|
|
return;
|
|
|
|
bary_mul_toom3_branch(zds, zl, xds, xl, yds, yl, wds, wl);
|
|
}
|
|
|
|
static void
|
|
bary_mul(BDIGIT *zds, size_t zl, BDIGIT *xds, size_t xl, BDIGIT *yds, size_t yl)
|
|
{
|
|
if (xl < KARATSUBA_MUL_DIGITS || yl < KARATSUBA_MUL_DIGITS) {
|
|
if (xds == yds && xl == yl)
|
|
bary_sq_fast(zds, zl, xds, xl);
|
|
else
|
|
bary_mul1(zds, zl, xds, xl, yds, yl);
|
|
return;
|
|
}
|
|
|
|
bary_mul_toom3_start(zds, zl, xds, xl, yds, yl, NULL, 0);
|
|
}
|
|
|
|
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 j;
|
|
long nyzero = bds->nyzero;
|
|
BDIGIT *yds = bds->yds, *zds = bds->zds;
|
|
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) {
|
|
num = bigdivrem_mulsub(zds+j-(ny-nyzero), ny-nyzero+1,
|
|
q,
|
|
yds+nyzero, ny-nyzero);
|
|
while (num) { /* "add back" required */
|
|
q--;
|
|
num = bary_add(zds+j-(ny-nyzero), ny-nyzero,
|
|
zds+j-(ny-nyzero), ny-nyzero,
|
|
yds+nyzero, ny-nyzero);
|
|
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) {
|
|
BDIGITS_ZERO(qds, nq);
|
|
BDIGITS_ZERO(rds, nr);
|
|
return;
|
|
}
|
|
|
|
if (nx < ny || (nx == ny && xds[nx - 1] < yds[ny - 1])) {
|
|
MEMCPY(rds, xds, BDIGIT, nx);
|
|
BDIGITS_ZERO(rds+nx, nr-nx);
|
|
BDIGITS_ZERO(qds, nq);
|
|
}
|
|
else if (ny == 1) {
|
|
MEMCPY(qds, xds, BDIGIT, nx);
|
|
BDIGITS_ZERO(qds+nx, nq-nx);
|
|
rds[0] = bigdivrem_single(qds, xds, nx, yds[0]);
|
|
BDIGITS_ZERO(rds+1, nr-1);
|
|
}
|
|
else if (nx == 2 && ny == 2) {
|
|
BDIGIT_DBL x = xds[0] | BIGUP(xds[1]);
|
|
BDIGIT_DBL y = yds[0] | BIGUP(yds[1]);
|
|
BDIGIT_DBL q = x / y;
|
|
BDIGIT_DBL r = x % y;
|
|
qds[0] = BIGLO(q);
|
|
qds[1] = BIGLO(BIGDN(q));
|
|
BDIGITS_ZERO(qds+2, nq-2);
|
|
rds[0] = BIGLO(r);
|
|
rds[1] = BIGLO(BIGDN(r));
|
|
BDIGITS_ZERO(rds+2, nr-2);
|
|
}
|
|
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);
|
|
BDIGITS_ZERO(zds+nx, 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);
|
|
BDIGITS_ZERO(rds+ny, nr-ny);
|
|
|
|
/* move quotient */
|
|
j = nz - ny;
|
|
MEMMOVE(qds, zds+ny, BDIGIT, j);
|
|
BDIGITS_ZERO(qds+j, nq-j);
|
|
|
|
if (tmpz)
|
|
ALLOCV_END(tmpz);
|
|
}
|
|
}
|
|
|
|
|
|
#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)
|
|
{
|
|
size_t len = RBIGNUM_LEN(x);
|
|
BDIGIT *ds = BDIGITS(x);
|
|
#if SIZEOF_BDIGITS < SIZEOF_LONG
|
|
unsigned long u;
|
|
#else
|
|
BDIGIT u;
|
|
#endif
|
|
|
|
while (0 < len && ds[len-1] == 0)
|
|
len--;
|
|
|
|
if (len == 0) return INT2FIX(0);
|
|
|
|
#if SIZEOF_BDIGITS < SIZEOF_LONG
|
|
if (sizeof(long)/SIZEOF_BDIGITS < len)
|
|
goto return_big;
|
|
else {
|
|
int i = (int)len;
|
|
u = 0;
|
|
while (i--) {
|
|
u = (unsigned long)(BIGUP(u) + ds[i]);
|
|
}
|
|
}
|
|
#else /* SIZEOF_BDIGITS >= SIZEOF_LONG */
|
|
if (1 < len)
|
|
goto return_big;
|
|
else
|
|
u = ds[0];
|
|
#endif
|
|
|
|
if (RBIGNUM_POSITIVE_P(x)) {
|
|
if (POSFIXABLE(u)) return LONG2FIX((long)u);
|
|
}
|
|
else {
|
|
if (u <= -FIXNUM_MIN) return LONG2FIX(-(long)u);
|
|
}
|
|
|
|
return_big:
|
|
rb_big_resize(x, len);
|
|
return x;
|
|
}
|
|
|
|
static VALUE
|
|
bignorm(VALUE x)
|
|
{
|
|
if (RB_TYPE_P(x, T_BIGNUM)) {
|
|
x = bigfixize(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);
|
|
BDIGITS_ZERO(zds, 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);
|
|
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));
|
|
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(bigsq(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 VALUE
|
|
big_shift3(VALUE x, int lshift_p, size_t shift_numdigits, int shift_numbits)
|
|
{
|
|
BDIGIT *xds, *zds;
|
|
long s1;
|
|
int s2;
|
|
VALUE z;
|
|
long xn;
|
|
|
|
if (lshift_p) {
|
|
if (LONG_MAX < shift_numdigits) {
|
|
rb_raise(rb_eArgError, "too big number");
|
|
}
|
|
s1 = shift_numdigits;
|
|
s2 = shift_numbits;
|
|
xn = RBIGNUM_LEN(x);
|
|
z = bignew(xn+s1+1, RBIGNUM_SIGN(x));
|
|
zds = BDIGITS(z);
|
|
BDIGITS_ZERO(zds, s1);
|
|
xds = BDIGITS(x);
|
|
zds[xn+s1] = bary_small_lshift(zds+s1, xds, xn, s2);
|
|
}
|
|
else {
|
|
long zn;
|
|
BDIGIT hibitsx;
|
|
if (LONG_MAX < shift_numdigits || (size_t)RBIGNUM_LEN(x) <= shift_numdigits) {
|
|
if (RBIGNUM_POSITIVE_P(x) ||
|
|
bary_zero_p(BDIGITS(x), RBIGNUM_LEN(x)))
|
|
return INT2FIX(0);
|
|
else
|
|
return INT2FIX(-1);
|
|
}
|
|
s1 = shift_numdigits;
|
|
s2 = shift_numbits;
|
|
hibitsx = abs2twocomp(&x, &xn);
|
|
xds = BDIGITS(x);
|
|
if (xn <= s1) {
|
|
return hibitsx ? INT2FIX(-1) : INT2FIX(0);
|
|
}
|
|
zn = xn - s1;
|
|
z = bignew(zn, 0);
|
|
zds = BDIGITS(z);
|
|
bary_small_rshift(zds, xds+s1, zn, s2, hibitsx != 0);
|
|
twocomp2abs_bang(z, hibitsx != 0);
|
|
}
|
|
RB_GC_GUARD(x);
|
|
return z;
|
|
}
|
|
|
|
static VALUE
|
|
big_shift2(VALUE x, int lshift_p, VALUE y)
|
|
{
|
|
int sign;
|
|
size_t lens[2];
|
|
size_t shift_numdigits;
|
|
int shift_numbits;
|
|
|
|
assert(POW2_P(CHAR_BIT));
|
|
assert(POW2_P(BITSPERDIG));
|
|
|
|
if (BIGZEROP(x))
|
|
return INT2FIX(0);
|
|
sign = rb_integer_pack(y, lens, numberof(lens), sizeof(size_t), 0,
|
|
INTEGER_PACK_LSWORD_FIRST|INTEGER_PACK_NATIVE_BYTE_ORDER);
|
|
if (sign < 0) {
|
|
lshift_p = !lshift_p;
|
|
sign = -sign;
|
|
}
|
|
if (lshift_p) {
|
|
if (1 < sign || CHAR_BIT <= lens[1])
|
|
rb_raise(rb_eRangeError, "shift width too big");
|
|
}
|
|
else {
|
|
if (1 < sign || CHAR_BIT <= lens[1])
|
|
return RBIGNUM_POSITIVE_P(x) ? INT2FIX(0) : INT2FIX(-1);
|
|
}
|
|
shift_numbits = (int)(lens[0] & (BITSPERDIG-1));
|
|
shift_numdigits = (lens[0] >> bitsize(BITSPERDIG-1)) |
|
|
(lens[1] << (CHAR_BIT*SIZEOF_SIZE_T - bitsize(BITSPERDIG-1)));
|
|
return big_shift3(x, lshift_p, shift_numdigits, shift_numbits);
|
|
}
|
|
|
|
static VALUE
|
|
big_lshift(VALUE x, unsigned long shift)
|
|
{
|
|
long s1 = shift/BITSPERDIG;
|
|
int s2 = (int)(shift%BITSPERDIG);
|
|
return big_shift3(x, 1, s1, s2);
|
|
}
|
|
|
|
static VALUE
|
|
big_rshift(VALUE x, unsigned long shift)
|
|
{
|
|
long s1 = shift/BITSPERDIG;
|
|
int s2 = (int)(shift%BITSPERDIG);
|
|
return big_shift3(x, 0, s1, s2);
|
|
}
|
|
|
|
#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))
|
|
: bigsq(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 = bitsize(n1-1); /* 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 = bigsq(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;
|
|
}
|
|
|
|
static VALUE
|
|
rb_big2str1(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;
|
|
}
|
|
|
|
/* deprecated */
|
|
VALUE
|
|
rb_big2str0(VALUE x, int base, int trim)
|
|
{
|
|
return rb_big2str1(x, base, trim);
|
|
}
|
|
|
|
VALUE
|
|
rb_big2str(VALUE x, int base)
|
|
{
|
|
return rb_big2str1(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_add_one(ds, n)) {
|
|
big_extend_carry(z);
|
|
}
|
|
RBIGNUM_SET_NEGATIVE_SIGN(z);
|
|
}
|
|
else {
|
|
bary_neg(ds, n);
|
|
if (bary_add_one(ds, n))
|
|
return INT2FIX(-1);
|
|
bary_neg(ds, n);
|
|
RBIGNUM_SET_POSITIVE_SIGN(z);
|
|
}
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
static VALUE
|
|
bigsub(VALUE x, VALUE y)
|
|
{
|
|
VALUE z;
|
|
BDIGIT *xds, *yds, *zds;
|
|
long xn, yn, zn;
|
|
|
|
xn = RBIGNUM_LEN(x);
|
|
yn = RBIGNUM_LEN(y);
|
|
zn = xn < yn ? yn : xn;
|
|
|
|
z = bignew(zn, 1);
|
|
|
|
xds = BDIGITS(x);
|
|
yds = BDIGITS(y);
|
|
zds = BDIGITS(z);
|
|
|
|
if (bary_sub(zds, zn, xds, xn, yds, yn)) {
|
|
bary_2comp(zds, zn);
|
|
RBIGNUM_SET_NEGATIVE_SIGN(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 VALUE bigdivrem(VALUE, VALUE, volatile VALUE*, volatile VALUE*);
|
|
|
|
static VALUE
|
|
bigsq(VALUE x)
|
|
{
|
|
long xn, zn;
|
|
VALUE z;
|
|
BDIGIT *xds, *zds;
|
|
|
|
xn = RBIGNUM_LEN(x);
|
|
zn = 2 * xn;
|
|
|
|
z = bignew(zn, 1);
|
|
|
|
xds = BDIGITS(x);
|
|
zds = BDIGITS(z);
|
|
|
|
if (xn < KARATSUBA_MUL_DIGITS)
|
|
bary_sq_fast(zds, zn, xds, xn);
|
|
else
|
|
bary_mul(zds, zn, xds, xn, xds, xn);
|
|
|
|
RB_GC_GUARD(x);
|
|
return z;
|
|
}
|
|
|
|
static VALUE
|
|
bigmul0(VALUE x, VALUE y)
|
|
{
|
|
long xn, yn, zn;
|
|
VALUE z;
|
|
BDIGIT *xds, *yds, *zds;
|
|
|
|
if (x == y)
|
|
return bigsq(x);
|
|
|
|
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);
|
|
|
|
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));
|
|
}
|
|
|
|
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, 1+(unsigned long)(-(n+1)));
|
|
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);
|
|
}
|
|
|
|
/*
|
|
* 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 = bigsq(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);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* big << numeric -> integer
|
|
*
|
|
* Shifts big left _numeric_ positions (right if _numeric_ is negative).
|
|
*/
|
|
|
|
VALUE
|
|
rb_big_lshift(VALUE x, VALUE y)
|
|
{
|
|
int lshift_p;
|
|
size_t shift_numdigits;
|
|
int shift_numbits;
|
|
|
|
for (;;) {
|
|
if (FIXNUM_P(y)) {
|
|
long l = FIX2LONG(y);
|
|
unsigned long shift;
|
|
if (0 <= l) {
|
|
lshift_p = 1;
|
|
shift = l;
|
|
}
|
|
else {
|
|
lshift_p = 0;
|
|
shift = 1+(unsigned long)(-(l+1));
|
|
}
|
|
shift_numbits = (int)(shift & (BITSPERDIG-1));
|
|
shift_numdigits = shift >> bitsize(BITSPERDIG-1);
|
|
return bignorm(big_shift3(x, lshift_p, shift_numdigits, shift_numbits));
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return bignorm(big_shift2(x, 1, y));
|
|
}
|
|
y = rb_to_int(y);
|
|
}
|
|
}
|
|
|
|
|
|
/*
|
|
* call-seq:
|
|
* big >> numeric -> integer
|
|
*
|
|
* Shifts big right _numeric_ positions (left if _numeric_ is negative).
|
|
*/
|
|
|
|
VALUE
|
|
rb_big_rshift(VALUE x, VALUE y)
|
|
{
|
|
int lshift_p;
|
|
size_t shift_numdigits;
|
|
int shift_numbits;
|
|
|
|
for (;;) {
|
|
if (FIXNUM_P(y)) {
|
|
long l = FIX2LONG(y);
|
|
unsigned long shift;
|
|
if (0 <= l) {
|
|
lshift_p = 0;
|
|
shift = l;
|
|
}
|
|
else {
|
|
lshift_p = 1;
|
|
shift = 1+(unsigned long)(-(l+1));
|
|
}
|
|
shift_numbits = (int)(shift & (BITSPERDIG-1));
|
|
shift_numdigits = shift >> bitsize(BITSPERDIG-1);
|
|
return bignorm(big_shift3(x, lshift_p, shift_numdigits, shift_numbits));
|
|
}
|
|
else if (RB_TYPE_P(y, T_BIGNUM)) {
|
|
return bignorm(big_shift2(x, 0, y));
|
|
}
|
|
y = rb_to_int(y);
|
|
}
|
|
}
|
|
|
|
/*
|
|
* 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;
|
|
unsigned long shift;
|
|
long i, s1, s2;
|
|
BDIGIT bit;
|
|
|
|
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;
|
|
bit = (BDIGIT)1 << s2;
|
|
|
|
if (s1 >= RBIGNUM_LEN(x)) goto out_of_range;
|
|
|
|
xds = BDIGITS(x);
|
|
if (RBIGNUM_POSITIVE_P(x))
|
|
return (xds[s1] & bit) ? INT2FIX(1) : INT2FIX(0);
|
|
if (xds[s1] & (bit-1))
|
|
return (xds[s1] & bit) ? INT2FIX(0) : INT2FIX(1);
|
|
for (i = 0; i < s1; i++)
|
|
if (xds[i])
|
|
return (xds[s1] & bit) ? INT2FIX(0) : INT2FIX(1);
|
|
return (xds[s1] & bit) ? INT2FIX(1) : 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);
|
|
}
|
|
|
|
/*
|
|
* call-seq:
|
|
* big.coerce(numeric) -> array
|
|
*
|
|
* Returns an array with both a +numeric+ and a +big+ represented as Bignum
|
|
* objects.
|
|
*
|
|
* This is achieved by converting +numeric+ to a Bignum.
|
|
*
|
|
* A TypeError is raised if the +numeric+ is not a Fixnum or Bignum type.
|
|
*
|
|
* (0x3FFFFFFFFFFFFFFF+1).coerce(42) #=> [42, 4611686018427387904]
|
|
*/
|
|
|
|
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 SIZET2NUM(BIGSIZE(big));
|
|
}
|
|
|
|
/*
|
|
* 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();
|
|
}
|