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ed935aa5be
which has been developed by Takashi Kokubun <takashikkbn@gmail> as YARV-MJIT. Many of its bugs are fixed by wanabe <s.wanabe@gmail.com>. This JIT compiler is designed to be a safe migration path to introduce JIT compiler to MRI. So this commit does not include any bytecode changes or dynamic instruction modifications, which are done in original MJIT. This commit even strips off some aggressive optimizations from YARV-MJIT, and thus it's slower than YARV-MJIT too. But it's still fairly faster than Ruby 2.5 in some benchmarks (attached below). Note that this JIT compiler passes `make test`, `make test-all`, `make test-spec` without JIT, and even with JIT. Not only it's perfectly safe with JIT disabled because it does not replace VM instructions unlike MJIT, but also with JIT enabled it stably runs Ruby applications including Rails applications. I'm expecting this version as just "initial" JIT compiler. I have many optimization ideas which are skipped for initial merging, and you may easily replace this JIT compiler with a faster one by just replacing mjit_compile.c. `mjit_compile` interface is designed for the purpose. common.mk: update dependencies for mjit_compile.c. internal.h: declare `rb_vm_insn_addr2insn` for MJIT. vm.c: exclude some definitions if `-DMJIT_HEADER` is provided to compiler. This avoids to include some functions which take a long time to compile, e.g. vm_exec_core. Some of the purpose is achieved in transform_mjit_header.rb (see `IGNORED_FUNCTIONS`) but others are manually resolved for now. Load mjit_helper.h for MJIT header. mjit_helper.h: New. This is a file used only by JIT-ed code. I'll refactor `mjit_call_cfunc` later. vm_eval.c: add some #ifdef switches to skip compiling some functions like Init_vm_eval. win32/mkexports.rb: export thread/ec functions, which are used by MJIT. include/ruby/defines.h: add MJIT_FUNC_EXPORTED macro alis to clarify that a function is exported only for MJIT. array.c: export a function used by MJIT. bignum.c: ditto. class.c: ditto. compile.c: ditto. error.c: ditto. gc.c: ditto. hash.c: ditto. iseq.c: ditto. numeric.c: ditto. object.c: ditto. proc.c: ditto. re.c: ditto. st.c: ditto. string.c: ditto. thread.c: ditto. variable.c: ditto. vm_backtrace.c: ditto. vm_insnhelper.c: ditto. vm_method.c: ditto. I would like to improve maintainability of function exports, but I believe this way is acceptable as initial merging if we clarify the new exports are for MJIT (so that we can use them as TODO list to fix) and add unit tests to detect unresolved symbols. I'll add unit tests of JIT compilations in succeeding commits. Author: Takashi Kokubun <takashikkbn@gmail.com> Contributor: wanabe <s.wanabe@gmail.com> Part of [Feature #14235] --- * Known issues * Code generated by gcc is faster than clang. The benchmark may be worse in macOS. Following benchmark result is provided by gcc w/ Linux. * Performance is decreased when Google Chrome is running * JIT can work on MinGW, but it doesn't improve performance at least in short running benchmark. * Currently it doesn't perform well with Rails. We'll try to fix this before release. --- * Benchmark reslts Benchmarked with: Intel 4.0GHz i7-4790K with 16GB memory under x86-64 Ubuntu 8 Cores - 2.0.0-p0: Ruby 2.0.0-p0 - r62186: Ruby trunk (early 2.6.0), before MJIT changes - JIT off: On this commit, but without `--jit` option - JIT on: On this commit, and with `--jit` option ** Optcarrot fps Benchmark: https://github.com/mame/optcarrot | |2.0.0-p0 |r62186 |JIT off |JIT on | |:--------|:--------|:--------|:--------|:--------| |fps |37.32 |51.46 |51.31 |58.88 | |vs 2.0.0 |1.00x |1.38x |1.37x |1.58x | ** MJIT benchmarks Benchmark: https://github.com/benchmark-driver/mjit-benchmarks (Original: https://github.com/vnmakarov/ruby/tree/rtl_mjit_branch/MJIT-benchmarks) | |2.0.0-p0 |r62186 |JIT off |JIT on | |:----------|:--------|:--------|:--------|:--------| |aread |1.00 |1.09 |1.07 |2.19 | |aref |1.00 |1.13 |1.11 |2.22 | |aset |1.00 |1.50 |1.45 |2.64 | |awrite |1.00 |1.17 |1.13 |2.20 | |call |1.00 |1.29 |1.26 |2.02 | |const2 |1.00 |1.10 |1.10 |2.19 | |const |1.00 |1.11 |1.10 |2.19 | |fannk |1.00 |1.04 |1.02 |1.00 | |fib |1.00 |1.32 |1.31 |1.84 | |ivread |1.00 |1.13 |1.12 |2.43 | |ivwrite |1.00 |1.23 |1.21 |2.40 | |mandelbrot |1.00 |1.13 |1.16 |1.28 | |meteor |1.00 |2.97 |2.92 |3.17 | |nbody |1.00 |1.17 |1.15 |1.49 | |nest-ntimes|1.00 |1.22 |1.20 |1.39 | |nest-while |1.00 |1.10 |1.10 |1.37 | |norm |1.00 |1.18 |1.16 |1.24 | |nsvb |1.00 |1.16 |1.16 |1.17 | |red-black |1.00 |1.02 |0.99 |1.12 | |sieve |1.00 |1.30 |1.28 |1.62 | |trees |1.00 |1.14 |1.13 |1.19 | |while |1.00 |1.12 |1.11 |2.41 | ** Discourse's script/bench.rb Benchmark: https://github.com/discourse/discourse/blob/v1.8.7/script/bench.rb NOTE: Rails performance was somehow a little degraded with JIT for now. We should fix this. (At least I know opt_aref is performing badly in JIT and I have an idea to fix it. Please wait for the fix.) *** JIT off Your Results: (note for timings- percentile is first, duration is second in millisecs) categories_admin: 50: 17 75: 18 90: 22 99: 29 home_admin: 50: 21 75: 21 90: 27 99: 40 topic_admin: 50: 17 75: 18 90: 22 99: 32 categories: 50: 35 75: 41 90: 43 99: 77 home: 50: 39 75: 46 90: 49 99: 95 topic: 50: 46 75: 52 90: 56 99: 101 *** JIT on Your Results: (note for timings- percentile is first, duration is second in millisecs) categories_admin: 50: 19 75: 21 90: 25 99: 33 home_admin: 50: 24 75: 26 90: 30 99: 35 topic_admin: 50: 19 75: 20 90: 25 99: 30 categories: 50: 40 75: 44 90: 48 99: 76 home: 50: 42 75: 48 90: 51 99: 89 topic: 50: 49 75: 55 90: 58 99: 99 git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@62197 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
7129 lines
181 KiB
C
7129 lines
181 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 "internal.h"
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#include "ruby/thread.h"
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#include "ruby/util.h"
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#include "id.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 "ruby_assert.h"
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#if defined(HAVE_LIBGMP) && defined(HAVE_GMP_H)
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#define USE_GMP
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#include <gmp.h>
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#endif
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#define RB_BIGNUM_TYPE_P(x) RB_TYPE_P((x), T_BIGNUM)
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#ifndef RUBY_INTEGER_UNIFICATION
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VALUE rb_cBignum;
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#endif
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const char ruby_digitmap[] = "0123456789abcdefghijklmnopqrstuvwxyz";
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#ifndef SIZEOF_BDIGIT_DBL
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# if 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_BDIGIT <= sizeof(BDIGIT));
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STATIC_ASSERT(sizeof_bdigit_and_dbl, SIZEOF_BDIGIT*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, BIGNUM_EMBED_LEN_MAX <= (BIGNUM_EMBED_LEN_MASK >> BIGNUM_EMBED_LEN_SHIFT));
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#if SIZEOF_BDIGIT < SIZEOF_LONG
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STATIC_ASSERT(sizeof_long_and_sizeof_bdigit, SIZEOF_LONG % SIZEOF_BDIGIT == 0);
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#else
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STATIC_ASSERT(sizeof_long_and_sizeof_bdigit, SIZEOF_BDIGIT % 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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/* (!LSHIFTABLE(d, 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) (BIGNUM_DIGITS(x))
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#define BITSPERDIG (SIZEOF_BDIGIT*CHAR_BIT)
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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_BDIGIT == 2
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# define swap_bdigit(x) swap16(x)
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#elif SIZEOF_BDIGIT == 4
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# define swap_bdigit(x) swap32(x)
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#elif SIZEOF_BDIGIT == 8
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# define swap_bdigit(x) swap64(x)
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#endif
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#define BIGZEROP(x) (BIGNUM_LEN(x) == 0 || \
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(BDIGITS(x)[0] == 0 && \
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(BIGNUM_LEN(x) == 1 || bigzero_p(x))))
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#define BIGSIZE(x) (BIGNUM_LEN(x) == 0 ? (size_t)0 : \
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BDIGITS(x)[BIGNUM_LEN(x)-1] ? \
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(size_t)(BIGNUM_LEN(x)*SIZEOF_BDIGIT - nlz(BDIGITS(x)[BIGNUM_LEN(x)-1])/CHAR_BIT) : \
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rb_absint_size(x, NULL))
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#define BIGDIVREM_EXTRA_WORDS 1
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#define bdigit_roomof(n) roomof(n, SIZEOF_BDIGIT)
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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_SHORT_MUL(z, x, y) bary_short_mul(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 BIGNUM_SET_NEGATIVE_SIGN(b) BIGNUM_SET_SIGN(b, 0)
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#define BIGNUM_SET_POSITIVE_SIGN(b) BIGNUM_SET_SIGN(b, 1)
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#define bignew(len,sign) bignew_1(rb_cInteger,(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 BARY_TRUNC(ds, n) do { \
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while (0 < (n) && (ds)[(n)-1] == 0) \
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(n)--; \
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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 GMP_MUL_DIGITS 20
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#define KARATSUBA_MUL_DIGITS 70
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#define TOOM3_MUL_DIGITS 150
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#define GMP_DIV_DIGITS 20
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#define GMP_BIG2STR_DIGITS 20
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#define GMP_STR2BIG_DIGITS 20
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#ifdef USE_GMP
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# define NAIVE_MUL_DIGITS GMP_MUL_DIGITS
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#else
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# define NAIVE_MUL_DIGITS KARATSUBA_MUL_DIGITS
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#endif
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typedef void (mulfunc_t)(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn);
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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, const BDIGIT *xds, size_t xn, BDIGIT y);
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static void bary_divmod(BDIGIT *qds, size_t qn, BDIGIT *rds, size_t rn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn);
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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, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn);
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static VALUE bignew_1(VALUE klass, size_t 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 inline VALUE power_cache_get_power(int base, int power_level, size_t *numdigits_ret);
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#if SIZEOF_BDIGIT <= SIZEOF_INT
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static int nlz(BDIGIT x) { return nlz_int((unsigned int)x) - (SIZEOF_INT-SIZEOF_BDIGIT) * CHAR_BIT; }
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#elif SIZEOF_BDIGIT <= SIZEOF_LONG
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static int nlz(BDIGIT x) { return nlz_long((unsigned long)x) - (SIZEOF_LONG-SIZEOF_BDIGIT) * CHAR_BIT; }
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#elif SIZEOF_BDIGIT <= SIZEOF_LONG_LONG
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static int nlz(BDIGIT x) { return nlz_long_long((unsigned LONG_LONG)x) - (SIZEOF_LONG_LONG-SIZEOF_BDIGIT) * CHAR_BIT; }
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#elif SIZEOF_BDIGIT <= SIZEOF_INT128_T
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static int nlz(BDIGIT x) { return nlz_int128((uint128_t)x) - (SIZEOF_INT128_T-SIZEOF_BDIGIT) * CHAR_BIT; }
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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 script, 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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#if SIZEOF_BDIGIT_DBL == 2
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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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#elif SIZEOF_BDIGIT_DBL == 4
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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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#elif SIZEOF_BDIGIT_DBL == 8 && defined 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),
|
|
U64(0x40000000,0x00000000), U64(0x6765c793,0xfa10079d),
|
|
U64(0x41c21cb8,0xe1000000), U64(0x36427987,0x50226111),
|
|
U64(0x80000000,0x00000000), U64(0xa8b8b452,0x291fe821),
|
|
U64(0x8ac72304,0x89e80000), U64(0x4d28cb56,0xc33fa539),
|
|
U64(0x1eca170c,0x00000000), U64(0x780c7372,0x621bd74d),
|
|
U64(0x1e39a505,0x7d810000), U64(0x5b27ac99,0x3df97701),
|
|
U64(0x10000000,0x00000000), U64(0x27b95e99,0x7e21d9f1),
|
|
U64(0x5da0e1e5,0x3c5c8000), U64(0xd2ae3299,0xc1c4aedb),
|
|
U64(0x16bcc41e,0x90000000), U64(0x2d04b7fd,0xd9c0ef49),
|
|
U64(0x5658597b,0xcaa24000), U64(0xa0e20737,0x37609371),
|
|
U64(0x0c29e980,0x00000000), U64(0x14adf4b7,0x320334b9),
|
|
U64(0x226ed364,0x78bfa000), U64(0x383d9170,0xb85ff80b),
|
|
U64(0x5a3c23e3,0x9c000000), U64(0x8e651373,0x88122bcd),
|
|
U64(0xdd41bb36,0xd259e000), U64(0x0aee5720,0xee830681),
|
|
U64(0x10000000,0x00000000), U64(0x172588ad,0x4f5f0981),
|
|
U64(0x211e44f7,0xd02c1000), U64(0x2ee56725,0xf06e5c71),
|
|
U64(0x41c21cb8,0xe1000000),
|
|
};
|
|
#elif SIZEOF_BDIGIT_DBL == 16 && defined HAVE_UINT128_T
|
|
static const int maxpow128_exp[35] = {
|
|
127, 80, 63, 55, 49, 45, 42, 40, 38, 37, 35, 34, 33, 32, 31, 31, 30,
|
|
30, 29, 29, 28, 28, 27, 27, 27, 26, 26, 26, 26, 25, 25, 25, 25, 24,
|
|
24,
|
|
};
|
|
static const uint128_t maxpow128_num[35] = {
|
|
U128(0x80000000,0x00000000,0x00000000,0x00000000),
|
|
U128(0x6f32f1ef,0x8b18a2bc,0x3cea5978,0x9c79d441),
|
|
U128(0x40000000,0x00000000,0x00000000,0x00000000),
|
|
U128(0xd0cf4b50,0xcfe20765,0xfff4b4e3,0xf741cf6d),
|
|
U128(0x6558e2a0,0x921fe069,0x42860000,0x00000000),
|
|
U128(0x5080c7b7,0xd0e31ba7,0x5911a67d,0xdd3d35e7),
|
|
U128(0x40000000,0x00000000,0x00000000,0x00000000),
|
|
U128(0x6f32f1ef,0x8b18a2bc,0x3cea5978,0x9c79d441),
|
|
U128(0x4b3b4ca8,0x5a86c47a,0x098a2240,0x00000000),
|
|
U128(0xffd1390a,0x0adc2fb8,0xdabbb817,0x4d95c99b),
|
|
U128(0x2c6fdb36,0x4c25e6c0,0x00000000,0x00000000),
|
|
U128(0x384bacd6,0x42c343b4,0xe90c4272,0x13506d29),
|
|
U128(0x31f5db32,0xa34aced6,0x0bf13a0e,0x00000000),
|
|
U128(0x20753ada,0xfd1e839f,0x53686d01,0x3143ee01),
|
|
U128(0x10000000,0x00000000,0x00000000,0x00000000),
|
|
U128(0x68ca11d6,0xb4f6d1d1,0xfaa82667,0x8073c2f1),
|
|
U128(0x223e493b,0xb3bb69ff,0xa4b87d6c,0x40000000),
|
|
U128(0xad62418d,0x14ea8247,0x01c4b488,0x6cc66f59),
|
|
U128(0x2863c1f5,0xcdae42f9,0x54000000,0x00000000),
|
|
U128(0xa63fd833,0xb9386b07,0x36039e82,0xbe651b25),
|
|
U128(0x1d1f7a9c,0xd087a14d,0x28cdf3d5,0x10000000),
|
|
U128(0x651b5095,0xc2ea8fc1,0xb30e2c57,0x77aaf7e1),
|
|
U128(0x0ddef20e,0xff760000,0x00000000,0x00000000),
|
|
U128(0x29c30f10,0x29939b14,0x6664242d,0x97d9f649),
|
|
U128(0x786a435a,0xe9558b0e,0x6aaf6d63,0xa8000000),
|
|
U128(0x0c5afe6f,0xf302bcbf,0x94fd9829,0xd87f5079),
|
|
U128(0x1fce575c,0xe1692706,0x07100000,0x00000000),
|
|
U128(0x4f34497c,0x8597e144,0x36e91802,0x00528229),
|
|
U128(0xbf3a8e1d,0x41ef2170,0x7802130d,0x84000000),
|
|
U128(0x0e7819e1,0x7f1eb0fb,0x6ee4fb89,0x01d9531f),
|
|
U128(0x20000000,0x00000000,0x00000000,0x00000000),
|
|
U128(0x4510460d,0xd9e879c0,0x14a82375,0x2f22b321),
|
|
U128(0x91abce3c,0x4b4117ad,0xe76d35db,0x22000000),
|
|
U128(0x08973ea3,0x55d75bc2,0x2e42c391,0x727d69e1),
|
|
U128(0x10e425c5,0x6daffabc,0x35c10000,0x00000000),
|
|
};
|
|
#endif
|
|
|
|
static BDIGIT_DBL
|
|
maxpow_in_bdigit_dbl(int base, int *exp_ret)
|
|
{
|
|
BDIGIT_DBL maxpow;
|
|
int exponent;
|
|
|
|
assert(2 <= base && base <= 36);
|
|
|
|
{
|
|
#if SIZEOF_BDIGIT_DBL == 2
|
|
maxpow = maxpow16_num[base-2];
|
|
exponent = maxpow16_exp[base-2];
|
|
#elif SIZEOF_BDIGIT_DBL == 4
|
|
maxpow = maxpow32_num[base-2];
|
|
exponent = maxpow32_exp[base-2];
|
|
#elif SIZEOF_BDIGIT_DBL == 8 && defined HAVE_UINT64_T
|
|
maxpow = maxpow64_num[base-2];
|
|
exponent = maxpow64_exp[base-2];
|
|
#elif SIZEOF_BDIGIT_DBL == 16 && defined HAVE_UINT128_T
|
|
maxpow = maxpow128_num[base-2];
|
|
exponent = maxpow128_exp[base-2];
|
|
#else
|
|
maxpow = base;
|
|
exponent = 1;
|
|
while (maxpow <= BDIGIT_DBL_MAX / base) {
|
|
maxpow *= base;
|
|
exponent++;
|
|
}
|
|
#endif
|
|
}
|
|
|
|
*exp_ret = exponent;
|
|
return maxpow;
|
|
}
|
|
|
|
static inline BDIGIT_DBL
|
|
bary2bdigitdbl(const BDIGIT *ds, size_t n)
|
|
{
|
|
assert(n <= 2);
|
|
|
|
if (n == 2)
|
|
return ds[0] | BIGUP(ds[1]);
|
|
if (n == 1)
|
|
return ds[0];
|
|
return 0;
|
|
}
|
|
|
|
static inline void
|
|
bdigitdbl2bary(BDIGIT *ds, size_t n, BDIGIT_DBL num)
|
|
{
|
|
assert(n == 2);
|
|
|
|
ds[0] = BIGLO(num);
|
|
ds[1] = (BDIGIT)BIGDN(num);
|
|
}
|
|
|
|
static int
|
|
bary_cmp(const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
BARY_TRUNC(xds, xn);
|
|
BARY_TRUNC(yds, yn);
|
|
|
|
if (xn < yn)
|
|
return -1;
|
|
if (xn > yn)
|
|
return 1;
|
|
|
|
while (xn-- && xds[xn] == yds[xn])
|
|
;
|
|
if (xn == (size_t)-1)
|
|
return 0;
|
|
return xds[xn] < yds[xn] ? -1 : 1;
|
|
}
|
|
|
|
static BDIGIT
|
|
bary_small_lshift(BDIGIT *zds, const BDIGIT *xds, size_t n, int shift)
|
|
{
|
|
size_t i;
|
|
BDIGIT_DBL num = 0;
|
|
assert(0 <= shift && shift < BITSPERDIG);
|
|
|
|
for (i=0; i<n; i++) {
|
|
num = num | (BDIGIT_DBL)*xds++ << shift;
|
|
*zds++ = BIGLO(num);
|
|
num = BIGDN(num);
|
|
}
|
|
return BIGLO(num);
|
|
}
|
|
|
|
static void
|
|
bary_small_rshift(BDIGIT *zds, const BDIGIT *xds, size_t n, int shift, BDIGIT higher_bdigit)
|
|
{
|
|
BDIGIT_DBL num = 0;
|
|
|
|
assert(0 <= shift && shift < BITSPERDIG);
|
|
|
|
num = BIGUP(higher_bdigit);
|
|
while (n--) {
|
|
BDIGIT x = xds[n];
|
|
num = (num | x) >> shift;
|
|
zds[n] = BIGLO(num);
|
|
num = BIGUP(x);
|
|
}
|
|
}
|
|
|
|
static int
|
|
bary_zero_p(const BDIGIT *xds, size_t xn)
|
|
{
|
|
if (xn == 0)
|
|
return 1;
|
|
do {
|
|
if (xds[--xn]) return 0;
|
|
} while (xn);
|
|
return 1;
|
|
}
|
|
|
|
static void
|
|
bary_neg(BDIGIT *ds, size_t n)
|
|
{
|
|
while (n--)
|
|
ds[n] = BIGLO(~ds[n]);
|
|
}
|
|
|
|
static int
|
|
bary_2comp(BDIGIT *ds, size_t n)
|
|
{
|
|
size_t i;
|
|
i = 0;
|
|
for (i = 0; i < n; i++) {
|
|
if (ds[i] != 0) {
|
|
goto non_zero;
|
|
}
|
|
}
|
|
return 1;
|
|
|
|
non_zero:
|
|
ds[i] = BIGLO(~ds[i] + 1);
|
|
i++;
|
|
for (; i < n; i++) {
|
|
ds[i] = BIGLO(~ds[i]);
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
static void
|
|
bary_swap(BDIGIT *ds, size_t num_bdigits)
|
|
{
|
|
BDIGIT *p1 = ds;
|
|
BDIGIT *p2 = ds + num_bdigits - 1;
|
|
for (; p1 < p2; p1++, p2--) {
|
|
BDIGIT tmp = *p1;
|
|
*p1 = *p2;
|
|
*p2 = tmp;
|
|
}
|
|
}
|
|
|
|
#define INTEGER_PACK_WORDORDER_MASK \
|
|
(INTEGER_PACK_MSWORD_FIRST | \
|
|
INTEGER_PACK_LSWORD_FIRST)
|
|
#define INTEGER_PACK_BYTEORDER_MASK \
|
|
(INTEGER_PACK_MSBYTE_FIRST | \
|
|
INTEGER_PACK_LSBYTE_FIRST | \
|
|
INTEGER_PACK_NATIVE_BYTE_ORDER)
|
|
|
|
static void
|
|
validate_integer_pack_format(size_t numwords, size_t wordsize, size_t nails, int flags, int supported_flags)
|
|
{
|
|
int wordorder_bits = flags & INTEGER_PACK_WORDORDER_MASK;
|
|
int byteorder_bits = flags & INTEGER_PACK_BYTEORDER_MASK;
|
|
|
|
if (flags & ~supported_flags) {
|
|
rb_raise(rb_eArgError, "unsupported flags specified");
|
|
}
|
|
if (wordorder_bits == 0) {
|
|
if (1 < numwords)
|
|
rb_raise(rb_eArgError, "word order not specified");
|
|
}
|
|
else if (wordorder_bits != INTEGER_PACK_MSWORD_FIRST &&
|
|
wordorder_bits != INTEGER_PACK_LSWORD_FIRST)
|
|
rb_raise(rb_eArgError, "unexpected word order");
|
|
if (byteorder_bits == 0) {
|
|
rb_raise(rb_eArgError, "byte order not specified");
|
|
}
|
|
else if (byteorder_bits != INTEGER_PACK_MSBYTE_FIRST &&
|
|
byteorder_bits != INTEGER_PACK_LSBYTE_FIRST &&
|
|
byteorder_bits != INTEGER_PACK_NATIVE_BYTE_ORDER)
|
|
rb_raise(rb_eArgError, "unexpected byte order");
|
|
if (wordsize == 0)
|
|
rb_raise(rb_eArgError, "invalid wordsize: %"PRI_SIZE_PREFIX"u", wordsize);
|
|
if (SSIZE_MAX < wordsize)
|
|
rb_raise(rb_eArgError, "too big wordsize: %"PRI_SIZE_PREFIX"u", wordsize);
|
|
if (wordsize <= nails / CHAR_BIT)
|
|
rb_raise(rb_eArgError, "too big nails: %"PRI_SIZE_PREFIX"u", nails);
|
|
if (SIZE_MAX / wordsize < numwords)
|
|
rb_raise(rb_eArgError, "too big numwords * wordsize: %"PRI_SIZE_PREFIX"u * %"PRI_SIZE_PREFIX"u", numwords, wordsize);
|
|
}
|
|
|
|
static void
|
|
integer_pack_loop_setup(
|
|
size_t numwords, size_t wordsize, size_t nails, int flags,
|
|
size_t *word_num_fullbytes_ret,
|
|
int *word_num_partialbits_ret,
|
|
size_t *word_start_ret,
|
|
ssize_t *word_step_ret,
|
|
size_t *word_last_ret,
|
|
size_t *byte_start_ret,
|
|
int *byte_step_ret)
|
|
{
|
|
int wordorder_bits = flags & INTEGER_PACK_WORDORDER_MASK;
|
|
int byteorder_bits = flags & INTEGER_PACK_BYTEORDER_MASK;
|
|
size_t word_num_fullbytes;
|
|
int word_num_partialbits;
|
|
size_t word_start;
|
|
ssize_t word_step;
|
|
size_t word_last;
|
|
size_t byte_start;
|
|
int byte_step;
|
|
|
|
word_num_partialbits = CHAR_BIT - (int)(nails % CHAR_BIT);
|
|
if (word_num_partialbits == CHAR_BIT)
|
|
word_num_partialbits = 0;
|
|
word_num_fullbytes = wordsize - (nails / CHAR_BIT);
|
|
if (word_num_partialbits != 0) {
|
|
word_num_fullbytes--;
|
|
}
|
|
|
|
if (wordorder_bits == INTEGER_PACK_MSWORD_FIRST) {
|
|
word_start = wordsize*(numwords-1);
|
|
word_step = -(ssize_t)wordsize;
|
|
word_last = 0;
|
|
}
|
|
else {
|
|
word_start = 0;
|
|
word_step = wordsize;
|
|
word_last = wordsize*(numwords-1);
|
|
}
|
|
|
|
if (byteorder_bits == INTEGER_PACK_NATIVE_BYTE_ORDER) {
|
|
#ifdef WORDS_BIGENDIAN
|
|
byteorder_bits = INTEGER_PACK_MSBYTE_FIRST;
|
|
#else
|
|
byteorder_bits = INTEGER_PACK_LSBYTE_FIRST;
|
|
#endif
|
|
}
|
|
if (byteorder_bits == INTEGER_PACK_MSBYTE_FIRST) {
|
|
byte_start = wordsize-1;
|
|
byte_step = -1;
|
|
}
|
|
else {
|
|
byte_start = 0;
|
|
byte_step = 1;
|
|
}
|
|
|
|
*word_num_partialbits_ret = word_num_partialbits;
|
|
*word_num_fullbytes_ret = word_num_fullbytes;
|
|
*word_start_ret = word_start;
|
|
*word_step_ret = word_step;
|
|
*word_last_ret = word_last;
|
|
*byte_start_ret = byte_start;
|
|
*byte_step_ret = byte_step;
|
|
}
|
|
|
|
static inline void
|
|
integer_pack_fill_dd(BDIGIT **dpp, BDIGIT **dep, BDIGIT_DBL *ddp, int *numbits_in_dd_p)
|
|
{
|
|
if (*dpp < *dep && BITSPERDIG <= (int)sizeof(*ddp) * CHAR_BIT - *numbits_in_dd_p) {
|
|
*ddp |= (BDIGIT_DBL)(*(*dpp)++) << *numbits_in_dd_p;
|
|
*numbits_in_dd_p += BITSPERDIG;
|
|
}
|
|
else if (*dpp == *dep) {
|
|
/* higher bits are infinity zeros */
|
|
*numbits_in_dd_p = (int)sizeof(*ddp) * CHAR_BIT;
|
|
}
|
|
}
|
|
|
|
static inline BDIGIT_DBL
|
|
integer_pack_take_lowbits(int n, BDIGIT_DBL *ddp, int *numbits_in_dd_p)
|
|
{
|
|
BDIGIT_DBL ret;
|
|
ret = (*ddp) & (((BDIGIT_DBL)1 << n) - 1);
|
|
*ddp >>= n;
|
|
*numbits_in_dd_p -= n;
|
|
return ret;
|
|
}
|
|
|
|
#if !defined(WORDS_BIGENDIAN)
|
|
static int
|
|
bytes_2comp(unsigned char *buf, size_t len)
|
|
{
|
|
size_t i;
|
|
for (i = 0; i < len; i++)
|
|
buf[i] = ~buf[i];
|
|
for (i = 0; i < len; i++) {
|
|
buf[i]++;
|
|
if (buf[i] != 0)
|
|
return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
#endif
|
|
|
|
static int
|
|
bary_pack(int sign, BDIGIT *ds, size_t num_bdigits, void *words, size_t numwords, size_t wordsize, size_t nails, int flags)
|
|
{
|
|
BDIGIT *dp, *de;
|
|
unsigned char *buf, *bufend;
|
|
|
|
dp = ds;
|
|
de = ds + num_bdigits;
|
|
|
|
validate_integer_pack_format(numwords, wordsize, nails, flags,
|
|
INTEGER_PACK_MSWORD_FIRST|
|
|
INTEGER_PACK_LSWORD_FIRST|
|
|
INTEGER_PACK_MSBYTE_FIRST|
|
|
INTEGER_PACK_LSBYTE_FIRST|
|
|
INTEGER_PACK_NATIVE_BYTE_ORDER|
|
|
INTEGER_PACK_2COMP|
|
|
INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION);
|
|
|
|
while (dp < de && de[-1] == 0)
|
|
de--;
|
|
if (dp == de) {
|
|
sign = 0;
|
|
}
|
|
|
|
if (!(flags & INTEGER_PACK_FORCE_GENERIC_IMPLEMENTATION)) {
|
|
if (sign == 0) {
|
|
MEMZERO(words, unsigned char, numwords * wordsize);
|
|
return 0;
|
|
}
|
|
if (nails == 0 && numwords == 1) {
|
|
int need_swap = wordsize != 1 &&
|
|
(flags & INTEGER_PACK_BYTEORDER_MASK) != INTEGER_PACK_NATIVE_BYTE_ORDER &&
|
|
((flags & INTEGER_PACK_MSBYTE_FIRST) ? !HOST_BIGENDIAN_P : HOST_BIGENDIAN_P);
|
|
if (0 < sign || !(flags & INTEGER_PACK_2COMP)) {
|
|
BDIGIT d;
|
|
if (wordsize == 1) {
|
|
*((unsigned char *)words) = (unsigned char)(d = dp[0]);
|
|
return ((1 < de - dp || CLEAR_LOWBITS(d, 8) != 0) ? 2 : 1) * sign;
|
|
}
|
|
#if defined(HAVE_UINT16_T) && 2 <= SIZEOF_BDIGIT
|
|
if (wordsize == 2 && (uintptr_t)words % RUBY_ALIGNOF(uint16_t) == 0) {
|
|
uint16_t u = (uint16_t)(d = dp[0]);
|
|
if (need_swap) u = swap16(u);
|
|
*((uint16_t *)words) = u;
|
|
return ((1 < de - dp || CLEAR_LOWBITS(d, 16) != 0) ? 2 : 1) * sign;
|
|
}
|
|
#endif
|
|
#if defined(HAVE_UINT32_T) && 4 <= SIZEOF_BDIGIT
|
|
if (wordsize == 4 && (uintptr_t)words % RUBY_ALIGNOF(uint32_t) == 0) {
|
|
uint32_t u = (uint32_t)(d = dp[0]);
|
|
if (need_swap) u = swap32(u);
|
|
*((uint32_t *)words) = u;
|
|
return ((1 < de - dp || CLEAR_LOWBITS(d, 32) != 0) ? 2 : 1) * sign;
|
|
}
|
|
#endif
|
|
#if defined(HAVE_UINT64_T) && 8 <= SIZEOF_BDIGIT
|
|
if (wordsize == 8 && (uintptr_t)words % RUBY_ALIGNOF(uint64_t) == 0) {
|
|
uint64_t u = (uint64_t)(d = dp[0]);
|
|
if (need_swap) u = swap64(u);
|
|
*((uint64_t *)words) = u;
|
|
return ((1 < de - dp || CLEAR_LOWBITS(d, 64) != 0) ? 2 : 1) * sign;
|
|
}
|
|
#endif
|
|
}
|
|
else { /* sign < 0 && (flags & INTEGER_PACK_2COMP) */
|
|
BDIGIT_DBL_SIGNED d;
|
|
if (wordsize == 1) {
|
|
*((unsigned char *)words) = (unsigned char)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
|
|
return (1 < de - dp || FILL_LOWBITS(d, 8) != -1) ? -2 : -1;
|
|
}
|
|
#if defined(HAVE_UINT16_T) && 2 <= SIZEOF_BDIGIT
|
|
if (wordsize == 2 && (uintptr_t)words % RUBY_ALIGNOF(uint16_t) == 0) {
|
|
uint16_t u = (uint16_t)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
|
|
if (need_swap) u = swap16(u);
|
|
*((uint16_t *)words) = u;
|
|
return (wordsize == SIZEOF_BDIGIT && de - dp == 2 && dp[1] == 1 && dp[0] == 0) ? -1 :
|
|
(1 < de - dp || FILL_LOWBITS(d, 16) != -1) ? -2 : -1;
|
|
}
|
|
#endif
|
|
#if defined(HAVE_UINT32_T) && 4 <= SIZEOF_BDIGIT
|
|
if (wordsize == 4 && (uintptr_t)words % RUBY_ALIGNOF(uint32_t) == 0) {
|
|
uint32_t u = (uint32_t)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
|
|
if (need_swap) u = swap32(u);
|
|
*((uint32_t *)words) = u;
|
|
return (wordsize == SIZEOF_BDIGIT && de - dp == 2 && dp[1] == 1 && dp[0] == 0) ? -1 :
|
|
(1 < de - dp || FILL_LOWBITS(d, 32) != -1) ? -2 : -1;
|
|
}
|
|
#endif
|
|
#if defined(HAVE_UINT64_T) && 8 <= SIZEOF_BDIGIT
|
|
if (wordsize == 8 && (uintptr_t)words % RUBY_ALIGNOF(uint64_t) == 0) {
|
|
uint64_t u = (uint64_t)(d = -(BDIGIT_DBL_SIGNED)dp[0]);
|
|
if (need_swap) u = swap64(u);
|
|
*((uint64_t *)words) = u;
|
|
return (wordsize == SIZEOF_BDIGIT && de - dp == 2 && dp[1] == 1 && dp[0] == 0) ? -1 :
|
|
(1 < de - dp || FILL_LOWBITS(d, 64) != -1) ? -2 : -1;
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
#if !defined(WORDS_BIGENDIAN)
|
|
if (nails == 0 && SIZEOF_BDIGIT == sizeof(BDIGIT) &&
|
|
(flags & INTEGER_PACK_WORDORDER_MASK) == INTEGER_PACK_LSWORD_FIRST &&
|
|
(flags & INTEGER_PACK_BYTEORDER_MASK) != INTEGER_PACK_MSBYTE_FIRST) {
|
|
size_t src_size = (de - dp) * SIZEOF_BDIGIT;
|
|
size_t dst_size = numwords * wordsize;
|
|
int overflow = 0;
|
|
while (0 < src_size && ((unsigned char *)ds)[src_size-1] == 0)
|
|
src_size--;
|
|
if (src_size <= dst_size) {
|
|
MEMCPY(words, dp, char, src_size);
|
|
MEMZERO((char*)words + src_size, char, dst_size - src_size);
|
|
}
|
|
else {
|
|
MEMCPY(words, dp, char, dst_size);
|
|
overflow = 1;
|
|
}
|
|
if (sign < 0 && (flags & INTEGER_PACK_2COMP)) {
|
|
int zero_p = bytes_2comp(words, dst_size);
|
|
if (zero_p && overflow) {
|
|
unsigned char *p = (unsigned char *)dp;
|
|
if (dst_size == src_size-1 &&
|
|
p[dst_size] == 1) {
|
|
overflow = 0;
|
|
}
|
|
}
|
|
}
|
|
if (overflow)
|
|
sign *= 2;
|
|
return sign;
|
|
}
|
|
#endif
|
|
if (nails == 0 && SIZEOF_BDIGIT == sizeof(BDIGIT) &&
|
|
wordsize % SIZEOF_BDIGIT == 0 && (uintptr_t)words % RUBY_ALIGNOF(BDIGIT) == 0) {
|
|
size_t bdigits_per_word = wordsize / SIZEOF_BDIGIT;
|
|
size_t src_num_bdigits = de - dp;
|
|
size_t dst_num_bdigits = numwords * bdigits_per_word;
|
|
int overflow = 0;
|
|
int mswordfirst_p = (flags & INTEGER_PACK_MSWORD_FIRST) != 0;
|
|
int msbytefirst_p = (flags & INTEGER_PACK_NATIVE_BYTE_ORDER) ? HOST_BIGENDIAN_P :
|
|
(flags & INTEGER_PACK_MSBYTE_FIRST) != 0;
|
|
if (src_num_bdigits <= dst_num_bdigits) {
|
|
MEMCPY(words, dp, BDIGIT, src_num_bdigits);
|
|
BDIGITS_ZERO((BDIGIT*)words + src_num_bdigits, dst_num_bdigits - src_num_bdigits);
|
|
}
|
|
else {
|
|
MEMCPY(words, dp, BDIGIT, dst_num_bdigits);
|
|
overflow = 1;
|
|
}
|
|
if (sign < 0 && (flags & INTEGER_PACK_2COMP)) {
|
|
int zero_p = bary_2comp(words, dst_num_bdigits);
|
|
if (zero_p && overflow &&
|
|
dst_num_bdigits == src_num_bdigits-1 &&
|
|
dp[dst_num_bdigits] == 1)
|
|
overflow = 0;
|
|
}
|
|
if (msbytefirst_p != HOST_BIGENDIAN_P) {
|
|
size_t i;
|
|
for (i = 0; i < dst_num_bdigits; i++) {
|
|
BDIGIT d = ((BDIGIT*)words)[i];
|
|
((BDIGIT*)words)[i] = swap_bdigit(d);
|
|
}
|
|
}
|
|
if (mswordfirst_p ? !msbytefirst_p : msbytefirst_p) {
|
|
size_t i;
|
|
BDIGIT *p = words;
|
|
for (i = 0; i < numwords; i++) {
|
|
bary_swap(p, bdigits_per_word);
|
|
p += bdigits_per_word;
|
|
}
|
|
}
|
|
if (mswordfirst_p) {
|
|
bary_swap(words, dst_num_bdigits);
|
|
}
|
|
if (overflow)
|
|
sign *= 2;
|
|
return sign;
|
|
}
|
|
}
|
|
|
|
buf = words;
|
|
bufend = buf + numwords * wordsize;
|
|
|
|
if (buf == bufend) {
|
|
/* overflow if non-zero*/
|
|
if (!(flags & INTEGER_PACK_2COMP) || 0 <= sign)
|
|
sign *= 2;
|
|
else {
|
|
if (de - dp == 1 && dp[0] == 1)
|
|
sign = -1; /* val == -1 == -2**(numwords*(wordsize*CHAR_BIT-nails)) */
|
|
else
|
|
sign = -2; /* val < -1 == -2**(numwords*(wordsize*CHAR_BIT-nails)) */
|
|
}
|
|
}
|
|
else if (dp == de) {
|
|
memset(buf, '\0', bufend - buf);
|
|
}
|
|
else if (dp < de && buf < bufend) {
|
|
int word_num_partialbits;
|
|
size_t word_num_fullbytes;
|
|
|
|
ssize_t word_step;
|
|
size_t byte_start;
|
|
int byte_step;
|
|
|
|
size_t word_start, word_last;
|
|
unsigned char *wordp, *last_wordp;
|
|
BDIGIT_DBL dd;
|
|
int numbits_in_dd;
|
|
|
|
integer_pack_loop_setup(numwords, wordsize, nails, flags,
|
|
&word_num_fullbytes, &word_num_partialbits,
|
|
&word_start, &word_step, &word_last, &byte_start, &byte_step);
|
|
|
|
wordp = buf + word_start;
|
|
last_wordp = buf + word_last;
|
|
|
|
dd = 0;
|
|
numbits_in_dd = 0;
|
|
|
|
#define FILL_DD \
|
|
integer_pack_fill_dd(&dp, &de, &dd, &numbits_in_dd)
|
|
#define TAKE_LOWBITS(n) \
|
|
integer_pack_take_lowbits(n, &dd, &numbits_in_dd)
|
|
|
|
while (1) {
|
|
size_t index_in_word = 0;
|
|
unsigned char *bytep = wordp + byte_start;
|
|
while (index_in_word < word_num_fullbytes) {
|
|
FILL_DD;
|
|
*bytep = TAKE_LOWBITS(CHAR_BIT);
|
|
bytep += byte_step;
|
|
index_in_word++;
|
|
}
|
|
if (word_num_partialbits) {
|
|
FILL_DD;
|
|
*bytep = TAKE_LOWBITS(word_num_partialbits);
|
|
bytep += byte_step;
|
|
index_in_word++;
|
|
}
|
|
while (index_in_word < wordsize) {
|
|
*bytep = 0;
|
|
bytep += byte_step;
|
|
index_in_word++;
|
|
}
|
|
|
|
if (wordp == last_wordp)
|
|
break;
|
|
|
|
wordp += word_step;
|
|
}
|
|
FILL_DD;
|
|
/* overflow tests */
|
|
if (dp != de || 1 < dd) {
|
|
/* 2**(numwords*(wordsize*CHAR_BIT-nails)+1) <= abs(val) */
|
|
sign *= 2;
|
|
}
|
|
else if (dd == 1) {
|
|
/* 2**(numwords*(wordsize*CHAR_BIT-nails)) <= abs(val) < 2**(numwords*(wordsize*CHAR_BIT-nails)+1) */
|
|
if (!(flags & INTEGER_PACK_2COMP) || 0 <= sign)
|
|
sign *= 2;
|
|
else { /* overflow_2comp && sign == -1 */
|
|
/* test lower bits are all zero. */
|
|
dp = ds;
|
|
while (dp < de && *dp == 0)
|
|
dp++;
|
|
if (de - dp == 1 && /* only one non-zero word. */
|
|
POW2_P(*dp)) /* *dp contains only one bit set. */
|
|
sign = -1; /* val == -2**(numwords*(wordsize*CHAR_BIT-nails)) */
|
|
else
|
|
sign = -2; /* val < -2**(numwords*(wordsize*CHAR_BIT-nails)) */
|
|
}
|
|
}
|
|
}
|
|
|
|
if ((flags & INTEGER_PACK_2COMP) && (sign < 0 && numwords != 0)) {
|
|
int word_num_partialbits;
|
|
size_t word_num_fullbytes;
|
|
|
|
ssize_t word_step;
|
|
size_t byte_start;
|
|
int byte_step;
|
|
|
|
size_t word_start, word_last;
|
|
unsigned char *wordp, *last_wordp;
|
|
|
|
unsigned int partialbits_mask;
|
|
int carry;
|
|
|
|
integer_pack_loop_setup(numwords, wordsize, nails, flags,
|
|
&word_num_fullbytes, &word_num_partialbits,
|
|
&word_start, &word_step, &word_last, &byte_start, &byte_step);
|
|
|
|
partialbits_mask = (1 << word_num_partialbits) - 1;
|
|
|
|
buf = words;
|
|
wordp = buf + word_start;
|
|
last_wordp = buf + word_last;
|
|
|
|
carry = 1;
|
|
while (1) {
|
|
size_t index_in_word = 0;
|
|
unsigned char *bytep = wordp + byte_start;
|
|
while (index_in_word < word_num_fullbytes) {
|
|
carry += (unsigned char)~*bytep;
|
|
*bytep = (unsigned char)carry;
|
|
carry >>= CHAR_BIT;
|
|
bytep += byte_step;
|
|
index_in_word++;
|
|
}
|
|
if (word_num_partialbits) {
|
|
carry += (*bytep & partialbits_mask) ^ partialbits_mask;
|
|
*bytep = carry & partialbits_mask;
|
|
carry >>= word_num_partialbits;
|
|
bytep += byte_step;
|
|
index_in_word++;
|
|
}
|
|
|
|
if (wordp == last_wordp)
|
|
break;
|
|
|
|
wordp += word_step;
|
|
}
|
|
}
|
|
|
|
return sign;
|
|
#undef FILL_DD
|
|
#undef TAKE_LOWBITS
|
|
}
|
|
|
|
static size_t
|
|
integer_unpack_num_bdigits_small(size_t numwords, size_t wordsize, size_t nails, int *nlp_bits_ret)
|
|
{
|
|
/* nlp_bits stands for number of leading padding bits */
|
|
size_t num_bits = (wordsize * CHAR_BIT - nails) * numwords;
|
|
size_t num_bdigits = (num_bits + BITSPERDIG - 1) / BITSPERDIG;
|
|
*nlp_bits_ret = (int)(num_bdigits * BITSPERDIG - num_bits);
|
|
return num_bdigits;
|
|
}
|
|
|
|
static size_t
|
|
integer_unpack_num_bdigits_generic(size_t numwords, size_t wordsize, size_t nails, int *nlp_bits_ret)
|
|
{
|
|
/* BITSPERDIG = SIZEOF_BDIGIT * CHAR_BIT */
|
|
/* num_bits = (wordsize * CHAR_BIT - nails) * numwords */
|
|
/* num_bdigits = (num_bits + BITSPERDIG - 1) / BITSPERDIG */
|
|
|
|
/* num_bits = CHAR_BIT * (wordsize * numwords) - nails * numwords = CHAR_BIT * num_bytes1 - nails * numwords */
|
|
size_t num_bytes1 = wordsize * numwords;
|
|
|
|
/* q1 * CHAR_BIT + r1 = numwords */
|
|
size_t q1 = numwords / CHAR_BIT;
|
|
size_t r1 = numwords % CHAR_BIT;
|
|
|
|
/* num_bits = CHAR_BIT * num_bytes1 - nails * (q1 * CHAR_BIT + r1) = CHAR_BIT * num_bytes2 - nails * r1 */
|
|
size_t num_bytes2 = num_bytes1 - nails * q1;
|
|
|
|
/* q2 * CHAR_BIT + r2 = nails */
|
|
size_t q2 = nails / CHAR_BIT;
|
|
size_t r2 = nails % CHAR_BIT;
|
|
|
|
/* num_bits = CHAR_BIT * num_bytes2 - (q2 * CHAR_BIT + r2) * r1 = CHAR_BIT * num_bytes3 - r1 * r2 */
|
|
size_t num_bytes3 = num_bytes2 - q2 * r1;
|
|
|
|
/* q3 * BITSPERDIG + r3 = num_bytes3 */
|
|
size_t q3 = num_bytes3 / BITSPERDIG;
|
|
size_t r3 = num_bytes3 % BITSPERDIG;
|
|
|
|
/* num_bits = CHAR_BIT * (q3 * BITSPERDIG + r3) - r1 * r2 = BITSPERDIG * num_digits1 + CHAR_BIT * r3 - r1 * r2 */
|
|
size_t num_digits1 = CHAR_BIT * q3;
|
|
|
|
/*
|
|
* if CHAR_BIT * r3 >= r1 * r2
|
|
* CHAR_BIT * r3 - r1 * r2 = CHAR_BIT * BITSPERDIG - (CHAR_BIT * BITSPERDIG - (CHAR_BIT * r3 - r1 * r2))
|
|
* 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_BDIGIT && 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;
|
|
}
|
|
|
|
#ifdef HAVE_BUILTIN___BUILTIN_ASSUME_ALIGNED
|
|
#define reinterpret_cast(type, value) (type) \
|
|
__builtin_assume_aligned((value), sizeof(*(type)NULL));
|
|
#else
|
|
#define reinterpret_cast(type, value) (type)value
|
|
#endif
|
|
|
|
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_BDIGIT
|
|
if (wordsize == 2 && (uintptr_t)words % RUBY_ALIGNOF(uint16_t) == 0) {
|
|
uint16_t u = *reinterpret_cast(const 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_BDIGIT
|
|
if (wordsize == 4 && (uintptr_t)words % RUBY_ALIGNOF(uint32_t) == 0) {
|
|
uint32_t u = *reinterpret_cast(const 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_BDIGIT
|
|
if (wordsize == 8 && (uintptr_t)words % RUBY_ALIGNOF(uint64_t) == 0) {
|
|
uint64_t u = *reinterpret_cast(const uint64_t *, buf);
|
|
return integer_unpack_single_bdigit(need_swap ? swap64(u) : u, sizeof(uint64_t), flags, dp);
|
|
}
|
|
#endif
|
|
#undef reinterpret_cast
|
|
}
|
|
#if !defined(WORDS_BIGENDIAN)
|
|
if (nails == 0 && SIZEOF_BDIGIT == sizeof(BDIGIT) &&
|
|
(flags & INTEGER_PACK_WORDORDER_MASK) == INTEGER_PACK_LSWORD_FIRST &&
|
|
(flags & INTEGER_PACK_BYTEORDER_MASK) != INTEGER_PACK_MSBYTE_FIRST) {
|
|
size_t src_size = numwords * wordsize;
|
|
size_t dst_size = num_bdigits * SIZEOF_BDIGIT;
|
|
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_BDIGIT == sizeof(BDIGIT) &&
|
|
wordsize % SIZEOF_BDIGIT == 0) {
|
|
size_t bdigits_per_word = wordsize / SIZEOF_BDIGIT;
|
|
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, const BDIGIT *xds, size_t xn, const 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, const BDIGIT *xds, size_t xn, const 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, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, int carry)
|
|
{
|
|
BDIGIT_DBL num;
|
|
size_t i;
|
|
|
|
assert(xn <= zn);
|
|
assert(yn <= zn);
|
|
|
|
if (xn > yn) {
|
|
const 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, const BDIGIT *xds, size_t xn, const 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 zn, BDIGIT x, BDIGIT y)
|
|
{
|
|
BDIGIT_DBL n;
|
|
|
|
assert(2 <= zn);
|
|
|
|
n = (BDIGIT_DBL)x * y;
|
|
bdigitdbl2bary(zds, 2, n);
|
|
BDIGITS_ZERO(zds + 2, zn - 2);
|
|
}
|
|
|
|
static int
|
|
bary_muladd_1xN(BDIGIT *zds, size_t zn, BDIGIT x, const BDIGIT *yds, size_t yn)
|
|
{
|
|
BDIGIT_DBL n;
|
|
BDIGIT_DBL dd;
|
|
size_t j;
|
|
|
|
assert(zn > yn);
|
|
|
|
if (x == 0)
|
|
return 0;
|
|
dd = x;
|
|
n = 0;
|
|
for (j = 0; j < yn; 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 < zn; 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, const 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, const 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 zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
size_t i;
|
|
|
|
assert(xn + yn <= zn);
|
|
|
|
BDIGITS_ZERO(zds, zn);
|
|
for (i = 0; i < xn; i++) {
|
|
bary_muladd_1xN(zds+i, zn-i, xds[i], yds, yn);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_big_mul_normal(VALUE x, VALUE y)
|
|
{
|
|
size_t xn = BIGNUM_LEN(x), yn = BIGNUM_LEN(y), zn = xn + yn;
|
|
VALUE z = bignew(zn, BIGNUM_SIGN(x)==BIGNUM_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, const 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 = BIGNUM_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 zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn, mulfunc_t *mulfunc)
|
|
{
|
|
VALUE work = 0;
|
|
size_t yn0 = yn;
|
|
size_t r, n;
|
|
|
|
assert(xn + yn <= zn);
|
|
assert(xn <= yn);
|
|
assert(!KARATSUBA_BALANCED(xn, yn) || !TOOM3_BALANCED(xn, yn));
|
|
|
|
BDIGITS_ZERO(zds, xn);
|
|
|
|
n = 0;
|
|
while (yn > 0) {
|
|
BDIGIT *tds;
|
|
size_t tn;
|
|
r = xn > yn ? yn : xn;
|
|
tn = xn + r;
|
|
if (2 * (xn + r) <= zn - n) {
|
|
tds = zds + n + xn + r;
|
|
mulfunc(tds, tn, xds, xn, yds + n, r, wds, wn);
|
|
BDIGITS_ZERO(zds + n + xn, r);
|
|
bary_add(zds + n, tn,
|
|
zds + n, tn,
|
|
tds, tn);
|
|
}
|
|
else {
|
|
if (wn < xn) {
|
|
wn = xn;
|
|
wds = ALLOCV_N(BDIGIT, work, wn);
|
|
}
|
|
tds = zds + n;
|
|
MEMCPY(wds, zds + n, BDIGIT, xn);
|
|
mulfunc(tds, tn, xds, xn, yds + n, r, wds+xn, wn-xn);
|
|
bary_add(zds + n, tn,
|
|
zds + n, tn,
|
|
wds, xn);
|
|
}
|
|
yn -= r;
|
|
n += r;
|
|
}
|
|
BDIGITS_ZERO(zds+xn+yn0, zn - (xn+yn0));
|
|
|
|
if (work)
|
|
ALLOCV_END(work);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_mul_balance(VALUE x, VALUE y)
|
|
{
|
|
size_t xn = BIGNUM_LEN(x), yn = BIGNUM_LEN(y), zn = xn + yn;
|
|
VALUE z = bignew(zn, BIGNUM_SIGN(x)==BIGNUM_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 zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn)
|
|
{
|
|
VALUE work = 0;
|
|
|
|
size_t n;
|
|
int sub_p, borrow, carry1, carry2, carry3;
|
|
|
|
int odd_y = 0;
|
|
int odd_xy = 0;
|
|
int sq;
|
|
|
|
const BDIGIT *xds0, *xds1, *yds0, *yds1;
|
|
BDIGIT *zds0, *zds1, *zds2, *zds3;
|
|
|
|
assert(xn + yn <= zn);
|
|
assert(xn <= yn);
|
|
assert(yn < 2 * xn);
|
|
|
|
sq = xds == yds && xn == yn;
|
|
|
|
if (yn & 1) {
|
|
odd_y = 1;
|
|
yn--;
|
|
if (yn < xn) {
|
|
odd_xy = 1;
|
|
xn--;
|
|
}
|
|
}
|
|
|
|
n = yn / 2;
|
|
|
|
assert(n < xn);
|
|
|
|
if (wn < 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.
|
|
*/
|
|
wn = 2*n;
|
|
wds = ALLOCV_N(BDIGIT, work, wn);
|
|
}
|
|
|
|
/* 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, xn-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, wn);
|
|
}
|
|
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, wn-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, wn-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, zn-2*n, xds1, xn-n, yds1, n, wds+n, wn-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 < zn ? n : zn-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, zn-2*n, zds2, zn-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, zn-2*n);
|
|
|
|
if (carry1 + carry3 - borrow < 0)
|
|
bary_sub_one(zds3, zn-3*n);
|
|
else if (carry1 + carry3 - borrow > 0) {
|
|
BDIGIT c = carry1 + carry3 - borrow;
|
|
bary_add(zds3, zn-3*n, zds3, zn-3*n, &c, 1);
|
|
}
|
|
|
|
/*
|
|
if (SIZEOF_BDIGIT * zn <= 16) {
|
|
uint128_t z, x, y;
|
|
ssize_t i;
|
|
for (x = 0, i = xn-1; 0 <= i; i--) { x <<= SIZEOF_BDIGIT*CHAR_BIT; x |= xds[i]; }
|
|
for (y = 0, i = yn-1; 0 <= i; i--) { y <<= SIZEOF_BDIGIT*CHAR_BIT; y |= yds[i]; }
|
|
for (z = 0, i = zn-1; 0 <= i; i--) { z <<= SIZEOF_BDIGIT*CHAR_BIT; z |= zds[i]; }
|
|
assert(z == x * y);
|
|
}
|
|
*/
|
|
|
|
if (odd_xy) {
|
|
bary_muladd_1xN(zds+yn, zn-yn, yds[yn], xds, xn);
|
|
bary_muladd_1xN(zds+xn, zn-xn, xds[xn], yds, yn+1);
|
|
}
|
|
else if (odd_y) {
|
|
bary_muladd_1xN(zds+yn, zn-yn, yds[yn], xds, xn);
|
|
}
|
|
|
|
if (work)
|
|
ALLOCV_END(work);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_mul_karatsuba(VALUE x, VALUE y)
|
|
{
|
|
size_t xn = BIGNUM_LEN(x), yn = BIGNUM_LEN(y), zn = xn + yn;
|
|
VALUE z = bignew(zn, BIGNUM_SIGN(x)==BIGNUM_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, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn)
|
|
{
|
|
size_t n;
|
|
size_t wnc;
|
|
VALUE work = 0;
|
|
|
|
/* "p" stands for "positive". Actually it means "non-negative", though. */
|
|
size_t x0n; const BDIGIT *x0ds;
|
|
size_t x1n; const BDIGIT *x1ds;
|
|
size_t x2n; const BDIGIT *x2ds;
|
|
size_t y0n; const BDIGIT *y0ds;
|
|
size_t y1n; const BDIGIT *y1ds;
|
|
size_t y2n; const 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;
|
|
|
|
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;
|
|
|
|
/* 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, 4*n - z0n);
|
|
MEMCPY(zzds + 4*n, z4ds, BDIGIT, z4n);
|
|
BDIGITS_ZERO(zzds + 4*n + z4n, zzn - (4*n + z4n));
|
|
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);
|
|
|
|
BARY_TRUNC(zzds, 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 = BIGNUM_LEN(x), yn = BIGNUM_LEN(y), zn = xn + yn;
|
|
VALUE z = bignew(zn, BIGNUM_SIGN(x)==BIGNUM_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;
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
static void
|
|
bary_mul_gmp(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
const size_t nails = (sizeof(BDIGIT)-SIZEOF_BDIGIT)*CHAR_BIT;
|
|
mpz_t x, y, z;
|
|
size_t count;
|
|
|
|
assert(xn + yn <= zn);
|
|
|
|
mpz_init(x);
|
|
mpz_init(y);
|
|
mpz_init(z);
|
|
mpz_import(x, xn, -1, sizeof(BDIGIT), 0, nails, xds);
|
|
if (xds == yds && xn == yn) {
|
|
mpz_mul(z, x, x);
|
|
}
|
|
else {
|
|
mpz_import(y, yn, -1, sizeof(BDIGIT), 0, nails, yds);
|
|
mpz_mul(z, x, y);
|
|
}
|
|
mpz_export(zds, &count, -1, sizeof(BDIGIT), 0, nails, z);
|
|
BDIGITS_ZERO(zds+count, zn-count);
|
|
mpz_clear(x);
|
|
mpz_clear(y);
|
|
mpz_clear(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_mul_gmp(VALUE x, VALUE y)
|
|
{
|
|
size_t xn = BIGNUM_LEN(x), yn = BIGNUM_LEN(y), zn = xn + yn;
|
|
VALUE z = bignew(zn, BIGNUM_SIGN(x)==BIGNUM_SIGN(y));
|
|
bary_mul_gmp(BDIGITS(z), zn, BDIGITS(x), xn, BDIGITS(y), yn);
|
|
RB_GC_GUARD(x);
|
|
RB_GC_GUARD(y);
|
|
return z;
|
|
}
|
|
#endif
|
|
|
|
static void
|
|
bary_short_mul(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
assert(xn + yn <= zn);
|
|
|
|
if (xn == 1 && yn == 1) {
|
|
bary_mul_single(zds, zn, xds[0], yds[0]);
|
|
}
|
|
else {
|
|
bary_mul_normal(zds, zn, xds, xn, yds, yn);
|
|
rb_thread_check_ints();
|
|
}
|
|
}
|
|
|
|
/* determine whether a bignum is sparse or not by random sampling */
|
|
static inline int
|
|
bary_sparse_p(const 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 *znp, const BDIGIT **xdsp, size_t *xnp, const BDIGIT **ydsp, size_t *ynp)
|
|
{
|
|
size_t nlsz; /* number of least significant zero BDIGITs */
|
|
|
|
BDIGIT *zds = *zdsp;
|
|
size_t zn = *znp;
|
|
const BDIGIT *xds = *xdsp;
|
|
size_t xn = *xnp;
|
|
const BDIGIT *yds = *ydsp;
|
|
size_t yn = *ynp;
|
|
|
|
assert(xn + yn <= zn);
|
|
|
|
nlsz = 0;
|
|
|
|
while (0 < xn) {
|
|
if (xds[xn-1] == 0) {
|
|
xn--;
|
|
}
|
|
else {
|
|
do {
|
|
if (xds[0] != 0)
|
|
break;
|
|
xds++;
|
|
xn--;
|
|
nlsz++;
|
|
} while (0 < xn);
|
|
break;
|
|
}
|
|
}
|
|
|
|
while (0 < yn) {
|
|
if (yds[yn-1] == 0) {
|
|
yn--;
|
|
}
|
|
else {
|
|
do {
|
|
if (yds[0] != 0)
|
|
break;
|
|
yds++;
|
|
yn--;
|
|
nlsz++;
|
|
} while (0 < yn);
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (nlsz) {
|
|
BDIGITS_ZERO(zds, nlsz);
|
|
zds += nlsz;
|
|
zn -= nlsz;
|
|
}
|
|
|
|
/* make sure that y is longer than x */
|
|
if (xn > yn) {
|
|
const BDIGIT *tds;
|
|
size_t tn;
|
|
tds = xds; xds = yds; yds = tds;
|
|
tn = xn; xn = yn; yn = tn;
|
|
}
|
|
assert(xn <= yn);
|
|
|
|
if (xn <= 1) {
|
|
if (xn == 0) {
|
|
BDIGITS_ZERO(zds, zn);
|
|
return 1;
|
|
}
|
|
|
|
if (xds[0] == 1) {
|
|
MEMCPY(zds, yds, BDIGIT, yn);
|
|
BDIGITS_ZERO(zds+yn, zn-yn);
|
|
return 1;
|
|
}
|
|
if (POW2_P(xds[0])) {
|
|
zds[yn] = bary_small_lshift(zds, yds, yn, bit_length(xds[0])-1);
|
|
BDIGITS_ZERO(zds+yn+1, zn-yn-1);
|
|
return 1;
|
|
}
|
|
if (yn == 1 && yds[0] == 1) {
|
|
zds[0] = xds[0];
|
|
BDIGITS_ZERO(zds+1, zn-1);
|
|
return 1;
|
|
}
|
|
bary_mul_normal(zds, zn, xds, xn, yds, yn);
|
|
return 1;
|
|
}
|
|
|
|
*zdsp = zds;
|
|
*znp = zn;
|
|
*xdsp = xds;
|
|
*xnp = xn;
|
|
*ydsp = yds;
|
|
*ynp = yn;
|
|
|
|
return 0;
|
|
}
|
|
|
|
static void
|
|
bary_mul_karatsuba_branch(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn)
|
|
{
|
|
/* normal multiplication when x is small */
|
|
if (xn < KARATSUBA_MUL_DIGITS) {
|
|
normal:
|
|
if (xds == yds && xn == yn)
|
|
bary_sq_fast(zds, zn, xds, xn);
|
|
else
|
|
bary_short_mul(zds, zn, xds, xn, yds, yn);
|
|
return;
|
|
}
|
|
|
|
/* normal multiplication when x or y is a sparse bignum */
|
|
if (bary_sparse_p(xds, xn)) goto normal;
|
|
if (bary_sparse_p(yds, yn)) {
|
|
bary_short_mul(zds, zn, yds, yn, xds, xn);
|
|
return;
|
|
}
|
|
|
|
/* balance multiplication by slicing y when x is much smaller than y */
|
|
if (!KARATSUBA_BALANCED(xn, yn)) {
|
|
bary_mul_balance_with_mulfunc(zds, zn, xds, xn, yds, yn, wds, wn, bary_mul_karatsuba_start);
|
|
return;
|
|
}
|
|
|
|
/* multiplication by karatsuba method */
|
|
bary_mul_karatsuba(zds, zn, xds, xn, yds, yn, wds, wn);
|
|
}
|
|
|
|
static void
|
|
bary_mul_karatsuba_start(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn)
|
|
{
|
|
if (bary_mul_precheck(&zds, &zn, &xds, &xn, &yds, &yn))
|
|
return;
|
|
|
|
bary_mul_karatsuba_branch(zds, zn, xds, xn, yds, yn, wds, wn);
|
|
}
|
|
|
|
static void
|
|
bary_mul_toom3_branch(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn)
|
|
{
|
|
if (xn < TOOM3_MUL_DIGITS) {
|
|
bary_mul_karatsuba_branch(zds, zn, xds, xn, yds, yn, wds, wn);
|
|
return;
|
|
}
|
|
|
|
if (!TOOM3_BALANCED(xn, yn)) {
|
|
bary_mul_balance_with_mulfunc(zds, zn, xds, xn, yds, yn, wds, wn, bary_mul_toom3_start);
|
|
return;
|
|
}
|
|
|
|
bary_mul_toom3(zds, zn, xds, xn, yds, yn, wds, wn);
|
|
}
|
|
|
|
static void
|
|
bary_mul_toom3_start(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, BDIGIT *wds, size_t wn)
|
|
{
|
|
if (bary_mul_precheck(&zds, &zn, &xds, &xn, &yds, &yn))
|
|
return;
|
|
|
|
bary_mul_toom3_branch(zds, zn, xds, xn, yds, yn, wds, wn);
|
|
}
|
|
|
|
static void
|
|
bary_mul(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
if (xn <= yn) {
|
|
if (xn < NAIVE_MUL_DIGITS) {
|
|
if (xds == yds && xn == yn)
|
|
bary_sq_fast(zds, zn, xds, xn);
|
|
else
|
|
bary_short_mul(zds, zn, xds, xn, yds, yn);
|
|
return;
|
|
}
|
|
}
|
|
else {
|
|
if (yn < NAIVE_MUL_DIGITS) {
|
|
bary_short_mul(zds, zn, yds, yn, xds, xn);
|
|
return;
|
|
}
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
bary_mul_gmp(zds, zn, xds, xn, yds, yn);
|
|
#else
|
|
bary_mul_toom3_start(zds, zn, xds, xn, yds, yn, NULL, 0);
|
|
#endif
|
|
}
|
|
|
|
struct big_div_struct {
|
|
size_t yn, zn;
|
|
BDIGIT *yds, *zds;
|
|
volatile VALUE stop;
|
|
};
|
|
|
|
static void *
|
|
bigdivrem1(void *ptr)
|
|
{
|
|
struct big_div_struct *bds = (struct big_div_struct*)ptr;
|
|
size_t yn = bds->yn;
|
|
size_t zn = bds->zn;
|
|
BDIGIT *yds = bds->yds, *zds = bds->zds;
|
|
BDIGIT_DBL_SIGNED num;
|
|
BDIGIT q;
|
|
|
|
do {
|
|
if (bds->stop) {
|
|
bds->zn = zn;
|
|
return 0;
|
|
}
|
|
if (zds[zn-1] == yds[yn-1]) q = BDIGMAX;
|
|
else q = (BDIGIT)((BIGUP(zds[zn-1]) + zds[zn-2])/yds[yn-1]);
|
|
if (q) {
|
|
num = bigdivrem_mulsub(zds+zn-(yn+1), yn+1,
|
|
q,
|
|
yds, yn);
|
|
while (num) { /* "add back" required */
|
|
q--;
|
|
num = bary_add(zds+zn-(yn+1), yn,
|
|
zds+zn-(yn+1), yn,
|
|
yds, yn);
|
|
num--;
|
|
}
|
|
}
|
|
zn--;
|
|
zds[zn] = q;
|
|
} while (zn > yn);
|
|
return 0;
|
|
}
|
|
|
|
static void
|
|
rb_big_stop(void *ptr)
|
|
{
|
|
struct big_div_struct *bds = ptr;
|
|
bds->stop = Qtrue;
|
|
}
|
|
|
|
static BDIGIT
|
|
bigdivrem_single1(BDIGIT *qds, const BDIGIT *xds, size_t xn, BDIGIT x_higher_bdigit, BDIGIT y)
|
|
{
|
|
assert(0 < xn);
|
|
assert(x_higher_bdigit < y);
|
|
if (POW2_P(y)) {
|
|
BDIGIT r;
|
|
r = xds[0] & (y-1);
|
|
bary_small_rshift(qds, xds, xn, bit_length(y)-1, x_higher_bdigit);
|
|
return r;
|
|
}
|
|
else {
|
|
size_t i;
|
|
BDIGIT_DBL t2;
|
|
t2 = x_higher_bdigit;
|
|
i = xn;
|
|
while (i--) {
|
|
t2 = BIGUP(t2) + xds[i];
|
|
qds[i] = (BDIGIT)(t2 / y);
|
|
t2 %= y;
|
|
}
|
|
return (BDIGIT)t2;
|
|
}
|
|
}
|
|
|
|
static BDIGIT
|
|
bigdivrem_single(BDIGIT *qds, const BDIGIT *xds, size_t xn, BDIGIT y)
|
|
{
|
|
return bigdivrem_single1(qds, xds, xn, 0, y);
|
|
}
|
|
|
|
static void
|
|
bigdivrem_restoring(BDIGIT *zds, size_t zn, BDIGIT *yds, size_t yn)
|
|
{
|
|
struct big_div_struct bds;
|
|
size_t ynzero;
|
|
|
|
assert(yn < zn);
|
|
assert(BDIGIT_MSB(yds[yn-1]));
|
|
assert(zds[zn-1] < yds[yn-1]);
|
|
|
|
for (ynzero = 0; !yds[ynzero]; ynzero++);
|
|
|
|
if (ynzero+1 == yn) {
|
|
BDIGIT r;
|
|
r = bigdivrem_single1(zds+yn, zds+ynzero, zn-yn, zds[zn-1], yds[ynzero]);
|
|
zds[ynzero] = r;
|
|
return;
|
|
}
|
|
|
|
bds.yn = yn - ynzero;
|
|
bds.zds = zds + ynzero;
|
|
bds.yds = yds + ynzero;
|
|
bds.stop = Qfalse;
|
|
bds.zn = zn - ynzero;
|
|
if (bds.zn > 10000 || bds.yn > 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);
|
|
}
|
|
}
|
|
|
|
static void
|
|
bary_divmod_normal(BDIGIT *qds, size_t qn, BDIGIT *rds, size_t rn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
int shift;
|
|
BDIGIT *zds, *yyds;
|
|
size_t zn;
|
|
VALUE tmpyz = 0;
|
|
|
|
assert(yn < xn || (xn == yn && yds[yn - 1] <= xds[xn - 1]));
|
|
assert(qds ? (xn - yn + 1) <= qn : 1);
|
|
assert(rds ? yn <= rn : 1);
|
|
|
|
zn = xn + BIGDIVREM_EXTRA_WORDS;
|
|
|
|
shift = nlz(yds[yn-1]);
|
|
if (shift) {
|
|
int alloc_y = !rds;
|
|
int alloc_z = !qds || qn < zn;
|
|
if (alloc_y && alloc_z) {
|
|
yyds = ALLOCV_N(BDIGIT, tmpyz, yn+zn);
|
|
zds = yyds + yn;
|
|
}
|
|
else {
|
|
yyds = alloc_y ? ALLOCV_N(BDIGIT, tmpyz, yn) : rds;
|
|
zds = alloc_z ? ALLOCV_N(BDIGIT, tmpyz, zn) : qds;
|
|
}
|
|
zds[xn] = bary_small_lshift(zds, xds, xn, shift);
|
|
bary_small_lshift(yyds, yds, yn, shift);
|
|
}
|
|
else {
|
|
if (qds && zn <= qn)
|
|
zds = qds;
|
|
else
|
|
zds = ALLOCV_N(BDIGIT, tmpyz, zn);
|
|
MEMCPY(zds, xds, BDIGIT, xn);
|
|
zds[xn] = 0;
|
|
/* bigdivrem_restoring will not modify y.
|
|
* So use yds directly. */
|
|
yyds = (BDIGIT *)yds;
|
|
}
|
|
|
|
bigdivrem_restoring(zds, zn, yyds, yn);
|
|
|
|
if (rds) {
|
|
if (shift)
|
|
bary_small_rshift(rds, zds, yn, shift, 0);
|
|
else
|
|
MEMCPY(rds, zds, BDIGIT, yn);
|
|
BDIGITS_ZERO(rds+yn, rn-yn);
|
|
}
|
|
|
|
if (qds) {
|
|
size_t j = zn - yn;
|
|
MEMMOVE(qds, zds+yn, BDIGIT, j);
|
|
BDIGITS_ZERO(qds+j, qn-j);
|
|
}
|
|
|
|
if (tmpyz)
|
|
ALLOCV_END(tmpyz);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_divrem_normal(VALUE x, VALUE y)
|
|
{
|
|
size_t xn = BIGNUM_LEN(x), yn = BIGNUM_LEN(y), qn, rn;
|
|
BDIGIT *xds = BDIGITS(x), *yds = BDIGITS(y), *qds, *rds;
|
|
VALUE q, r;
|
|
|
|
BARY_TRUNC(yds, yn);
|
|
if (yn == 0)
|
|
rb_num_zerodiv();
|
|
BARY_TRUNC(xds, xn);
|
|
|
|
if (xn < yn || (xn == yn && xds[xn - 1] < yds[yn - 1]))
|
|
return rb_assoc_new(LONG2FIX(0), x);
|
|
|
|
qn = xn + BIGDIVREM_EXTRA_WORDS;
|
|
q = bignew(qn, BIGNUM_SIGN(x)==BIGNUM_SIGN(y));
|
|
qds = BDIGITS(q);
|
|
|
|
rn = yn;
|
|
r = bignew(rn, BIGNUM_SIGN(x));
|
|
rds = BDIGITS(r);
|
|
|
|
bary_divmod_normal(qds, qn, rds, rn, xds, xn, yds, yn);
|
|
|
|
bigtrunc(q);
|
|
bigtrunc(r);
|
|
|
|
RB_GC_GUARD(x);
|
|
RB_GC_GUARD(y);
|
|
|
|
return rb_assoc_new(q, r);
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
static void
|
|
bary_divmod_gmp(BDIGIT *qds, size_t qn, BDIGIT *rds, size_t rn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
const size_t nails = (sizeof(BDIGIT)-SIZEOF_BDIGIT)*CHAR_BIT;
|
|
mpz_t x, y, q, r;
|
|
size_t count;
|
|
|
|
assert(yn < xn || (xn == yn && yds[yn - 1] <= xds[xn - 1]));
|
|
assert(qds ? (xn - yn + 1) <= qn : 1);
|
|
assert(rds ? yn <= rn : 1);
|
|
assert(qds || rds);
|
|
|
|
mpz_init(x);
|
|
mpz_init(y);
|
|
if (qds) mpz_init(q);
|
|
if (rds) mpz_init(r);
|
|
|
|
mpz_import(x, xn, -1, sizeof(BDIGIT), 0, nails, xds);
|
|
mpz_import(y, yn, -1, sizeof(BDIGIT), 0, nails, yds);
|
|
|
|
if (!rds) {
|
|
mpz_fdiv_q(q, x, y);
|
|
}
|
|
else if (!qds) {
|
|
mpz_fdiv_r(r, x, y);
|
|
}
|
|
else {
|
|
mpz_fdiv_qr(q, r, x, y);
|
|
}
|
|
|
|
mpz_clear(x);
|
|
mpz_clear(y);
|
|
|
|
if (qds) {
|
|
mpz_export(qds, &count, -1, sizeof(BDIGIT), 0, nails, q);
|
|
BDIGITS_ZERO(qds+count, qn-count);
|
|
mpz_clear(q);
|
|
}
|
|
|
|
if (rds) {
|
|
mpz_export(rds, &count, -1, sizeof(BDIGIT), 0, nails, r);
|
|
BDIGITS_ZERO(rds+count, rn-count);
|
|
mpz_clear(r);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_big_divrem_gmp(VALUE x, VALUE y)
|
|
{
|
|
size_t xn = BIGNUM_LEN(x), yn = BIGNUM_LEN(y), qn, rn;
|
|
BDIGIT *xds = BDIGITS(x), *yds = BDIGITS(y), *qds, *rds;
|
|
VALUE q, r;
|
|
|
|
BARY_TRUNC(yds, yn);
|
|
if (yn == 0)
|
|
rb_num_zerodiv();
|
|
BARY_TRUNC(xds, xn);
|
|
|
|
if (xn < yn || (xn == yn && xds[xn - 1] < yds[yn - 1]))
|
|
return rb_assoc_new(LONG2FIX(0), x);
|
|
|
|
qn = xn - yn + 1;
|
|
q = bignew(qn, BIGNUM_SIGN(x)==BIGNUM_SIGN(y));
|
|
qds = BDIGITS(q);
|
|
|
|
rn = yn;
|
|
r = bignew(rn, BIGNUM_SIGN(x));
|
|
rds = BDIGITS(r);
|
|
|
|
bary_divmod_gmp(qds, qn, rds, rn, xds, xn, yds, yn);
|
|
|
|
bigtrunc(q);
|
|
bigtrunc(r);
|
|
|
|
RB_GC_GUARD(x);
|
|
RB_GC_GUARD(y);
|
|
|
|
return rb_assoc_new(q, r);
|
|
}
|
|
#endif
|
|
|
|
static void
|
|
bary_divmod_branch(BDIGIT *qds, size_t qn, BDIGIT *rds, size_t rn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
#ifdef USE_GMP
|
|
if (GMP_DIV_DIGITS < xn) {
|
|
bary_divmod_gmp(qds, qn, rds, rn, xds, xn, yds, yn);
|
|
return;
|
|
}
|
|
#endif
|
|
bary_divmod_normal(qds, qn, rds, rn, xds, xn, yds, yn);
|
|
}
|
|
|
|
static void
|
|
bary_divmod(BDIGIT *qds, size_t qn, BDIGIT *rds, size_t rn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn)
|
|
{
|
|
assert(xn <= qn);
|
|
assert(yn <= rn);
|
|
|
|
BARY_TRUNC(yds, yn);
|
|
if (yn == 0)
|
|
rb_num_zerodiv();
|
|
|
|
BARY_TRUNC(xds, xn);
|
|
if (xn == 0) {
|
|
BDIGITS_ZERO(qds, qn);
|
|
BDIGITS_ZERO(rds, rn);
|
|
return;
|
|
}
|
|
|
|
if (xn < yn || (xn == yn && xds[xn - 1] < yds[yn - 1])) {
|
|
MEMCPY(rds, xds, BDIGIT, xn);
|
|
BDIGITS_ZERO(rds+xn, rn-xn);
|
|
BDIGITS_ZERO(qds, qn);
|
|
}
|
|
else if (yn == 1) {
|
|
MEMCPY(qds, xds, BDIGIT, xn);
|
|
BDIGITS_ZERO(qds+xn, qn-xn);
|
|
rds[0] = bigdivrem_single(qds, xds, xn, yds[0]);
|
|
BDIGITS_ZERO(rds+1, rn-1);
|
|
}
|
|
else if (xn == 2 && yn == 2) {
|
|
BDIGIT_DBL x = bary2bdigitdbl(xds, 2);
|
|
BDIGIT_DBL y = bary2bdigitdbl(yds, 2);
|
|
BDIGIT_DBL q = x / y;
|
|
BDIGIT_DBL r = x % y;
|
|
qds[0] = BIGLO(q);
|
|
qds[1] = BIGLO(BIGDN(q));
|
|
BDIGITS_ZERO(qds+2, qn-2);
|
|
rds[0] = BIGLO(r);
|
|
rds[1] = BIGLO(BIGDN(r));
|
|
BDIGITS_ZERO(rds+2, rn-2);
|
|
}
|
|
else {
|
|
bary_divmod_branch(qds, qn, rds, rn, xds, xn, yds, yn);
|
|
}
|
|
}
|
|
|
|
|
|
#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", BIGNUM_SIGN(x) ? '+' : '-');
|
|
for (i = BIGNUM_LEN(x); i--; ) {
|
|
printf("_%0*"PRIxBDIGIT, SIZEOF_BDIGIT*2, BDIGITS(x)[i]);
|
|
}
|
|
printf(", len=%"PRIuSIZE, BIGNUM_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), BIGNUM_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_BIGNUM_TYPE_P(val)) {
|
|
if (BIGZEROP(val)) return 0;
|
|
if (BIGNUM_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 BIGNUM_SET_LEN(b,l) \
|
|
((RBASIC(b)->flags & BIGNUM_EMBED_FLAG) ? \
|
|
(void)(RBASIC(b)->flags = \
|
|
(RBASIC(b)->flags & ~BIGNUM_EMBED_LEN_MASK) | \
|
|
((l) << BIGNUM_EMBED_LEN_SHIFT)) : \
|
|
(void)(RBIGNUM(b)->as.heap.len = (l)))
|
|
|
|
static void
|
|
rb_big_realloc(VALUE big, size_t len)
|
|
{
|
|
BDIGIT *ds;
|
|
if (RBASIC(big)->flags & BIGNUM_EMBED_FLAG) {
|
|
if (BIGNUM_EMBED_LEN_MAX < len) {
|
|
ds = ALLOC_N(BDIGIT, len);
|
|
MEMCPY(ds, RBIGNUM(big)->as.ary, BDIGIT, BIGNUM_EMBED_LEN_MAX);
|
|
RBIGNUM(big)->as.heap.len = BIGNUM_LEN(big);
|
|
RBIGNUM(big)->as.heap.digits = ds;
|
|
RBASIC(big)->flags &= ~BIGNUM_EMBED_FLAG;
|
|
}
|
|
}
|
|
else {
|
|
if (len <= BIGNUM_EMBED_LEN_MAX) {
|
|
ds = RBIGNUM(big)->as.heap.digits;
|
|
RBASIC(big)->flags |= BIGNUM_EMBED_FLAG;
|
|
BIGNUM_SET_LEN(big, len);
|
|
(void)VALGRIND_MAKE_MEM_UNDEFINED((void*)RBIGNUM(big)->as.ary, sizeof(RBIGNUM(big)->as.ary));
|
|
if (ds) {
|
|
MEMCPY(RBIGNUM(big)->as.ary, ds, BDIGIT, len);
|
|
xfree(ds);
|
|
}
|
|
}
|
|
else {
|
|
if (BIGNUM_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, size_t len)
|
|
{
|
|
rb_big_realloc(big, len);
|
|
BIGNUM_SET_LEN(big, len);
|
|
}
|
|
|
|
static VALUE
|
|
bignew_1(VALUE klass, size_t len, int sign)
|
|
{
|
|
NEWOBJ_OF(big, struct RBignum, klass, T_BIGNUM | (RGENGC_WB_PROTECTED_BIGNUM ? FL_WB_PROTECTED : 0));
|
|
BIGNUM_SET_SIGN(big, sign);
|
|
if (len <= BIGNUM_EMBED_LEN_MAX) {
|
|
RBASIC(big)->flags |= BIGNUM_EMBED_FLAG;
|
|
BIGNUM_SET_LEN(big, len);
|
|
(void)VALGRIND_MAKE_MEM_UNDEFINED((void*)RBIGNUM(big)->as.ary, sizeof(RBIGNUM(big)->as.ary));
|
|
}
|
|
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(size_t len, int sign)
|
|
{
|
|
return bignew(len, sign != 0);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_clone(VALUE x)
|
|
{
|
|
size_t len = BIGNUM_LEN(x);
|
|
VALUE z = bignew_1(CLASS_OF(x), len, BIGNUM_SIGN(x));
|
|
|
|
MEMCPY(BDIGITS(z), BDIGITS(x), BDIGIT, len);
|
|
return z;
|
|
}
|
|
|
|
static void
|
|
big_extend_carry(VALUE x)
|
|
{
|
|
rb_big_resize(x, BIGNUM_LEN(x)+1);
|
|
BDIGITS(x)[BIGNUM_LEN(x)-1] = 1;
|
|
}
|
|
|
|
/* modify a bignum by 2's complement */
|
|
static void
|
|
get2comp(VALUE x)
|
|
{
|
|
long i = BIGNUM_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 = BIGNUM_LEN(x);
|
|
BDIGIT *ds = BDIGITS(x);
|
|
BDIGIT hibits = 0;
|
|
|
|
BARY_TRUNC(ds, n);
|
|
|
|
if (n != 0 && BIGNUM_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)
|
|
{
|
|
BIGNUM_SET_SIGN(x, !hibits);
|
|
if (hibits) {
|
|
get2comp(x);
|
|
}
|
|
}
|
|
|
|
static inline VALUE
|
|
bigtrunc(VALUE x)
|
|
{
|
|
size_t len = BIGNUM_LEN(x);
|
|
BDIGIT *ds = BDIGITS(x);
|
|
|
|
if (len == 0) return x;
|
|
while (--len && !ds[len]);
|
|
if (BIGNUM_LEN(x) > len+1) {
|
|
rb_big_resize(x, len+1);
|
|
}
|
|
return x;
|
|
}
|
|
|
|
static inline VALUE
|
|
bigfixize(VALUE x)
|
|
{
|
|
size_t n = BIGNUM_LEN(x);
|
|
BDIGIT *ds = BDIGITS(x);
|
|
#if SIZEOF_BDIGIT < SIZEOF_LONG
|
|
unsigned long u;
|
|
#else
|
|
BDIGIT u;
|
|
#endif
|
|
|
|
BARY_TRUNC(ds, n);
|
|
|
|
if (n == 0) return INT2FIX(0);
|
|
|
|
#if SIZEOF_BDIGIT < SIZEOF_LONG
|
|
if (sizeof(long)/SIZEOF_BDIGIT < n)
|
|
goto return_big;
|
|
else {
|
|
int i = (int)n;
|
|
u = 0;
|
|
while (i--) {
|
|
u = (unsigned long)(BIGUP(u) + ds[i]);
|
|
}
|
|
}
|
|
#else /* SIZEOF_BDIGIT >= SIZEOF_LONG */
|
|
if (1 < n)
|
|
goto return_big;
|
|
else
|
|
u = ds[0];
|
|
#endif
|
|
|
|
if (BIGNUM_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, n);
|
|
return x;
|
|
}
|
|
|
|
static VALUE
|
|
bignorm(VALUE x)
|
|
{
|
|
if (RB_BIGNUM_TYPE_P(x)) {
|
|
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_BDIGIT >= 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]) ;
|
|
BIGNUM_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) {
|
|
BIGNUM_SET_NEGATIVE_SIGN(big);
|
|
}
|
|
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_BDIGIT >= 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 + BIGNUM_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_BDIGIT - 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)
|
|
{
|
|
static const BDIGIT char_bit[1] = { CHAR_BIT };
|
|
BDIGIT numbytes_bary[bdigit_roomof(sizeof(numbytes))];
|
|
BDIGIT val_numbits_bary[bdigit_roomof(sizeof(numbytes) + 1)];
|
|
BDIGIT nlz_bits_in_msbyte_bary[1];
|
|
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;
|
|
|
|
nlz_bits_in_msbyte_bary[0] = nlz_bits_in_msbyte;
|
|
|
|
/*
|
|
* 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_SHORT_MUL(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) {
|
|
#if defined __GNUC__ && (__GNUC__ == 4 && __GNUC_MINOR__ == 4)
|
|
*nlz_bits_ret = 0;
|
|
#endif
|
|
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;
|
|
}
|
|
|
|
/* Test abs(val) consists only a bit or not.
|
|
*
|
|
* Returns 1 if abs(val) == 1 << n for some n >= 0.
|
|
* Returns 0 otherwise.
|
|
*
|
|
* rb_absint_singlebit_p can be used to determine required buffer size
|
|
* for rb_integer_pack used with INTEGER_PACK_2COMP (two's complement).
|
|
*
|
|
* Following example calculates number of bits required to
|
|
* represent val in two's complement number, without sign bit.
|
|
*
|
|
* size_t size;
|
|
* int neg = FIXNUM_P(val) ? FIX2LONG(val) < 0 : BIGNUM_NEGATIVE_P(val);
|
|
* size = rb_absint_numwords(val, 1, NULL)
|
|
* if (size == (size_t)-1) ...overflow...
|
|
* if (neg && rb_absint_singlebit_p(val))
|
|
* size--;
|
|
*
|
|
* Following example calculates number of bytes required to
|
|
* represent val in two's complement number, with sign bit.
|
|
*
|
|
* size_t size;
|
|
* int neg = FIXNUM_P(val) ? FIX2LONG(val) < 0 : BIGNUM_NEGATIVE_P(val);
|
|
* int nlz_bits;
|
|
* size = rb_absint_size(val, &nlz_bits);
|
|
* if (nlz_bits == 0 && !(neg && rb_absint_singlebit_p(val)))
|
|
* size++;
|
|
*/
|
|
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_BDIGIT >= 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 + BIGNUM_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_BDIGIT >= 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 = BIGNUM_POSITIVE_P(val) ? 1 : -1;
|
|
ds = BDIGITS(val);
|
|
num_bdigits = BIGNUM_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), BIGNUM_LEN(val)))
|
|
sign = 0;
|
|
BIGNUM_SET_SIGN(val, 0 <= sign);
|
|
|
|
if (flags & INTEGER_PACK_FORCE_BIGNUM)
|
|
return bigtrunc(val);
|
|
return bignorm(val);
|
|
}
|
|
|
|
#define conv_digit(c) (ruby_digit36_to_number_table[(unsigned char)(c)])
|
|
|
|
NORETURN(static inline void invalid_radix(int base));
|
|
NORETURN(static inline void invalid_integer(VALUE s));
|
|
|
|
static inline int
|
|
valid_radix_p(int base)
|
|
{
|
|
return (1 < base && base <= 36);
|
|
}
|
|
|
|
static inline void
|
|
invalid_radix(int base)
|
|
{
|
|
rb_raise(rb_eArgError, "invalid radix %d", base);
|
|
}
|
|
|
|
static inline void
|
|
invalid_integer(VALUE s)
|
|
{
|
|
rb_raise(rb_eArgError, "invalid value for Integer(): %+"PRIsVALUE, s);
|
|
}
|
|
|
|
static int
|
|
str2big_scan_digits(const char *s, const char *str, int base, int badcheck, size_t *num_digits_p, ssize_t *len_p)
|
|
{
|
|
char nondigit = 0;
|
|
size_t num_digits = 0;
|
|
const char *digits_start = str;
|
|
const char *digits_end = str;
|
|
ssize_t len = *len_p;
|
|
|
|
int c;
|
|
|
|
if (!len) {
|
|
*num_digits_p = 0;
|
|
*len_p = 0;
|
|
return TRUE;
|
|
}
|
|
|
|
if (badcheck && *str == '_') goto bad;
|
|
|
|
while ((c = *str++) != 0) {
|
|
if (c == '_') {
|
|
if (nondigit) {
|
|
if (badcheck) goto bad;
|
|
break;
|
|
}
|
|
nondigit = (char) c;
|
|
}
|
|
else if ((c = conv_digit(c)) < 0 || c >= base) {
|
|
break;
|
|
}
|
|
else {
|
|
nondigit = 0;
|
|
num_digits++;
|
|
digits_end = str;
|
|
}
|
|
if (len > 0 && !--len) break;
|
|
}
|
|
if (badcheck && nondigit) goto bad;
|
|
if (badcheck && len) {
|
|
str--;
|
|
while (*str && ISSPACE(*str)) {
|
|
str++;
|
|
if (len > 0 && !--len) break;
|
|
}
|
|
if (len && *str) {
|
|
bad:
|
|
return FALSE;
|
|
}
|
|
}
|
|
*num_digits_p = num_digits;
|
|
*len_p = digits_end - digits_start;
|
|
return TRUE;
|
|
}
|
|
|
|
static VALUE
|
|
str2big_poweroftwo(
|
|
int sign,
|
|
const char *digits_start,
|
|
const char *digits_end,
|
|
size_t num_digits,
|
|
int bits_per_digit)
|
|
{
|
|
BDIGIT *dp;
|
|
BDIGIT_DBL dd;
|
|
int numbits;
|
|
|
|
size_t num_bdigits;
|
|
const char *p;
|
|
int c;
|
|
VALUE z;
|
|
|
|
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);
|
|
|
|
return z;
|
|
}
|
|
|
|
static VALUE
|
|
str2big_normal(
|
|
int sign,
|
|
const char *digits_start,
|
|
const char *digits_end,
|
|
size_t num_bdigits,
|
|
int base)
|
|
{
|
|
size_t blen = 1;
|
|
BDIGIT *zds;
|
|
BDIGIT_DBL num;
|
|
|
|
size_t i;
|
|
const char *p;
|
|
int c;
|
|
VALUE z;
|
|
|
|
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);
|
|
}
|
|
|
|
return z;
|
|
}
|
|
|
|
static VALUE
|
|
str2big_karatsuba(
|
|
int sign,
|
|
const char *digits_start,
|
|
const char *digits_end,
|
|
size_t num_digits,
|
|
size_t num_bdigits,
|
|
int digits_per_bdigits_dbl,
|
|
int base)
|
|
{
|
|
VALUE powerv;
|
|
size_t unit;
|
|
VALUE tmpuv = 0;
|
|
BDIGIT *uds, *vds, *tds;
|
|
BDIGIT_DBL dd;
|
|
BDIGIT_DBL current_base;
|
|
int m;
|
|
int power_level = 0;
|
|
|
|
size_t i;
|
|
const char *p;
|
|
int c;
|
|
VALUE z;
|
|
|
|
uds = ALLOCV_N(BDIGIT, tmpuv, 2*num_bdigits);
|
|
vds = uds + num_bdigits;
|
|
|
|
powerv = power_cache_get_power(base, power_level, NULL);
|
|
|
|
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), BIGNUM_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), BIGNUM_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);
|
|
}
|
|
}
|
|
power_level++;
|
|
powerv = power_cache_get_power(base, power_level, NULL);
|
|
tds = vds;
|
|
vds = uds;
|
|
uds = tds;
|
|
}
|
|
BARY_TRUNC(uds, num_bdigits);
|
|
z = bignew(num_bdigits, sign);
|
|
MEMCPY(BDIGITS(z), uds, BDIGIT, num_bdigits);
|
|
|
|
if (tmpuv)
|
|
ALLOCV_END(tmpuv);
|
|
|
|
return z;
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
static VALUE
|
|
str2big_gmp(
|
|
int sign,
|
|
const char *digits_start,
|
|
const char *digits_end,
|
|
size_t num_digits,
|
|
size_t num_bdigits,
|
|
int base)
|
|
{
|
|
const size_t nails = (sizeof(BDIGIT)-SIZEOF_BDIGIT)*CHAR_BIT;
|
|
char *buf, *p;
|
|
const char *q;
|
|
VALUE tmps;
|
|
mpz_t mz;
|
|
VALUE z;
|
|
BDIGIT *zds;
|
|
size_t zn, count;
|
|
|
|
buf = ALLOCV_N(char, tmps, num_digits+1);
|
|
p = buf;
|
|
for (q = digits_start; q < digits_end; q++) {
|
|
if (conv_digit(*q) < 0)
|
|
continue;
|
|
*p++ = *q;
|
|
}
|
|
*p = '\0';
|
|
|
|
mpz_init(mz);
|
|
mpz_set_str(mz, buf, base);
|
|
zn = num_bdigits;
|
|
z = bignew(zn, sign);
|
|
zds = BDIGITS(z);
|
|
mpz_export(BDIGITS(z), &count, -1, sizeof(BDIGIT), 0, nails, mz);
|
|
BDIGITS_ZERO(zds+count, zn-count);
|
|
mpz_clear(mz);
|
|
|
|
if (tmps)
|
|
ALLOCV_END(tmps);
|
|
|
|
return z;
|
|
}
|
|
#endif
|
|
|
|
/*
|
|
* Parse +str+ as Ruby Integer, i.e., underscores, 0d and 0b prefixes.
|
|
*
|
|
* str: pointer to the string to be parsed.
|
|
* should be NUL-terminated.
|
|
* base: base of conversion, must be 2..36, or -36..0.
|
|
* if +base+ > 0, the conversion is done according to the +base+
|
|
* and unmatched prefix is parsed as a part of the result if
|
|
* present.
|
|
* if +base+ <= 0, the conversion is done according to the
|
|
* prefix if present, in base <code>-base</code> if +base+ < -1,
|
|
* or in base 10.
|
|
* badcheck: if non-zero, +ArgumentError+ is raised when +str+ is not
|
|
* valid as an Integer. if zero, Fixnum 0 is returned in
|
|
* that case.
|
|
*/
|
|
VALUE
|
|
rb_cstr_to_inum(const char *str, int base, int badcheck)
|
|
{
|
|
char *end;
|
|
VALUE ret = rb_cstr_parse_inum(str, -1, (badcheck ? NULL : &end), base);
|
|
if (NIL_P(ret)) {
|
|
if (badcheck) rb_invalid_str(str, "Integer()");
|
|
ret = INT2FIX(0);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
/*
|
|
* Parse +str+ as Ruby Integer, i.e., underscores, 0d and 0b prefixes.
|
|
*
|
|
* str: pointer to the string to be parsed.
|
|
* should be NUL-terminated if +len+ is negative.
|
|
* len: length of +str+ if >= 0. if +len+ is negative, +str+ should
|
|
* be NUL-terminated.
|
|
* endp: if non-NULL, the address after parsed part is stored. if
|
|
* NULL, Qnil is returned when +str+ is not valid as an Integer.
|
|
* ndigits: if non-NULL, the number of parsed digits is stored.
|
|
* base: see +rb_cstr_to_inum+
|
|
* flags: bitwise OR of below flags:
|
|
* RB_INT_PARSE_SIGN: allow preceding spaces and +/- sign
|
|
* RB_INT_PARSE_UNDERSCORE: allow an underscore between digits
|
|
* RB_INT_PARSE_PREFIX: allow preceding prefix
|
|
*/
|
|
|
|
VALUE
|
|
rb_int_parse_cstr(const char *str, ssize_t len, char **endp, size_t *ndigits,
|
|
int base, int flags)
|
|
{
|
|
const char *const s = str;
|
|
char sign = 1;
|
|
int c;
|
|
VALUE z = Qnil;
|
|
|
|
unsigned long val;
|
|
int ov;
|
|
|
|
const char *digits_start, *digits_end;
|
|
size_t num_digits = 0;
|
|
size_t num_bdigits;
|
|
const ssize_t len0 = len;
|
|
const int badcheck = !endp;
|
|
|
|
#define ADV(n) do {\
|
|
if (len > 0 && len <= (n)) goto bad; \
|
|
str += (n); \
|
|
len -= (n); \
|
|
} while (0)
|
|
#define ASSERT_LEN() do {\
|
|
assert(len != 0); \
|
|
if (len0 >= 0) assert(s + len0 == str + len); \
|
|
} while (0)
|
|
|
|
if (!str) {
|
|
bad:
|
|
if (endp) *endp = (char *)str;
|
|
if (ndigits) *ndigits = num_digits;
|
|
return z;
|
|
}
|
|
if (len && (flags & RB_INT_PARSE_SIGN)) {
|
|
while (ISSPACE(*str)) ADV(1);
|
|
|
|
if (str[0] == '+') {
|
|
ADV(1);
|
|
}
|
|
else if (str[0] == '-') {
|
|
ADV(1);
|
|
sign = 0;
|
|
}
|
|
ASSERT_LEN();
|
|
}
|
|
if (base <= 0) {
|
|
if (str[0] == '0' && len > 1) {
|
|
switch (str[1]) {
|
|
case 'x': case 'X':
|
|
base = 16;
|
|
ADV(2);
|
|
break;
|
|
case 'b': case 'B':
|
|
base = 2;
|
|
ADV(2);
|
|
break;
|
|
case 'o': case 'O':
|
|
base = 8;
|
|
ADV(2);
|
|
break;
|
|
case 'd': case 'D':
|
|
base = 10;
|
|
ADV(2);
|
|
break;
|
|
default:
|
|
base = 8;
|
|
}
|
|
}
|
|
else if (base < -1) {
|
|
base = -base;
|
|
}
|
|
else {
|
|
base = 10;
|
|
}
|
|
}
|
|
else if (len == 1 || !(flags & RB_INT_PARSE_PREFIX)) {
|
|
/* no prefix */
|
|
}
|
|
else if (base == 2) {
|
|
if (str[0] == '0' && (str[1] == 'b'||str[1] == 'B')) {
|
|
ADV(2);
|
|
}
|
|
}
|
|
else if (base == 8) {
|
|
if (str[0] == '0' && (str[1] == 'o'||str[1] == 'O')) {
|
|
ADV(2);
|
|
}
|
|
}
|
|
else if (base == 10) {
|
|
if (str[0] == '0' && (str[1] == 'd'||str[1] == 'D')) {
|
|
ADV(2);
|
|
}
|
|
}
|
|
else if (base == 16) {
|
|
if (str[0] == '0' && (str[1] == 'x'||str[1] == 'X')) {
|
|
ADV(2);
|
|
}
|
|
}
|
|
if (!valid_radix_p(base)) {
|
|
invalid_radix(base);
|
|
}
|
|
if (!len) goto bad;
|
|
num_digits = str - s;
|
|
if (*str == '0' && len != 1) { /* squeeze preceding 0s */
|
|
int us = 0;
|
|
const char *end = len < 0 ? NULL : str + len;
|
|
++num_digits;
|
|
while ((c = *++str) == '0' ||
|
|
((flags & RB_INT_PARSE_UNDERSCORE) && c == '_')) {
|
|
if (c == '_') {
|
|
if (++us >= 2)
|
|
break;
|
|
}
|
|
else {
|
|
++num_digits;
|
|
us = 0;
|
|
}
|
|
if (str == end) break;
|
|
}
|
|
if (!c || ISSPACE(c)) --str;
|
|
if (end) len = end - str;
|
|
ASSERT_LEN();
|
|
}
|
|
c = *str;
|
|
c = conv_digit(c);
|
|
if (c < 0 || c >= base) {
|
|
if (!badcheck && num_digits) z = INT2FIX(0);
|
|
goto bad;
|
|
}
|
|
|
|
if (ndigits) *ndigits = num_digits;
|
|
val = ruby_scan_digits(str, len, base, &num_digits, &ov);
|
|
if (!ov) {
|
|
const char *end = &str[num_digits];
|
|
if (num_digits > 0 && *end == '_' && (flags & RB_INT_PARSE_UNDERSCORE))
|
|
goto bigparse;
|
|
if (endp) *endp = (char *)end;
|
|
if (ndigits) *ndigits += num_digits;
|
|
if (badcheck) {
|
|
if (num_digits == 0) return Qnil; /* no number */
|
|
while (len < 0 ? *end : end < str + len) {
|
|
if (!ISSPACE(*end)) return Qnil; /* trailing garbage */
|
|
end++;
|
|
}
|
|
}
|
|
|
|
if (POSFIXABLE(val)) {
|
|
if (sign) return LONG2FIX(val);
|
|
else {
|
|
long result = -(long)val;
|
|
return LONG2FIX(result);
|
|
}
|
|
}
|
|
else {
|
|
VALUE big = rb_uint2big(val);
|
|
BIGNUM_SET_SIGN(big, sign);
|
|
return bignorm(big);
|
|
}
|
|
}
|
|
|
|
bigparse:
|
|
digits_start = str;
|
|
if (!str2big_scan_digits(s, str, base, badcheck, &num_digits, &len))
|
|
goto bad;
|
|
if (endp) *endp = (char *)(str + len);
|
|
if (ndigits) *ndigits += num_digits;
|
|
digits_end = digits_start + len;
|
|
|
|
if (POW2_P(base)) {
|
|
z = str2big_poweroftwo(sign, digits_start, digits_end, num_digits,
|
|
bit_length(base-1));
|
|
}
|
|
else {
|
|
int digits_per_bdigits_dbl;
|
|
maxpow_in_bdigit_dbl(base, &digits_per_bdigits_dbl);
|
|
num_bdigits = roomof(num_digits, digits_per_bdigits_dbl)*2;
|
|
|
|
#ifdef USE_GMP
|
|
if (GMP_STR2BIG_DIGITS < num_bdigits) {
|
|
z = str2big_gmp(sign, digits_start, digits_end, num_digits,
|
|
num_bdigits, base);
|
|
}
|
|
else
|
|
#endif
|
|
if (num_bdigits < KARATSUBA_MUL_DIGITS) {
|
|
z = str2big_normal(sign, digits_start, digits_end,
|
|
num_bdigits, base);
|
|
}
|
|
else {
|
|
z = str2big_karatsuba(sign, digits_start, digits_end, num_digits,
|
|
num_bdigits, digits_per_bdigits_dbl, base);
|
|
}
|
|
}
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_cstr_parse_inum(const char *str, ssize_t len, char **endp, int base)
|
|
{
|
|
return rb_int_parse_cstr(str, len, endp, NULL, base,
|
|
RB_INT_PARSE_DEFAULT);
|
|
}
|
|
|
|
VALUE
|
|
rb_str_to_inum(VALUE str, int base, int badcheck)
|
|
{
|
|
VALUE ret;
|
|
const char *s;
|
|
long len;
|
|
char *end;
|
|
|
|
StringValue(str);
|
|
rb_must_asciicompat(str);
|
|
RSTRING_GETMEM(str, s, len);
|
|
ret = rb_cstr_parse_inum(s, len, (badcheck ? NULL : &end), base);
|
|
if (NIL_P(ret)) {
|
|
if (badcheck) invalid_integer(str);
|
|
ret = INT2FIX(0);
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
VALUE
|
|
rb_str2big_poweroftwo(VALUE arg, int base, int badcheck)
|
|
{
|
|
int positive_p = 1;
|
|
const char *s, *str;
|
|
const char *digits_start, *digits_end;
|
|
size_t num_digits;
|
|
ssize_t len;
|
|
VALUE z;
|
|
|
|
if (!valid_radix_p(base) || !POW2_P(base)) {
|
|
invalid_radix(base);
|
|
}
|
|
|
|
rb_must_asciicompat(arg);
|
|
s = str = StringValueCStr(arg);
|
|
len = RSTRING_LEN(arg);
|
|
if (*str == '-') {
|
|
len--;
|
|
str++;
|
|
positive_p = 0;
|
|
}
|
|
|
|
digits_start = str;
|
|
if (!str2big_scan_digits(s, str, base, badcheck, &num_digits, &len))
|
|
invalid_integer(arg);
|
|
digits_end = digits_start + len;
|
|
|
|
z = str2big_poweroftwo(positive_p, digits_start, digits_end, num_digits,
|
|
bit_length(base-1));
|
|
|
|
RB_GC_GUARD(arg);
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_str2big_normal(VALUE arg, int base, int badcheck)
|
|
{
|
|
int positive_p = 1;
|
|
const char *s, *str;
|
|
const char *digits_start, *digits_end;
|
|
size_t num_digits;
|
|
ssize_t len;
|
|
VALUE z;
|
|
|
|
int digits_per_bdigits_dbl;
|
|
size_t num_bdigits;
|
|
|
|
if (!valid_radix_p(base)) {
|
|
invalid_radix(base);
|
|
}
|
|
|
|
rb_must_asciicompat(arg);
|
|
s = str = StringValuePtr(arg);
|
|
len = RSTRING_LEN(arg);
|
|
if (len > 0 && *str == '-') {
|
|
len--;
|
|
str++;
|
|
positive_p = 0;
|
|
}
|
|
|
|
digits_start = str;
|
|
if (!str2big_scan_digits(s, str, base, badcheck, &num_digits, &len))
|
|
invalid_integer(arg);
|
|
digits_end = digits_start + len;
|
|
|
|
maxpow_in_bdigit_dbl(base, &digits_per_bdigits_dbl);
|
|
num_bdigits = roomof(num_digits, digits_per_bdigits_dbl)*2;
|
|
|
|
z = str2big_normal(positive_p, digits_start, digits_end,
|
|
num_bdigits, base);
|
|
|
|
RB_GC_GUARD(arg);
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_str2big_karatsuba(VALUE arg, int base, int badcheck)
|
|
{
|
|
int positive_p = 1;
|
|
const char *s, *str;
|
|
const char *digits_start, *digits_end;
|
|
size_t num_digits;
|
|
ssize_t len;
|
|
VALUE z;
|
|
|
|
int digits_per_bdigits_dbl;
|
|
size_t num_bdigits;
|
|
|
|
if (!valid_radix_p(base)) {
|
|
invalid_radix(base);
|
|
}
|
|
|
|
rb_must_asciicompat(arg);
|
|
s = str = StringValuePtr(arg);
|
|
len = RSTRING_LEN(arg);
|
|
if (len > 0 && *str == '-') {
|
|
len--;
|
|
str++;
|
|
positive_p = 0;
|
|
}
|
|
|
|
digits_start = str;
|
|
if (!str2big_scan_digits(s, str, base, badcheck, &num_digits, &len))
|
|
invalid_integer(arg);
|
|
digits_end = digits_start + len;
|
|
|
|
maxpow_in_bdigit_dbl(base, &digits_per_bdigits_dbl);
|
|
num_bdigits = roomof(num_digits, digits_per_bdigits_dbl)*2;
|
|
|
|
z = str2big_karatsuba(positive_p, digits_start, digits_end, num_digits,
|
|
num_bdigits, digits_per_bdigits_dbl, base);
|
|
|
|
RB_GC_GUARD(arg);
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
VALUE
|
|
rb_str2big_gmp(VALUE arg, int base, int badcheck)
|
|
{
|
|
int positive_p = 1;
|
|
const char *s, *str;
|
|
const char *digits_start, *digits_end;
|
|
size_t num_digits;
|
|
ssize_t len;
|
|
VALUE z;
|
|
|
|
int digits_per_bdigits_dbl;
|
|
size_t num_bdigits;
|
|
|
|
if (!valid_radix_p(base)) {
|
|
invalid_radix(base);
|
|
}
|
|
|
|
rb_must_asciicompat(arg);
|
|
s = str = StringValuePtr(arg);
|
|
len = RSTRING_LEN(arg);
|
|
if (len > 0 && *str == '-') {
|
|
len--;
|
|
str++;
|
|
positive_p = 0;
|
|
}
|
|
|
|
digits_start = str;
|
|
if (!str2big_scan_digits(s, str, base, badcheck, &num_digits, &len))
|
|
invalid_integer(arg);
|
|
digits_end = digits_start + len;
|
|
|
|
maxpow_in_bdigit_dbl(base, &digits_per_bdigits_dbl);
|
|
num_bdigits = roomof(num_digits, digits_per_bdigits_dbl)*2;
|
|
|
|
z = str2big_gmp(positive_p, digits_start, digits_end, num_digits, num_bdigits, base);
|
|
|
|
RB_GC_GUARD(arg);
|
|
|
|
return bignorm(z);
|
|
}
|
|
#endif
|
|
|
|
#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_BDIGIT >= 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]) ;
|
|
BIGNUM_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) {
|
|
BIGNUM_SET_NEGATIVE_SIGN(big);
|
|
}
|
|
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 */
|
|
|
|
#ifdef HAVE_INT128_T
|
|
static VALUE
|
|
rb_uint128t2big(uint128_t n)
|
|
{
|
|
long i;
|
|
VALUE big = bignew(bdigit_roomof(SIZEOF_INT128_T), 1);
|
|
BDIGIT *digits = BDIGITS(big);
|
|
|
|
for (i = 0; i < bdigit_roomof(SIZEOF_INT128_T); i++) {
|
|
digits[i] = BIGLO(RSHIFT(n ,BITSPERDIG*i));
|
|
}
|
|
|
|
i = bdigit_roomof(SIZEOF_INT128_T);
|
|
while (i-- && !digits[i]) ;
|
|
BIGNUM_SET_LEN(big, i+1);
|
|
return big;
|
|
}
|
|
|
|
MJIT_FUNC_EXPORTED VALUE
|
|
rb_int128t2big(int128_t n)
|
|
{
|
|
int neg = 0;
|
|
uint128_t u;
|
|
VALUE big;
|
|
|
|
if (n < 0) {
|
|
u = 1 + (uint128_t)(-(n + 1)); /* u = -n avoiding overflow */
|
|
neg = 1;
|
|
}
|
|
else {
|
|
u = n;
|
|
}
|
|
big = rb_uint128t2big(u);
|
|
if (neg) {
|
|
BIGNUM_SET_NEGATIVE_SIGN(big);
|
|
}
|
|
return big;
|
|
}
|
|
#endif
|
|
|
|
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 = BIGNUM_LEN(x);
|
|
z = bignew(xn+s1+1, BIGNUM_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)BIGNUM_LEN(x) <= shift_numdigits) {
|
|
if (BIGNUM_POSITIVE_P(x) ||
|
|
bary_zero_p(BDIGITS(x), BIGNUM_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 ? BDIGMAX : 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 BIGNUM_POSITIVE_P(x) ? INT2FIX(0) : INT2FIX(-1);
|
|
}
|
|
shift_numbits = (int)(lens[0] & (BITSPERDIG-1));
|
|
shift_numdigits = (lens[0] >> bit_length(BITSPERDIG-1)) |
|
|
(lens[1] << (CHAR_BIT*SIZEOF_SIZE_T - bit_length(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 MAX_BASE36_POWER_TABLE_ENTRIES (SIZEOF_SIZE_T * CHAR_BIT + 1)
|
|
|
|
static VALUE base36_power_cache[35][MAX_BASE36_POWER_TABLE_ENTRIES];
|
|
static size_t base36_numdigits_cache[35][MAX_BASE36_POWER_TABLE_ENTRIES];
|
|
|
|
static void
|
|
power_cache_init(void)
|
|
{
|
|
int i, j;
|
|
for (i = 0; i < 35; ++i) {
|
|
for (j = 0; j < MAX_BASE36_POWER_TABLE_ENTRIES; ++j) {
|
|
base36_power_cache[i][j] = Qnil;
|
|
}
|
|
}
|
|
}
|
|
|
|
static inline VALUE
|
|
power_cache_get_power(int base, int power_level, size_t *numdigits_ret)
|
|
{
|
|
/*
|
|
* MAX_BASE36_POWER_TABLE_ENTRIES is big enough to that
|
|
* base36_power_cache[base][MAX_BASE36_POWER_TABLE_ENTRIES-1] fills whole memory.
|
|
* So MAX_BASE36_POWER_TABLE_ENTRIES <= power_level is not possible to calculate.
|
|
*
|
|
* number-of-bytes =
|
|
* log256(base36_power_cache[base][MAX_BASE36_POWER_TABLE_ENTRIES-1]) =
|
|
* log256(maxpow_in_bdigit_dbl(base)**(2**(MAX_BASE36_POWER_TABLE_ENTRIES-1))) =
|
|
* log256(maxpow_in_bdigit_dbl(base)**(2**(SIZEOF_SIZE_T*CHAR_BIT))) =
|
|
* (2**(SIZEOF_SIZE_T*CHAR_BIT))*log256(maxpow_in_bdigit_dbl(base)) =
|
|
* (256**SIZEOF_SIZE_T)*log256(maxpow_in_bdigit_dbl(base)) >
|
|
* (256**SIZEOF_SIZE_T)*(sizeof(BDIGIT_DBL)-1) >
|
|
* 256**SIZEOF_SIZE_T
|
|
*/
|
|
if (MAX_BASE36_POWER_TABLE_ENTRIES <= power_level)
|
|
rb_bug("too big power number requested: maxpow_in_bdigit_dbl(%d)**(2**%d)", base, power_level);
|
|
|
|
if (NIL_P(base36_power_cache[base - 2][power_level])) {
|
|
VALUE power;
|
|
size_t numdigits;
|
|
if (power_level == 0) {
|
|
int numdigits0;
|
|
BDIGIT_DBL dd = maxpow_in_bdigit_dbl(base, &numdigits0);
|
|
power = bignew(2, 1);
|
|
bdigitdbl2bary(BDIGITS(power), 2, dd);
|
|
numdigits = numdigits0;
|
|
}
|
|
else {
|
|
power = bigtrunc(bigsq(power_cache_get_power(base, power_level - 1, &numdigits)));
|
|
numdigits *= 2;
|
|
}
|
|
rb_obj_hide(power);
|
|
base36_power_cache[base - 2][power_level] = power;
|
|
base36_numdigits_cache[base - 2][power_level] = numdigits;
|
|
rb_gc_register_mark_object(power);
|
|
}
|
|
if (numdigits_ret)
|
|
*numdigits_ret = base36_numdigits_cache[base - 2][power_level];
|
|
return base36_power_cache[base - 2][power_level];
|
|
}
|
|
|
|
struct big2str_struct {
|
|
int negative;
|
|
int base;
|
|
BDIGIT_DBL hbase2;
|
|
int hbase2_numdigits;
|
|
VALUE result;
|
|
char *ptr;
|
|
};
|
|
|
|
static void
|
|
big2str_alloc(struct big2str_struct *b2s, size_t len)
|
|
{
|
|
if (LONG_MAX-1 < len)
|
|
rb_raise(rb_eArgError, "too big number");
|
|
b2s->result = rb_usascii_str_new(0, (long)(len + 1)); /* plus one for sign */
|
|
b2s->ptr = RSTRING_PTR(b2s->result);
|
|
if (b2s->negative)
|
|
*b2s->ptr++ = '-';
|
|
}
|
|
|
|
static void
|
|
big2str_2bdigits(struct big2str_struct *b2s, BDIGIT *xds, size_t xn, size_t taillen)
|
|
{
|
|
size_t j;
|
|
BDIGIT_DBL num;
|
|
char buf[SIZEOF_BDIGIT_DBL*CHAR_BIT], *p;
|
|
int beginning = !b2s->ptr;
|
|
size_t len = 0;
|
|
|
|
assert(xn <= 2);
|
|
num = bary2bdigitdbl(xds, xn);
|
|
|
|
if (beginning) {
|
|
if (num == 0)
|
|
return;
|
|
p = buf;
|
|
j = sizeof(buf);
|
|
do {
|
|
BDIGIT_DBL idx = num % b2s->base;
|
|
num /= b2s->base;
|
|
p[--j] = ruby_digitmap[idx];
|
|
} while (num);
|
|
len = sizeof(buf) - j;
|
|
big2str_alloc(b2s, len + taillen);
|
|
MEMCPY(b2s->ptr, buf + j, char, len);
|
|
}
|
|
else {
|
|
p = b2s->ptr;
|
|
j = b2s->hbase2_numdigits;
|
|
do {
|
|
BDIGIT_DBL idx = num % b2s->base;
|
|
num /= b2s->base;
|
|
p[--j] = ruby_digitmap[idx];
|
|
} while (j);
|
|
len = b2s->hbase2_numdigits;
|
|
}
|
|
b2s->ptr += len;
|
|
}
|
|
|
|
static void
|
|
big2str_karatsuba(struct big2str_struct *b2s, BDIGIT *xds, size_t xn, size_t wn,
|
|
int power_level, size_t taillen)
|
|
{
|
|
VALUE b;
|
|
size_t half_numdigits, lower_numdigits;
|
|
int lower_power_level;
|
|
size_t bn;
|
|
const BDIGIT *bds;
|
|
size_t len;
|
|
|
|
/*
|
|
* Precondition:
|
|
* abs(x) < maxpow**(2**power_level)
|
|
* where
|
|
* maxpow = maxpow_in_bdigit_dbl(base, &numdigits)
|
|
*
|
|
* This function generates sequence of zeros, and then stringized abs(x) into b2s->ptr.
|
|
*
|
|
* b2s->ptr can be NULL.
|
|
* It is allocated when the first character is generated via big2str_alloc.
|
|
*
|
|
* The prefix zeros should be generated if and only if b2s->ptr is not NULL.
|
|
* When the zeros are generated, the zeros and abs(x) consists
|
|
* numdigits*(2**power_level) characters at total.
|
|
*
|
|
* Note:
|
|
* power_cache_get_power(base, power_level, &len) may not be cached yet. It should not be called.
|
|
* power_cache_get_power(base, power_level-1, &len) should be cached already if 0 <= power_level-1.
|
|
*/
|
|
|
|
if (xn == 0 || bary_zero_p(xds, xn)) {
|
|
if (b2s->ptr) {
|
|
/* When x is zero, power_cache_get_power(base, power_level) should be cached already. */
|
|
power_cache_get_power(b2s->base, power_level, &len);
|
|
memset(b2s->ptr, '0', len);
|
|
b2s->ptr += len;
|
|
}
|
|
return;
|
|
}
|
|
|
|
if (power_level == 0) {
|
|
big2str_2bdigits(b2s, xds, xn, taillen);
|
|
return;
|
|
}
|
|
|
|
lower_power_level = power_level-1;
|
|
b = power_cache_get_power(b2s->base, lower_power_level, &lower_numdigits);
|
|
bn = BIGNUM_LEN(b);
|
|
bds = BDIGITS(b);
|
|
|
|
half_numdigits = lower_numdigits;
|
|
|
|
while (0 < lower_power_level &&
|
|
(xn < bn ||
|
|
(xn == bn && bary_cmp(xds, xn, bds, bn) < 0))) {
|
|
lower_power_level--;
|
|
b = power_cache_get_power(b2s->base, lower_power_level, &lower_numdigits);
|
|
bn = BIGNUM_LEN(b);
|
|
bds = BDIGITS(b);
|
|
}
|
|
|
|
if (lower_power_level == 0 &&
|
|
(xn < bn ||
|
|
(xn == bn && bary_cmp(xds, xn, bds, bn) < 0))) {
|
|
if (b2s->ptr) {
|
|
len = half_numdigits * 2 - lower_numdigits;
|
|
memset(b2s->ptr, '0', len);
|
|
b2s->ptr += len;
|
|
}
|
|
big2str_2bdigits(b2s, xds, xn, taillen);
|
|
}
|
|
else {
|
|
BDIGIT *qds, *rds;
|
|
size_t qn, rn;
|
|
BDIGIT *tds;
|
|
int shift;
|
|
|
|
if (lower_power_level != power_level-1 && b2s->ptr) {
|
|
len = (half_numdigits - lower_numdigits) * 2;
|
|
memset(b2s->ptr, '0', len);
|
|
b2s->ptr += len;
|
|
}
|
|
|
|
shift = nlz(bds[bn-1]);
|
|
|
|
qn = xn + BIGDIVREM_EXTRA_WORDS;
|
|
|
|
if (shift == 0) {
|
|
/* bigdivrem_restoring will not modify y.
|
|
* So use bds directly. */
|
|
tds = (BDIGIT *)bds;
|
|
xds[xn] = 0;
|
|
}
|
|
else {
|
|
/* bigdivrem_restoring will modify y.
|
|
* So use temporary buffer. */
|
|
tds = xds + qn;
|
|
assert(qn + bn <= xn + wn);
|
|
bary_small_lshift(tds, bds, bn, shift);
|
|
xds[xn] = bary_small_lshift(xds, xds, xn, shift);
|
|
}
|
|
|
|
bigdivrem_restoring(xds, qn, tds, bn);
|
|
|
|
rds = xds;
|
|
rn = bn;
|
|
|
|
qds = xds + bn;
|
|
qn = qn - bn;
|
|
|
|
if (shift) {
|
|
bary_small_rshift(rds, rds, rn, shift, 0);
|
|
}
|
|
|
|
BARY_TRUNC(qds, qn);
|
|
assert(qn <= bn);
|
|
big2str_karatsuba(b2s, qds, qn, xn+wn - (rn+qn), lower_power_level, lower_numdigits+taillen);
|
|
BARY_TRUNC(rds, rn);
|
|
big2str_karatsuba(b2s, rds, rn, xn+wn - rn, lower_power_level, taillen);
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
big2str_base_poweroftwo(VALUE x, int base)
|
|
{
|
|
int word_numbits = ffs(base) - 1;
|
|
size_t numwords;
|
|
VALUE result;
|
|
char *ptr;
|
|
numwords = rb_absint_numwords(x, word_numbits, NULL);
|
|
if (BIGNUM_NEGATIVE_P(x)) {
|
|
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++ = BIGNUM_POSITIVE_P(x) ? '+' : '-';
|
|
}
|
|
else {
|
|
if (LONG_MAX < numwords)
|
|
rb_raise(rb_eArgError, "too big number");
|
|
result = rb_usascii_str_new(0, numwords);
|
|
ptr = RSTRING_PTR(result);
|
|
}
|
|
rb_integer_pack(x, ptr, numwords, 1, CHAR_BIT-word_numbits,
|
|
INTEGER_PACK_BIG_ENDIAN);
|
|
while (0 < numwords) {
|
|
*ptr = ruby_digitmap[*(unsigned char *)ptr];
|
|
ptr++;
|
|
numwords--;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
VALUE
|
|
rb_big2str_poweroftwo(VALUE x, int base)
|
|
{
|
|
return big2str_base_poweroftwo(x, base);
|
|
}
|
|
|
|
static VALUE
|
|
big2str_generic(VALUE x, int base)
|
|
{
|
|
BDIGIT *xds;
|
|
size_t xn;
|
|
struct big2str_struct b2s_data;
|
|
int power_level;
|
|
VALUE power;
|
|
|
|
xds = BDIGITS(x);
|
|
xn = BIGNUM_LEN(x);
|
|
BARY_TRUNC(xds, xn);
|
|
|
|
if (xn == 0) {
|
|
return rb_usascii_str_new2("0");
|
|
}
|
|
|
|
if (!valid_radix_p(base))
|
|
invalid_radix(base);
|
|
|
|
if (xn >= LONG_MAX/BITSPERDIG) {
|
|
rb_raise(rb_eRangeError, "bignum too big to convert into `string'");
|
|
}
|
|
|
|
power_level = 0;
|
|
power = power_cache_get_power(base, power_level, NULL);
|
|
while (power_level < MAX_BASE36_POWER_TABLE_ENTRIES &&
|
|
(size_t)BIGNUM_LEN(power) <= (xn+1)/2) {
|
|
power_level++;
|
|
power = power_cache_get_power(base, power_level, NULL);
|
|
}
|
|
assert(power_level != MAX_BASE36_POWER_TABLE_ENTRIES);
|
|
|
|
if ((size_t)BIGNUM_LEN(power) <= xn) {
|
|
/*
|
|
* This increment guarantees x < power_cache_get_power(base, power_level)
|
|
* without invoking it actually.
|
|
* (power_cache_get_power(base, power_level) can be slow and not used
|
|
* in big2str_karatsuba.)
|
|
*
|
|
* Although it is possible that x < power_cache_get_power(base, power_level-1),
|
|
* it is no problem because big2str_karatsuba checks it and
|
|
* doesn't affect the result when b2s_data.ptr is NULL.
|
|
*/
|
|
power_level++;
|
|
}
|
|
|
|
b2s_data.negative = BIGNUM_NEGATIVE_P(x);
|
|
b2s_data.base = base;
|
|
b2s_data.hbase2 = maxpow_in_bdigit_dbl(base, &b2s_data.hbase2_numdigits);
|
|
|
|
b2s_data.result = Qnil;
|
|
b2s_data.ptr = NULL;
|
|
|
|
if (power_level == 0) {
|
|
big2str_2bdigits(&b2s_data, xds, xn, 0);
|
|
}
|
|
else {
|
|
VALUE tmpw = 0;
|
|
BDIGIT *wds;
|
|
size_t wn;
|
|
wn = power_level * BIGDIVREM_EXTRA_WORDS + BIGNUM_LEN(power);
|
|
wds = ALLOCV_N(BDIGIT, tmpw, xn + wn);
|
|
MEMCPY(wds, xds, BDIGIT, xn);
|
|
big2str_karatsuba(&b2s_data, wds, xn, wn, power_level, 0);
|
|
if (tmpw)
|
|
ALLOCV_END(tmpw);
|
|
}
|
|
RB_GC_GUARD(x);
|
|
|
|
*b2s_data.ptr = '\0';
|
|
rb_str_resize(b2s_data.result, (long)(b2s_data.ptr - RSTRING_PTR(b2s_data.result)));
|
|
|
|
RB_GC_GUARD(x);
|
|
return b2s_data.result;
|
|
}
|
|
|
|
VALUE
|
|
rb_big2str_generic(VALUE x, int base)
|
|
{
|
|
return big2str_generic(x, base);
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
static VALUE
|
|
big2str_gmp(VALUE x, int base)
|
|
{
|
|
const size_t nails = (sizeof(BDIGIT)-SIZEOF_BDIGIT)*CHAR_BIT;
|
|
mpz_t mx;
|
|
size_t size;
|
|
VALUE str;
|
|
BDIGIT *xds = BDIGITS(x);
|
|
size_t xn = BIGNUM_LEN(x);
|
|
|
|
mpz_init(mx);
|
|
mpz_import(mx, xn, -1, sizeof(BDIGIT), 0, nails, xds);
|
|
|
|
size = mpz_sizeinbase(mx, base);
|
|
|
|
if (BIGNUM_NEGATIVE_P(x)) {
|
|
mpz_neg(mx, mx);
|
|
str = rb_usascii_str_new(0, size+1);
|
|
}
|
|
else {
|
|
str = rb_usascii_str_new(0, size);
|
|
}
|
|
mpz_get_str(RSTRING_PTR(str), base, mx);
|
|
mpz_clear(mx);
|
|
|
|
if (RSTRING_PTR(str)[RSTRING_LEN(str)-1] == '\0') {
|
|
rb_str_set_len(str, RSTRING_LEN(str)-1);
|
|
}
|
|
|
|
RB_GC_GUARD(x);
|
|
return str;
|
|
}
|
|
|
|
VALUE
|
|
rb_big2str_gmp(VALUE x, int base)
|
|
{
|
|
return big2str_gmp(x, base);
|
|
}
|
|
#endif
|
|
|
|
static VALUE
|
|
rb_big2str1(VALUE x, int base)
|
|
{
|
|
BDIGIT *xds;
|
|
size_t xn;
|
|
|
|
if (FIXNUM_P(x)) {
|
|
return rb_fix2str(x, base);
|
|
}
|
|
|
|
bigtrunc(x);
|
|
xds = BDIGITS(x);
|
|
xn = BIGNUM_LEN(x);
|
|
BARY_TRUNC(xds, xn);
|
|
|
|
if (xn == 0) {
|
|
return rb_usascii_str_new2("0");
|
|
}
|
|
|
|
if (!valid_radix_p(base))
|
|
invalid_radix(base);
|
|
|
|
if (xn >= LONG_MAX/BITSPERDIG) {
|
|
rb_raise(rb_eRangeError, "bignum too big to convert into `string'");
|
|
}
|
|
|
|
if (POW2_P(base)) {
|
|
/* base == 2 || base == 4 || base == 8 || base == 16 || base == 32 */
|
|
return big2str_base_poweroftwo(x, base);
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
if (GMP_BIG2STR_DIGITS < xn) {
|
|
return big2str_gmp(x, base);
|
|
}
|
|
#endif
|
|
|
|
return big2str_generic(x, base);
|
|
}
|
|
|
|
VALUE
|
|
rb_big2str(VALUE x, int base)
|
|
{
|
|
return rb_big2str1(x, base);
|
|
}
|
|
|
|
static unsigned long
|
|
big2ulong(VALUE x, const char *type)
|
|
{
|
|
size_t len = BIGNUM_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_BDIGIT
|
|
num = (unsigned long)ds[0];
|
|
#else
|
|
num = 0;
|
|
while (len--) {
|
|
num <<= BITSPERDIG;
|
|
num += (unsigned long)ds[len]; /* overflow is already checked */
|
|
}
|
|
#endif
|
|
return num;
|
|
}
|
|
|
|
unsigned long
|
|
rb_big2ulong(VALUE x)
|
|
{
|
|
unsigned long num = big2ulong(x, "unsigned long");
|
|
|
|
if (BIGNUM_POSITIVE_P(x)) {
|
|
return num;
|
|
}
|
|
else {
|
|
if (num <= 1+(unsigned long)(-(LONG_MIN+1)))
|
|
return -(long)(num-1)-1;
|
|
}
|
|
rb_raise(rb_eRangeError, "bignum out of range of unsigned long");
|
|
}
|
|
|
|
long
|
|
rb_big2long(VALUE x)
|
|
{
|
|
unsigned long num = big2ulong(x, "long");
|
|
|
|
if (BIGNUM_POSITIVE_P(x)) {
|
|
if (num <= LONG_MAX)
|
|
return num;
|
|
}
|
|
else {
|
|
if (num <= 1+(unsigned long)(-(LONG_MIN+1)))
|
|
return -(long)(num-1)-1;
|
|
}
|
|
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)
|
|
{
|
|
size_t len = BIGNUM_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_BDIGIT
|
|
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 (BIGNUM_POSITIVE_P(x)) {
|
|
return num;
|
|
}
|
|
else {
|
|
if (num <= 1+(unsigned LONG_LONG)(-(LLONG_MIN+1)))
|
|
return -(LONG_LONG)(num-1)-1;
|
|
}
|
|
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 (BIGNUM_POSITIVE_P(x)) {
|
|
if (num <= LLONG_MAX)
|
|
return num;
|
|
}
|
|
else {
|
|
if (num <= 1+(unsigned LONG_LONG)(-(LLONG_MIN+1)))
|
|
return -(LONG_LONG)(num-1)-1;
|
|
}
|
|
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 (1.0 <= 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), BIGNUM_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 (BIGNUM_NEGATIVE_P(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;
|
|
}
|
|
|
|
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 xn, yn;
|
|
if (yi < FIXNUM_MIN)
|
|
return INT2FIX(1);
|
|
if (FIXNUM_MAX+1 <= yi)
|
|
return INT2FIX(-1);
|
|
xn = FIX2LONG(x);
|
|
yn = (long)yi;
|
|
if (xn < yn)
|
|
return INT2FIX(-1);
|
|
if (xn > yn)
|
|
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 xn, yn;
|
|
if (yi < LONG_MIN || LONG_MAX < yi)
|
|
return Qfalse;
|
|
xn = FIX2LONG(x);
|
|
yn = (long)yi;
|
|
if (xn != yn)
|
|
return Qfalse;
|
|
return Qtrue;
|
|
#endif
|
|
}
|
|
y = rb_dbl2big(yi);
|
|
return rb_big_eq(x, y);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_cmp(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
x = bigfixize(x);
|
|
if (FIXNUM_P(x)) {
|
|
/* SIGNED_VALUE and Fixnum have same sign-bits, same
|
|
* order */
|
|
SIGNED_VALUE sx = (SIGNED_VALUE)x, sy = (SIGNED_VALUE)y;
|
|
if (sx < sy) return INT2FIX(-1);
|
|
return INT2FIX(sx > sy);
|
|
}
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
if (BIGNUM_SIGN(x) == BIGNUM_SIGN(y)) {
|
|
int cmp = bary_cmp(BDIGITS(x), BIGNUM_LEN(x), BDIGITS(y), BIGNUM_LEN(y));
|
|
return INT2FIX(BIGNUM_SIGN(x) ? cmp : -cmp);
|
|
}
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return rb_integer_float_cmp(x, y);
|
|
}
|
|
else {
|
|
return rb_num_coerce_cmp(x, y, idCmp);
|
|
}
|
|
return INT2FIX(BIGNUM_SIGN(x) ? 1 : -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;
|
|
|
|
if (RB_INTEGER_TYPE_P(y)) {
|
|
rel = rb_big_cmp(x, y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
rel = rb_integer_float_cmp(x, y);
|
|
}
|
|
else {
|
|
ID id = 0;
|
|
switch (op) {
|
|
case big_op_gt: id = '>'; break;
|
|
case big_op_ge: id = idGE; break;
|
|
case big_op_lt: id = '<'; break;
|
|
case big_op_le: id = idLE; 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;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_gt(VALUE x, VALUE y)
|
|
{
|
|
return big_op(x, y, big_op_gt);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_ge(VALUE x, VALUE y)
|
|
{
|
|
return big_op(x, y, big_op_ge);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_lt(VALUE x, VALUE y)
|
|
{
|
|
return big_op(x, y, big_op_lt);
|
|
}
|
|
|
|
VALUE
|
|
rb_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>Integer#eql?</code>, which
|
|
* requires <i>obj</i> to be a <code>Integer</code>.
|
|
*
|
|
* 68719476736 == 68719476736.0 #=> true
|
|
*/
|
|
|
|
VALUE
|
|
rb_big_eq(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
return bignorm(x) == y ? Qtrue : Qfalse;
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return rb_integer_float_eq(x, y);
|
|
}
|
|
else {
|
|
return rb_equal(y, x);
|
|
}
|
|
if (BIGNUM_SIGN(x) != BIGNUM_SIGN(y)) return Qfalse;
|
|
if (BIGNUM_LEN(x) != BIGNUM_LEN(y)) return Qfalse;
|
|
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,BIGNUM_LEN(y)) != 0) return Qfalse;
|
|
return Qtrue;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_eql(VALUE x, VALUE y)
|
|
{
|
|
if (!RB_BIGNUM_TYPE_P(y)) return Qfalse;
|
|
if (BIGNUM_SIGN(x) != BIGNUM_SIGN(y)) return Qfalse;
|
|
if (BIGNUM_LEN(x) != BIGNUM_LEN(y)) return Qfalse;
|
|
if (MEMCMP(BDIGITS(x),BDIGITS(y),BDIGIT,BIGNUM_LEN(y)) != 0) return Qfalse;
|
|
return Qtrue;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_uminus(VALUE x)
|
|
{
|
|
VALUE z = rb_big_clone(x);
|
|
|
|
BIGNUM_NEGATE(z);
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_comp(VALUE x)
|
|
{
|
|
VALUE z = rb_big_clone(x);
|
|
BDIGIT *ds = BDIGITS(z);
|
|
long n = BIGNUM_LEN(z);
|
|
|
|
if (!n) return INT2FIX(-1);
|
|
|
|
if (BIGNUM_POSITIVE_P(z)) {
|
|
if (bary_add_one(ds, n)) {
|
|
big_extend_carry(z);
|
|
}
|
|
BIGNUM_SET_NEGATIVE_SIGN(z);
|
|
}
|
|
else {
|
|
bary_neg(ds, n);
|
|
if (bary_add_one(ds, n))
|
|
return INT2FIX(-1);
|
|
bary_neg(ds, n);
|
|
BIGNUM_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 = BIGNUM_LEN(x);
|
|
yn = BIGNUM_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);
|
|
BIGNUM_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 = BIGNUM_LEN(x);
|
|
|
|
if (xn == 0)
|
|
return LONG2NUM(-y0);
|
|
|
|
zn = xn;
|
|
#if SIZEOF_BDIGIT < SIZEOF_LONG
|
|
if (zn < bdigit_roomof(SIZEOF_LONG))
|
|
zn = bdigit_roomof(SIZEOF_LONG);
|
|
#endif
|
|
z = bignew(zn, BIGNUM_SIGN(x));
|
|
zds = BDIGITS(z);
|
|
|
|
#if SIZEOF_BDIGIT >= SIZEOF_LONG
|
|
assert(xn == zn);
|
|
num = (BDIGIT_DBL_SIGNED)xds[0] - y;
|
|
if (xn == 1 && num < 0) {
|
|
BIGNUM_NEGATE(z);
|
|
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_BDIGIT < 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_BDIGIT < 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);
|
|
BIGNUM_NEGATE(z);
|
|
}
|
|
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 = BIGNUM_LEN(x);
|
|
|
|
if (xn == 0)
|
|
return LONG2NUM(y);
|
|
|
|
zn = xn;
|
|
#if SIZEOF_BDIGIT < SIZEOF_LONG
|
|
if (zn < bdigit_roomof(SIZEOF_LONG))
|
|
zn = bdigit_roomof(SIZEOF_LONG);
|
|
#endif
|
|
zn++;
|
|
|
|
z = bignew(zn, BIGNUM_SIGN(x));
|
|
zds = BDIGITS(z);
|
|
|
|
#if SIZEOF_BDIGIT >= 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 VALUE
|
|
bigadd(VALUE x, VALUE y, int sign)
|
|
{
|
|
VALUE z;
|
|
size_t len;
|
|
|
|
sign = (sign == BIGNUM_SIGN(y));
|
|
if (BIGNUM_SIGN(x) != sign) {
|
|
if (sign) return bigsub(y, x);
|
|
return bigsub(x, y);
|
|
}
|
|
|
|
if (BIGNUM_LEN(x) > BIGNUM_LEN(y)) {
|
|
len = BIGNUM_LEN(x) + 1;
|
|
}
|
|
else {
|
|
len = BIGNUM_LEN(y) + 1;
|
|
}
|
|
z = bignew(len, sign);
|
|
|
|
bary_add(BDIGITS(z), BIGNUM_LEN(z),
|
|
BDIGITS(x), BIGNUM_LEN(x),
|
|
BDIGITS(y), BIGNUM_LEN(y));
|
|
|
|
return z;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_plus(VALUE x, VALUE y)
|
|
{
|
|
long n;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
n = FIX2LONG(y);
|
|
if ((n > 0) != BIGNUM_SIGN(x)) {
|
|
if (n < 0) {
|
|
n = -n;
|
|
}
|
|
return bigsub_int(x, n);
|
|
}
|
|
if (n < 0) {
|
|
n = -n;
|
|
}
|
|
return bigadd_int(x, n);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return bignorm(bigadd(x, y, 1));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM(rb_big2dbl(x) + RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '+');
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_big_minus(VALUE x, VALUE y)
|
|
{
|
|
long n;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
n = FIX2LONG(y);
|
|
if ((n > 0) != BIGNUM_SIGN(x)) {
|
|
if (n < 0) {
|
|
n = -n;
|
|
}
|
|
return bigadd_int(x, n);
|
|
}
|
|
if (n < 0) {
|
|
n = -n;
|
|
}
|
|
return bigsub_int(x, n);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return bignorm(bigadd(x, y, 0));
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM(rb_big2dbl(x) - RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, '-');
|
|
}
|
|
}
|
|
|
|
static VALUE
|
|
bigsq(VALUE x)
|
|
{
|
|
long xn, zn;
|
|
VALUE z;
|
|
BDIGIT *xds, *zds;
|
|
|
|
xn = BIGNUM_LEN(x);
|
|
zn = 2 * xn;
|
|
|
|
z = bignew(zn, 1);
|
|
|
|
xds = BDIGITS(x);
|
|
zds = BDIGITS(z);
|
|
|
|
if (xn < NAIVE_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 = BIGNUM_LEN(x);
|
|
yn = BIGNUM_LEN(y);
|
|
zn = xn + yn;
|
|
|
|
z = bignew(zn, BIGNUM_SIGN(x)==BIGNUM_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;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_mul(VALUE x, VALUE y)
|
|
{
|
|
if (FIXNUM_P(y)) {
|
|
y = rb_int2big(FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
return DBL2NUM(rb_big2dbl(x) * RFLOAT_VALUE(y));
|
|
}
|
|
else {
|
|
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 xn = BIGNUM_LEN(x), yn = BIGNUM_LEN(y);
|
|
VALUE z;
|
|
BDIGIT *xds, *yds, *zds;
|
|
BDIGIT dd;
|
|
|
|
VALUE q = Qnil, r = Qnil;
|
|
BDIGIT *qds, *rds;
|
|
long qn, rn;
|
|
|
|
yds = BDIGITS(y);
|
|
BARY_TRUNC(yds, yn);
|
|
if (yn == 0)
|
|
rb_num_zerodiv();
|
|
|
|
xds = BDIGITS(x);
|
|
BARY_TRUNC(xds, xn);
|
|
|
|
if (xn < yn || (xn == yn && xds[xn - 1] < yds[yn - 1])) {
|
|
if (divp) *divp = rb_int2big(0);
|
|
if (modp) *modp = x;
|
|
return Qnil;
|
|
}
|
|
if (yn == 1) {
|
|
dd = yds[0];
|
|
z = bignew(xn, BIGNUM_SIGN(x)==BIGNUM_SIGN(y));
|
|
zds = BDIGITS(z);
|
|
dd = bigdivrem_single(zds, xds, xn, dd);
|
|
if (modp) {
|
|
*modp = rb_uint2big((VALUE)dd);
|
|
BIGNUM_SET_SIGN(*modp, BIGNUM_SIGN(x));
|
|
}
|
|
if (divp) *divp = z;
|
|
return Qnil;
|
|
}
|
|
if (xn == 2 && yn == 2) {
|
|
BDIGIT_DBL x0 = bary2bdigitdbl(xds, 2);
|
|
BDIGIT_DBL y0 = bary2bdigitdbl(yds, 2);
|
|
BDIGIT_DBL q0 = x0 / y0;
|
|
BDIGIT_DBL r0 = x0 % y0;
|
|
if (divp) {
|
|
z = bignew(bdigit_roomof(sizeof(BDIGIT_DBL)), BIGNUM_SIGN(x)==BIGNUM_SIGN(y));
|
|
zds = BDIGITS(z);
|
|
zds[0] = BIGLO(q0);
|
|
zds[1] = BIGLO(BIGDN(q0));
|
|
*divp = z;
|
|
}
|
|
if (modp) {
|
|
z = bignew(bdigit_roomof(sizeof(BDIGIT_DBL)), BIGNUM_SIGN(x));
|
|
zds = BDIGITS(z);
|
|
zds[0] = BIGLO(r0);
|
|
zds[1] = BIGLO(BIGDN(r0));
|
|
*modp = z;
|
|
}
|
|
return Qnil;
|
|
}
|
|
|
|
if (divp) {
|
|
qn = xn + BIGDIVREM_EXTRA_WORDS;
|
|
q = bignew(qn, BIGNUM_SIGN(x)==BIGNUM_SIGN(y));
|
|
qds = BDIGITS(q);
|
|
}
|
|
else {
|
|
qn = 0;
|
|
qds = NULL;
|
|
}
|
|
|
|
if (modp) {
|
|
rn = yn;
|
|
r = bignew(rn, BIGNUM_SIGN(x));
|
|
rds = BDIGITS(r);
|
|
}
|
|
else {
|
|
rn = 0;
|
|
rds = NULL;
|
|
}
|
|
|
|
bary_divmod_branch(qds, qn, rds, rn, xds, xn, yds, yn);
|
|
|
|
if (divp) {
|
|
bigtrunc(q);
|
|
*divp = q;
|
|
}
|
|
if (modp) {
|
|
bigtrunc(r);
|
|
*modp = r;
|
|
}
|
|
|
|
return Qnil;
|
|
}
|
|
|
|
static void
|
|
bigdivmod(VALUE x, VALUE y, volatile VALUE *divp, volatile VALUE *modp)
|
|
{
|
|
VALUE mod;
|
|
|
|
bigdivrem(x, y, divp, &mod);
|
|
if (BIGNUM_SIGN(x) != BIGNUM_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;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
y = rb_int2big(FIX2LONG(y));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
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);
|
|
}
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, op);
|
|
}
|
|
bigdivmod(x, y, &z, 0);
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_div(VALUE x, VALUE y)
|
|
{
|
|
return rb_big_divide(x, y, '/');
|
|
}
|
|
|
|
VALUE
|
|
rb_big_idiv(VALUE x, VALUE y)
|
|
{
|
|
return rb_big_divide(x, y, rb_intern("div"));
|
|
}
|
|
|
|
VALUE
|
|
rb_big_modulo(VALUE x, VALUE y)
|
|
{
|
|
VALUE z;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
y = rb_int2big(FIX2LONG(y));
|
|
}
|
|
else if (!RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_num_coerce_bin(x, y, '%');
|
|
}
|
|
bigdivmod(x, y, 0, &z);
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_remainder(VALUE x, VALUE y)
|
|
{
|
|
VALUE z;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
y = rb_int2big(FIX2LONG(y));
|
|
}
|
|
else if (!RB_BIGNUM_TYPE_P(y)) {
|
|
return rb_num_coerce_bin(x, y, rb_intern("remainder"));
|
|
}
|
|
bigdivrem(x, y, 0, &z);
|
|
|
|
return bignorm(z);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_divmod(VALUE x, VALUE y)
|
|
{
|
|
VALUE div, mod;
|
|
|
|
if (FIXNUM_P(y)) {
|
|
y = rb_int2big(FIX2LONG(y));
|
|
}
|
|
else if (!RB_BIGNUM_TYPE_P(y)) {
|
|
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;
|
|
}
|
|
|
|
enum {DBL_BIGDIG = ((DBL_MANT_DIG + BITSPERDIG) / BITSPERDIG)};
|
|
|
|
static double
|
|
big_fdiv(VALUE x, VALUE y, long ey)
|
|
{
|
|
VALUE z;
|
|
long l, ex;
|
|
|
|
bigtrunc(x);
|
|
l = BIGNUM_LEN(x);
|
|
ex = l * BITSPERDIG - nlz(BDIGITS(x)[l-1]);
|
|
ex -= 2 * DBL_BIGDIG * BITSPERDIG;
|
|
if (ex > BITSPERDIG) ex -= BITSPERDIG;
|
|
else if (ex > 0) ex = 0;
|
|
if (ex) x = big_shift(x, ex);
|
|
|
|
bigdivrem(x, y, &z, 0);
|
|
l = ex - ey;
|
|
#if SIZEOF_LONG > SIZEOF_INT
|
|
{
|
|
/* Visual C++ can't be here */
|
|
if (l > INT_MAX) return HUGE_VAL;
|
|
if (l < INT_MIN) return 0.0;
|
|
}
|
|
#endif
|
|
return ldexp(big2dbl(z), (int)l);
|
|
}
|
|
|
|
static double
|
|
big_fdiv_int(VALUE x, VALUE y)
|
|
{
|
|
long l, ey;
|
|
bigtrunc(y);
|
|
l = BIGNUM_LEN(y);
|
|
ey = l * BITSPERDIG - nlz(BDIGITS(y)[l-1]);
|
|
ey -= DBL_BIGDIG * BITSPERDIG;
|
|
if (ey) y = big_shift(y, ey);
|
|
return big_fdiv(x, y, ey);
|
|
}
|
|
|
|
static double
|
|
big_fdiv_float(VALUE x, VALUE y)
|
|
{
|
|
int i;
|
|
y = dbl2big(ldexp(frexp(RFLOAT_VALUE(y), &i), DBL_MANT_DIG));
|
|
return big_fdiv(x, y, i - DBL_MANT_DIG);
|
|
}
|
|
|
|
double
|
|
rb_big_fdiv_double(VALUE x, VALUE y)
|
|
{
|
|
double dx, dy;
|
|
|
|
dx = big2dbl(x);
|
|
if (FIXNUM_P(y)) {
|
|
dy = (double)FIX2LONG(y);
|
|
if (isinf(dx))
|
|
return big_fdiv_int(x, rb_int2big(FIX2LONG(y)));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
dy = rb_big2dbl(y);
|
|
if (isinf(dx) || isinf(dy))
|
|
return big_fdiv_int(x, y);
|
|
}
|
|
else if (RB_FLOAT_TYPE_P(y)) {
|
|
dy = RFLOAT_VALUE(y);
|
|
if (isnan(dy))
|
|
return dy;
|
|
if (isinf(dx))
|
|
return big_fdiv_float(x, y);
|
|
}
|
|
else {
|
|
return NUM2DBL(rb_num_coerce_bin(x, y, rb_intern("fdiv")));
|
|
}
|
|
return dx / dy;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_fdiv(VALUE x, VALUE y)
|
|
{
|
|
return DBL2NUM(rb_big_fdiv_double(x, y));
|
|
}
|
|
|
|
VALUE
|
|
rb_big_pow(VALUE x, VALUE y)
|
|
{
|
|
double d;
|
|
SIGNED_VALUE yy;
|
|
|
|
again:
|
|
if (y == INT2FIX(0)) return INT2FIX(1);
|
|
if (RB_FLOAT_TYPE_P(y)) {
|
|
d = RFLOAT_VALUE(y);
|
|
if ((BIGNUM_NEGATIVE_P(x) && !BIGZEROP(x)) && d != round(d))
|
|
return rb_funcall(rb_complex_raw1(x), idPow, 1, y);
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
y = bignorm(y);
|
|
if (FIXNUM_P(y))
|
|
goto again;
|
|
rb_warn("in a**b, b may be too big");
|
|
d = rb_big2dbl(y);
|
|
}
|
|
else if (FIXNUM_P(y)) {
|
|
yy = FIX2LONG(y);
|
|
|
|
if (yy < 0)
|
|
return rb_funcall(rb_rational_raw1(x), idPow, 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;
|
|
}
|
|
else {
|
|
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);
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
return rb_num_coerce_bin(x, y, idPow);
|
|
}
|
|
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_BDIGIT >= SIZEOF_LONG
|
|
if (!hibitsy) {
|
|
y &= xds[0];
|
|
return LONG2NUM(y);
|
|
}
|
|
#endif
|
|
|
|
zn = xn;
|
|
#if SIZEOF_BDIGIT < SIZEOF_LONG
|
|
if (hibitsx && zn < bdigit_roomof(SIZEOF_LONG))
|
|
zn = bdigit_roomof(SIZEOF_LONG);
|
|
#endif
|
|
|
|
z = bignew(zn, 0);
|
|
zds = BDIGITS(z);
|
|
|
|
#if SIZEOF_BDIGIT >= SIZEOF_LONG
|
|
i = 1;
|
|
zds[0] = xds[0] & BIGLO(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);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_and(VALUE x, VALUE y)
|
|
{
|
|
VALUE z;
|
|
BDIGIT *ds1, *ds2, *zds;
|
|
long i, xn, yn, n1, n2;
|
|
BDIGIT hibitsx, hibitsy;
|
|
BDIGIT hibits1, hibits2;
|
|
VALUE tmpv;
|
|
BDIGIT tmph;
|
|
long tmpn;
|
|
|
|
if (!RB_INTEGER_TYPE_P(y)) {
|
|
return rb_num_coerce_bit(x, y, '&');
|
|
}
|
|
|
|
hibitsx = abs2twocomp(&x, &xn);
|
|
if (FIXNUM_P(y)) {
|
|
return bigand_int(x, xn, hibitsx, FIX2LONG(y));
|
|
}
|
|
hibitsy = abs2twocomp(&y, &yn);
|
|
if (xn > yn) {
|
|
tmpv = x; x = y; y = tmpv;
|
|
tmpn = xn; xn = yn; yn = tmpn;
|
|
tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
|
|
}
|
|
n1 = xn;
|
|
n2 = yn;
|
|
ds1 = BDIGITS(x);
|
|
ds2 = BDIGITS(y);
|
|
hibits1 = hibitsx;
|
|
hibits2 = hibitsy;
|
|
|
|
if (!hibits1)
|
|
n2 = n1;
|
|
|
|
z = bignew(n2, 0);
|
|
zds = BDIGITS(z);
|
|
|
|
for (i=0; i<n1; i++) {
|
|
zds[i] = ds1[i] & ds2[i];
|
|
}
|
|
for (; i<n2; 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 = BIGNUM_LEN(x);
|
|
#if SIZEOF_BDIGIT < SIZEOF_LONG
|
|
if (zn < bdigit_roomof(SIZEOF_LONG))
|
|
zn = bdigit_roomof(SIZEOF_LONG);
|
|
#endif
|
|
z = bignew(zn, 0);
|
|
zds = BDIGITS(z);
|
|
|
|
#if SIZEOF_BDIGIT >= SIZEOF_LONG
|
|
i = 1;
|
|
zds[0] = xds[0] | BIGLO(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);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_or(VALUE x, VALUE y)
|
|
{
|
|
VALUE z;
|
|
BDIGIT *ds1, *ds2, *zds;
|
|
long i, xn, yn, n1, n2;
|
|
BDIGIT hibitsx, hibitsy;
|
|
BDIGIT hibits1, hibits2;
|
|
VALUE tmpv;
|
|
BDIGIT tmph;
|
|
long tmpn;
|
|
|
|
if (!RB_INTEGER_TYPE_P(y)) {
|
|
return rb_num_coerce_bit(x, y, '|');
|
|
}
|
|
|
|
hibitsx = abs2twocomp(&x, &xn);
|
|
if (FIXNUM_P(y)) {
|
|
return bigor_int(x, xn, hibitsx, FIX2LONG(y));
|
|
}
|
|
hibitsy = abs2twocomp(&y, &yn);
|
|
if (xn > yn) {
|
|
tmpv = x; x = y; y = tmpv;
|
|
tmpn = xn; xn = yn; yn = tmpn;
|
|
tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
|
|
}
|
|
n1 = xn;
|
|
n2 = yn;
|
|
ds1 = BDIGITS(x);
|
|
ds2 = BDIGITS(y);
|
|
hibits1 = hibitsx;
|
|
hibits2 = hibitsy;
|
|
|
|
if (hibits1)
|
|
n2 = n1;
|
|
|
|
z = bignew(n2, 0);
|
|
zds = BDIGITS(z);
|
|
|
|
for (i=0; i<n1; i++) {
|
|
zds[i] = ds1[i] | ds2[i];
|
|
}
|
|
for (; i<n2; 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 = BIGNUM_LEN(x);
|
|
#if SIZEOF_BDIGIT < SIZEOF_LONG
|
|
if (zn < bdigit_roomof(SIZEOF_LONG))
|
|
zn = bdigit_roomof(SIZEOF_LONG);
|
|
#endif
|
|
z = bignew(zn, 0);
|
|
zds = BDIGITS(z);
|
|
|
|
#if SIZEOF_BDIGIT >= SIZEOF_LONG
|
|
i = 1;
|
|
zds[0] = xds[0] ^ BIGLO(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);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_xor(VALUE x, VALUE y)
|
|
{
|
|
VALUE z;
|
|
BDIGIT *ds1, *ds2, *zds;
|
|
long i, xn, yn, n1, n2;
|
|
BDIGIT hibitsx, hibitsy;
|
|
BDIGIT hibits1, hibits2;
|
|
VALUE tmpv;
|
|
BDIGIT tmph;
|
|
long tmpn;
|
|
|
|
if (!RB_INTEGER_TYPE_P(y)) {
|
|
return rb_num_coerce_bit(x, y, '^');
|
|
}
|
|
|
|
hibitsx = abs2twocomp(&x, &xn);
|
|
if (FIXNUM_P(y)) {
|
|
return bigxor_int(x, xn, hibitsx, FIX2LONG(y));
|
|
}
|
|
hibitsy = abs2twocomp(&y, &yn);
|
|
if (xn > yn) {
|
|
tmpv = x; x = y; y = tmpv;
|
|
tmpn = xn; xn = yn; yn = tmpn;
|
|
tmph = hibitsx; hibitsx = hibitsy; hibitsy = tmph;
|
|
}
|
|
n1 = xn;
|
|
n2 = yn;
|
|
ds1 = BDIGITS(x);
|
|
ds2 = BDIGITS(y);
|
|
hibits1 = hibitsx;
|
|
hibits2 = hibitsy;
|
|
|
|
z = bignew(n2, 0);
|
|
zds = BDIGITS(z);
|
|
|
|
for (i=0; i<n1; i++) {
|
|
zds[i] = ds1[i] ^ ds2[i];
|
|
}
|
|
for (; i<n2; i++) {
|
|
zds[i] = hibitsx ^ ds2[i];
|
|
}
|
|
twocomp2abs_bang(z, (hibits1 ^ hibits2) != 0);
|
|
RB_GC_GUARD(x);
|
|
RB_GC_GUARD(y);
|
|
return bignorm(z);
|
|
}
|
|
|
|
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 >> bit_length(BITSPERDIG-1);
|
|
return bignorm(big_shift3(x, lshift_p, shift_numdigits, shift_numbits));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return bignorm(big_shift2(x, 1, y));
|
|
}
|
|
y = rb_to_int(y);
|
|
}
|
|
}
|
|
|
|
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 >> bit_length(BITSPERDIG-1);
|
|
return bignorm(big_shift3(x, lshift_p, shift_numdigits, shift_numbits));
|
|
}
|
|
else if (RB_BIGNUM_TYPE_P(y)) {
|
|
return bignorm(big_shift2(x, 0, y));
|
|
}
|
|
y = rb_to_int(y);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_big_aref(VALUE x, VALUE y)
|
|
{
|
|
BDIGIT *xds;
|
|
size_t shift;
|
|
size_t i, s1, s2;
|
|
long l;
|
|
BDIGIT bit;
|
|
|
|
if (RB_BIGNUM_TYPE_P(y)) {
|
|
if (BIGNUM_NEGATIVE_P(y))
|
|
return INT2FIX(0);
|
|
bigtrunc(y);
|
|
if (BIGSIZE(y) > sizeof(size_t)) {
|
|
out_of_range:
|
|
return BIGNUM_SIGN(x) ? INT2FIX(0) : INT2FIX(1);
|
|
}
|
|
#if SIZEOF_SIZE_T <= SIZEOF_LONG
|
|
shift = big2ulong(y, "long");
|
|
#else
|
|
shift = big2ull(y, "long long");
|
|
#endif
|
|
}
|
|
else {
|
|
l = NUM2LONG(y);
|
|
if (l < 0) return INT2FIX(0);
|
|
shift = (size_t)l;
|
|
}
|
|
s1 = shift/BITSPERDIG;
|
|
s2 = shift%BITSPERDIG;
|
|
bit = (BDIGIT)1 << s2;
|
|
|
|
if (s1 >= BIGNUM_LEN(x)) goto out_of_range;
|
|
|
|
xds = BDIGITS(x);
|
|
if (BIGNUM_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);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_hash(VALUE x)
|
|
{
|
|
st_index_t hash;
|
|
|
|
hash = rb_memhash(BDIGITS(x), sizeof(BDIGIT)*BIGNUM_LEN(x)) ^ BIGNUM_SIGN(x);
|
|
return ST2FIX(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_int_coerce(VALUE x, VALUE y)
|
|
{
|
|
if (RB_INTEGER_TYPE_P(y)) {
|
|
return rb_assoc_new(y, x);
|
|
}
|
|
else {
|
|
x = rb_Float(x);
|
|
y = rb_Float(y);
|
|
return rb_assoc_new(y, x);
|
|
}
|
|
}
|
|
|
|
VALUE
|
|
rb_big_abs(VALUE x)
|
|
{
|
|
if (BIGNUM_NEGATIVE_P(x)) {
|
|
x = rb_big_clone(x);
|
|
BIGNUM_SET_POSITIVE_SIGN(x);
|
|
}
|
|
return x;
|
|
}
|
|
|
|
int
|
|
rb_big_sign(VALUE x)
|
|
{
|
|
return BIGNUM_SIGN(x);
|
|
}
|
|
|
|
size_t
|
|
rb_big_size(VALUE big)
|
|
{
|
|
return BIGSIZE(big);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_size_m(VALUE big)
|
|
{
|
|
return SIZET2NUM(rb_big_size(big));
|
|
}
|
|
|
|
VALUE
|
|
rb_big_bit_length(VALUE big)
|
|
{
|
|
int nlz_bits;
|
|
size_t numbytes;
|
|
|
|
static const BDIGIT char_bit[1] = { CHAR_BIT };
|
|
BDIGIT numbytes_bary[bdigit_roomof(sizeof(size_t))];
|
|
BDIGIT nlz_bary[1];
|
|
BDIGIT result_bary[bdigit_roomof(sizeof(size_t)+1)];
|
|
|
|
numbytes = rb_absint_size(big, &nlz_bits);
|
|
|
|
if (numbytes == 0)
|
|
return LONG2FIX(0);
|
|
|
|
if (BIGNUM_NEGATIVE_P(big) && rb_absint_singlebit_p(big)) {
|
|
if (nlz_bits != CHAR_BIT-1) {
|
|
nlz_bits++;
|
|
}
|
|
else {
|
|
nlz_bits = 0;
|
|
numbytes--;
|
|
}
|
|
}
|
|
|
|
if (numbytes <= SIZE_MAX / CHAR_BIT) {
|
|
return SIZET2NUM(numbytes * CHAR_BIT - nlz_bits);
|
|
}
|
|
|
|
nlz_bary[0] = nlz_bits;
|
|
|
|
bary_unpack(BARY_ARGS(numbytes_bary), &numbytes, 1, sizeof(numbytes), 0,
|
|
INTEGER_PACK_NATIVE_BYTE_ORDER);
|
|
BARY_SHORT_MUL(result_bary, numbytes_bary, char_bit);
|
|
BARY_SUB(result_bary, result_bary, nlz_bary);
|
|
|
|
return rb_integer_unpack(result_bary, numberof(result_bary), sizeof(BDIGIT), 0,
|
|
INTEGER_PACK_LSWORD_FIRST|INTEGER_PACK_NATIVE_BYTE_ORDER);
|
|
}
|
|
|
|
VALUE
|
|
rb_big_odd_p(VALUE num)
|
|
{
|
|
if (BIGNUM_LEN(num) != 0 && BDIGITS(num)[0] & 1) {
|
|
return Qtrue;
|
|
}
|
|
return Qfalse;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_even_p(VALUE num)
|
|
{
|
|
if (BIGNUM_LEN(num) != 0 && BDIGITS(num)[0] & 1) {
|
|
return Qfalse;
|
|
}
|
|
return Qtrue;
|
|
}
|
|
|
|
unsigned long rb_ulong_isqrt(unsigned long);
|
|
#if SIZEOF_BDIGIT*2 > SIZEOF_LONG
|
|
BDIGIT rb_bdigit_dbl_isqrt(BDIGIT_DBL);
|
|
# ifdef ULL_TO_DOUBLE
|
|
# define BDIGIT_DBL_TO_DOUBLE(n) ULL_TO_DOUBLE(n)
|
|
# endif
|
|
#else
|
|
# define rb_bdigit_dbl_isqrt(x) (BDIGIT)rb_ulong_isqrt(x)
|
|
#endif
|
|
#ifndef BDIGIT_DBL_TO_DOUBLE
|
|
# define BDIGIT_DBL_TO_DOUBLE(n) (double)(n)
|
|
#endif
|
|
|
|
static BDIGIT *
|
|
estimate_initial_sqrt(VALUE *xp, const size_t xn, const BDIGIT *nds, size_t len)
|
|
{
|
|
enum {dbl_per_bdig = roomof(DBL_MANT_DIG,BITSPERDIG)};
|
|
const int zbits = nlz(nds[len-1]);
|
|
VALUE x = *xp = bignew_1(0, xn, 1); /* division may release the GVL */
|
|
BDIGIT *xds = BDIGITS(x);
|
|
BDIGIT_DBL d = bary2bdigitdbl(nds+len-dbl_per_bdig, dbl_per_bdig);
|
|
BDIGIT lowbits = 1;
|
|
int rshift = (int)((BITSPERDIG*2-zbits+(len&BITSPERDIG&1) - DBL_MANT_DIG + 1) & ~1);
|
|
double f;
|
|
|
|
if (rshift > 0) {
|
|
lowbits = (BDIGIT)d & ~(~(BDIGIT)1U << rshift);
|
|
d >>= rshift;
|
|
}
|
|
else if (rshift < 0) {
|
|
d <<= -rshift;
|
|
d |= nds[len-dbl_per_bdig-1] >> (BITSPERDIG+rshift);
|
|
}
|
|
f = sqrt(BDIGIT_DBL_TO_DOUBLE(d));
|
|
d = (BDIGIT_DBL)ceil(f);
|
|
if (BDIGIT_DBL_TO_DOUBLE(d) == f) {
|
|
if (lowbits || (lowbits = !bary_zero_p(nds, len-dbl_per_bdig)))
|
|
++d;
|
|
}
|
|
else {
|
|
lowbits = 1;
|
|
}
|
|
rshift /= 2;
|
|
rshift += (2-(len&1))*BITSPERDIG/2;
|
|
if (rshift >= 0) {
|
|
d <<= rshift;
|
|
}
|
|
BDIGITS_ZERO(xds, xn-2);
|
|
bdigitdbl2bary(&xds[xn-2], 2, d);
|
|
|
|
if (!lowbits) return NULL; /* special case, exact result */
|
|
return xds;
|
|
}
|
|
|
|
VALUE
|
|
rb_big_isqrt(VALUE n)
|
|
{
|
|
BDIGIT *nds = BDIGITS(n);
|
|
size_t len = BIGNUM_LEN(n);
|
|
size_t xn = (len+1) / 2;
|
|
VALUE x;
|
|
BDIGIT *xds;
|
|
|
|
if (len <= 2) {
|
|
BDIGIT sq = rb_bdigit_dbl_isqrt(bary2bdigitdbl(nds, len));
|
|
#if SIZEOF_BDIGIT > SIZEOF_LONG
|
|
return ULL2NUM(sq);
|
|
#else
|
|
return ULONG2NUM(sq);
|
|
#endif
|
|
}
|
|
else if ((xds = estimate_initial_sqrt(&x, xn, nds, len)) != 0) {
|
|
size_t tn = xn + BIGDIVREM_EXTRA_WORDS;
|
|
VALUE t = bignew_1(0, tn, 1);
|
|
BDIGIT *tds = BDIGITS(t);
|
|
tn = BIGNUM_LEN(t);
|
|
|
|
/* t = n/x */
|
|
while (bary_divmod_branch(tds, tn, NULL, 0, nds, len, xds, xn),
|
|
bary_cmp(tds, tn, xds, xn) < 0) {
|
|
int carry;
|
|
BARY_TRUNC(tds, tn);
|
|
/* x = (x+t)/2 */
|
|
carry = bary_add(xds, xn, xds, xn, tds, tn);
|
|
bary_small_rshift(xds, xds, xn, 1, carry);
|
|
tn = BIGNUM_LEN(t);
|
|
}
|
|
rb_big_realloc(t, 0);
|
|
rb_gc_force_recycle(t);
|
|
}
|
|
RBASIC_SET_CLASS_RAW(x, rb_cInteger);
|
|
return x;
|
|
}
|
|
|
|
#ifdef USE_GMP
|
|
static void
|
|
bary_powm_gmp(BDIGIT *zds, size_t zn, const BDIGIT *xds, size_t xn, const BDIGIT *yds, size_t yn, const BDIGIT *mds, size_t mn)
|
|
{
|
|
const size_t nails = (sizeof(BDIGIT)-SIZEOF_BDIGIT)*CHAR_BIT;
|
|
mpz_t z, x, y, m;
|
|
size_t count;
|
|
mpz_init(x);
|
|
mpz_init(y);
|
|
mpz_init(m);
|
|
mpz_init(z);
|
|
mpz_import(x, xn, -1, sizeof(BDIGIT), 0, nails, xds);
|
|
mpz_import(y, yn, -1, sizeof(BDIGIT), 0, nails, yds);
|
|
mpz_import(m, mn, -1, sizeof(BDIGIT), 0, nails, mds);
|
|
mpz_powm(z, x, y, m);
|
|
mpz_export(zds, &count, -1, sizeof(BDIGIT), 0, nails, z);
|
|
BDIGITS_ZERO(zds+count, zn-count);
|
|
mpz_clear(x);
|
|
mpz_clear(y);
|
|
mpz_clear(m);
|
|
mpz_clear(z);
|
|
}
|
|
#endif
|
|
|
|
static VALUE
|
|
int_pow_tmp3(VALUE x, VALUE y, VALUE m, int nega_flg)
|
|
{
|
|
#ifdef USE_GMP
|
|
VALUE z;
|
|
size_t xn, yn, mn, zn;
|
|
|
|
if (FIXNUM_P(x)) {
|
|
x = rb_int2big(FIX2LONG(x));
|
|
}
|
|
if (FIXNUM_P(y)) {
|
|
y = rb_int2big(FIX2LONG(y));
|
|
}
|
|
assert(RB_BIGNUM_TYPE_P(m));
|
|
xn = BIGNUM_LEN(x);
|
|
yn = BIGNUM_LEN(y);
|
|
mn = BIGNUM_LEN(m);
|
|
zn = mn;
|
|
z = bignew(zn, 1);
|
|
bary_powm_gmp(BDIGITS(z), zn, BDIGITS(x), xn, BDIGITS(y), yn, BDIGITS(m), mn);
|
|
if (nega_flg & BIGNUM_POSITIVE_P(z)) {
|
|
z = rb_funcall(z, '-', 1, m);
|
|
}
|
|
RB_GC_GUARD(x);
|
|
RB_GC_GUARD(y);
|
|
RB_GC_GUARD(m);
|
|
return rb_big_norm(z);
|
|
#else
|
|
VALUE tmp = LONG2FIX(1L);
|
|
long yy;
|
|
|
|
for (/*NOP*/; ! FIXNUM_P(y); y = rb_funcall(y, rb_intern(">>"), 1, LONG2FIX(1L))) {
|
|
if (RTEST(rb_funcall(y, rb_intern("odd?"), 0))) {
|
|
tmp = rb_funcall(tmp, '*', 1, x);
|
|
tmp = rb_int_modulo(tmp, m);
|
|
}
|
|
x = rb_funcall(x, '*', 1, x);
|
|
x = rb_int_modulo(x, m);
|
|
}
|
|
for (yy = FIX2LONG(y); yy; yy >>= 1L) {
|
|
if (yy & 1L) {
|
|
tmp = rb_funcall(tmp, '*', 1, x);
|
|
tmp = rb_int_modulo(tmp, m);
|
|
}
|
|
x = rb_funcall(x, '*', 1, x);
|
|
x = rb_int_modulo(x, m);
|
|
}
|
|
|
|
if (nega_flg && RTEST(rb_funcall(tmp, rb_intern("positive?"), 0))) {
|
|
tmp = rb_funcall(tmp, '-', 1, m);
|
|
}
|
|
return tmp;
|
|
#endif
|
|
}
|
|
|
|
/*
|
|
* Integer#pow
|
|
*/
|
|
|
|
static VALUE
|
|
int_pow_tmp1(VALUE x, VALUE y, long mm, int nega_flg)
|
|
{
|
|
long xx = FIX2LONG(x);
|
|
long tmp = 1L;
|
|
long yy;
|
|
|
|
for (/*NOP*/; ! FIXNUM_P(y); y = rb_funcall(y, idGTGT, 1, LONG2FIX(1L))) {
|
|
if (RTEST(rb_int_odd_p(y))) {
|
|
tmp = (tmp * xx) % mm;
|
|
}
|
|
xx = (xx * xx) % mm;
|
|
}
|
|
for (yy = FIX2LONG(y); yy; yy >>= 1L) {
|
|
if (yy & 1L) {
|
|
tmp = (tmp * xx) % mm;
|
|
}
|
|
xx = (xx * xx) % mm;
|
|
}
|
|
|
|
if (nega_flg && tmp) {
|
|
tmp -= mm;
|
|
}
|
|
return LONG2FIX(tmp);
|
|
}
|
|
|
|
static VALUE
|
|
int_pow_tmp2(VALUE x, VALUE y, long mm, int nega_flg)
|
|
{
|
|
long tmp = 1L;
|
|
long yy;
|
|
#ifdef DLONG
|
|
const DLONG m = mm;
|
|
long tmp2 = tmp;
|
|
long xx = FIX2LONG(x);
|
|
# define MUL_MODULO(a, b, c) (long)(((DLONG)(a) * (DLONG)(b)) % (c))
|
|
#else
|
|
const VALUE m = LONG2FIX(mm);
|
|
VALUE tmp2 = LONG2FIX(tmp);
|
|
VALUE xx = x;
|
|
# define MUL_MODULO(a, b, c) rb_int_modulo(rb_fix_mul_fix((a), (b)), (c))
|
|
#endif
|
|
|
|
for (/*NOP*/; ! FIXNUM_P(y); y = rb_funcall(y, idGTGT, 1, LONG2FIX(1L))) {
|
|
if (RTEST(rb_int_odd_p(y))) {
|
|
tmp2 = MUL_MODULO(tmp2, xx, m);
|
|
}
|
|
xx = MUL_MODULO(xx, xx, m);
|
|
}
|
|
for (yy = FIX2LONG(y); yy; yy >>= 1L) {
|
|
if (yy & 1L) {
|
|
tmp2 = MUL_MODULO(tmp2, xx, m);
|
|
}
|
|
xx = MUL_MODULO(xx, xx, m);
|
|
}
|
|
|
|
#ifdef DLONG
|
|
tmp = tmp2;
|
|
#else
|
|
tmp = FIX2LONG(tmp2);
|
|
#endif
|
|
if (nega_flg && tmp) {
|
|
tmp -= mm;
|
|
}
|
|
return LONG2FIX(tmp);
|
|
}
|
|
|
|
/*
|
|
* Document-method: Integer#pow
|
|
* call-seq:
|
|
* integer.pow(numeric) -> numeric
|
|
* integer.pow(integer, integer) -> integer
|
|
*
|
|
* Returns (modular) exponentiation as:
|
|
*
|
|
* a.pow(b) #=> same as a**b
|
|
* a.pow(b, m) #=> same as (a**b) % m, but avoids huge temporary values
|
|
*/
|
|
VALUE
|
|
rb_int_powm(int const argc, VALUE * const argv, VALUE const num)
|
|
{
|
|
rb_check_arity(argc, 1, 2);
|
|
|
|
if (argc == 1) {
|
|
return rb_funcall(num, rb_intern("**"), 1, argv[0]);
|
|
}
|
|
else {
|
|
VALUE const a = num;
|
|
VALUE const b = argv[0];
|
|
VALUE m = argv[1];
|
|
int nega_flg = 0;
|
|
if ( ! RB_INTEGER_TYPE_P(b)) {
|
|
rb_raise(rb_eTypeError, "Integer#pow() 2nd argument not allowed unless a 1st argument is integer");
|
|
}
|
|
if (rb_num_negative_int_p(b)) {
|
|
rb_raise(rb_eRangeError, "Integer#pow() 1st argument cannot be negative when 2nd argument specified");
|
|
}
|
|
if (!RB_INTEGER_TYPE_P(m)) {
|
|
rb_raise(rb_eTypeError, "Integer#pow() 2nd argument not allowed unless all arguments are integers");
|
|
}
|
|
|
|
if (rb_num_negative_int_p(m)) {
|
|
m = rb_funcall(m, idUMinus, 0);
|
|
nega_flg = 1;
|
|
}
|
|
|
|
if (!rb_num_positive_int_p(m)) {
|
|
rb_num_zerodiv();
|
|
}
|
|
if (FIXNUM_P(m)) {
|
|
long const half_val = (long)HALF_LONG_MSB;
|
|
long const mm = FIX2LONG(m);
|
|
if (mm <= half_val) {
|
|
return int_pow_tmp1(rb_int_modulo(a, m), b, mm, nega_flg);
|
|
} else {
|
|
return int_pow_tmp2(rb_int_modulo(a, m), b, mm, nega_flg);
|
|
}
|
|
} else if (RB_TYPE_P(m, T_BIGNUM)) {
|
|
return int_pow_tmp3(rb_int_modulo(a, m), b, m, nega_flg);
|
|
}
|
|
}
|
|
UNREACHABLE;
|
|
}
|
|
|
|
/*
|
|
* 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)
|
|
{
|
|
#ifndef RUBY_INTEGER_UNIFICATION
|
|
rb_cBignum = rb_cInteger;
|
|
#endif
|
|
rb_define_const(rb_cObject, "Bignum", rb_cInteger);
|
|
rb_deprecate_constant(rb_cObject, "Bignum");
|
|
|
|
rb_define_method(rb_cInteger, "coerce", rb_int_coerce, 1);
|
|
|
|
#ifdef USE_GMP
|
|
/* The version of loaded GMP. */
|
|
rb_define_const(rb_cInteger, "GMP_VERSION", rb_sprintf("GMP %s", gmp_version));
|
|
#endif
|
|
|
|
power_cache_init();
|
|
}
|