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76950b4281
On x86-64-MinGW the size of long is 4. As long is used for
SCM_FIXNUM_BIT, that would mean incompatible .go files, and waste of
cell space. So we would like to use long long, but the GMP interface
uses long.
To get around this, the x86-64-MinGW port now requires the use of
mini-GMP. Mini-GMP has been changed to use intptr_t and uintptr_t.
Likewise, "integers.{h,c}" and "numbers.{h,c}" now use intptr_t instead
of scm_t_inum or long, and uintptr_t instead of unsigned long.
* configure.ac: When x86_64-w64-mingw32, require mini-GMP.
* libguile/mini-gmp.h: Use intptr_t instead of long, uintptr_t instead
of unsigned long throughout.
* libguile/mini-gmp.c: Likewise.
* libguile/scm.h (SCM_INTPTR_T_BIT): New define.
* libguile/numbers.h (SCM_FIXNUM_BIT): Use it.
* libguile/numbers.c (L1, UL1): New macros. Use them thoughout instead
of 1L, 1UL.
(verify): Use SCM_INTPTR_T_BIT.
(verify): Use SCM_INTPTR_T_MAX and SCM_INTPTR_T_MIN.
(scm_from_inum): Remove macro.
Use intptr_t and uintptr_t instead of scm_t_inum or long, and unsigned
long.
* libguile/numbers.h (scm_from_intptr, scm_from_uintptr, scm_to_intptr,
scm_to_uintptr): New defines.
* libguile/integers.h: Use intptr_t and uintptr_t instead of scm_t_inum
and unsigned long.
* libguile/integers.c (L1) : New macro. Use it thoughout instead of 1L.
Use intptr_t and uintptr_t instead of long and unsigned long.
(long_magnitude): Rename to...
(intptr_t_magnitude): ...this. Use intptr_t, uintptr_t.
(negative_long): Rename to...
(negative_t_intptr): ...this. Use uintptr_t, INTPTR_MIN.
(inum_magnitude): Use intptr_t.
(ulong_to_bignum): Rename to...
(uintptr_t_to_bignum): ...this. Use uintptr_t.
(long_to_bignum): Rename to...
(intptr_t_to_bignum): ...this. Use intptr_t.
(long_to_scm): Rename to...
(intptr_t_to_scm): ...this. Use intptr_to_bignum.
(ulong_to_scm): Rename to...
(uintptr_t_to_scm): ...this. Use uintptr_to_bignum.
(long_sign): Rename to..
(intptr_t_sign): ...this. Use SCM_SIZEOF_INTPTR_T.
(bignum_cmp_long): Rename to...
(bignum_cmp_intptr_t): ...this. Use uintptr_t.
* libguile/array-map.c (array_compare): Use uintptr_t instead of
unsigned long and intptr_t instead of long.
* libguile/arrays.c (make-shared-array): Use ssize_t instead of long.
* libguile/bytevectors.c (is_signed_int32, is_unsigned_int32)
[MINGW32 && __x86_64__]: Use ULL.
(twos_complement): Use uintptr_t instead of unsigned long.
* libguile/hash.c (JENKINS_LOOKUP3_HASHWORD2): Likewise.
(narrow_string_hash, wide_string_hash, scm_i_string_hash,
scm_i_locale_string_hash, scm_i_latin1_string_hash,
scm_i_utf8_string_hash, scm_i_struct_hash, scm_raw_ihashq,
scm_raw_ihash): Use and return uintptr_t instead of unsigned long.
(scm_hashv, scm_hash): Use SCM_UINTPTR_T_MAX.
* libguile/hash.h (scm_i_locale_string_hash, scm_i_latin1_string_hash,
scm_i_utf8_string_hash): update prototypes.
* libguile/scmsigs.c (sigaction): Use intptr_t instead of long.
* libguile/strings.c (scm_i_make_symbol, (scm_i_c_make_symbol): Use
uintptr_t instead of unsigned long.
* libguile/strings.h (scm_i_make_symbol, (scm_i_c_make_symbol): Update
declacations.
* libguile/srfi-60.c: Use scm_to_uintptr, scm_from_intptr and variants
throughout.
* libguile/symbols.c (symbol-hash): Use scm_from_uintptr.
Co-authored-by: Mike Gran <spk121@yahoo.com>
Co-authored-by: Andy Wingo <wingo@pobox.com>
4578 lines
87 KiB
C
4578 lines
87 KiB
C
/* mini-gmp, a minimalistic implementation of a GNU GMP subset.
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Contributed to the GNU project by Niels Möller
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Copyright 1991-1997, 1999-2019,2021 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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/* NOTE: All functions in this file which are not declared in
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mini-gmp.h are internal, and are not intended to be compatible
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with GMP or with future versions of mini-gmp. */
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/* Much of the material copied from GMP files, including: gmp-impl.h,
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longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c,
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mpn/generic/lshift.c, mpn/generic/mul_1.c,
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mpn/generic/mul_basecase.c, mpn/generic/rshift.c,
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mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c,
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mpn/generic/submul_1.c. */
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#ifdef HAVE_CONFIG_H
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# include <config.h>
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#endif
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#include <assert.h>
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#include <ctype.h>
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#include <limits.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include "mini-gmp.h"
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#if !defined(MINI_GMP_DONT_USE_FLOAT_H)
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#include <float.h>
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#endif
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/* Macros */
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#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT)
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#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0)
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#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1))
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#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2))
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#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1)
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#define GMP_ULONG_BITS (sizeof(uintptr_t) * CHAR_BIT)
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#define GMP_ULONG_HIGHBIT ((uintptr_t) 1 << (GMP_ULONG_BITS - 1))
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#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x))
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#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1))
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#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b))
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#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b))
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#define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b)))
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#if defined(DBL_MANT_DIG) && FLT_RADIX == 2
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#define GMP_DBL_MANT_BITS DBL_MANT_DIG
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#else
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#define GMP_DBL_MANT_BITS (53)
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#endif
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/* Return non-zero if xp,xsize and yp,ysize overlap.
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If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no
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overlap. If both these are false, there's an overlap. */
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#define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize) \
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((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp))
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#define gmp_assert_nocarry(x) do { \
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mp_limb_t __cy = (x); \
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assert (__cy == 0); \
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} while (0)
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#define gmp_clz(count, x) do { \
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mp_limb_t __clz_x = (x); \
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unsigned __clz_c = 0; \
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int LOCAL_SHIFT_BITS = 8; \
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if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS) \
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for (; \
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(__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \
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__clz_c += 8) \
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{ __clz_x <<= LOCAL_SHIFT_BITS; } \
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for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \
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__clz_x <<= 1; \
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(count) = __clz_c; \
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} while (0)
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#define gmp_ctz(count, x) do { \
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mp_limb_t __ctz_x = (x); \
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unsigned __ctz_c = 0; \
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gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \
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(count) = GMP_LIMB_BITS - 1 - __ctz_c; \
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} while (0)
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#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \
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do { \
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mp_limb_t __x; \
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__x = (al) + (bl); \
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(sh) = (ah) + (bh) + (__x < (al)); \
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(sl) = __x; \
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} while (0)
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#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \
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do { \
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mp_limb_t __x; \
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__x = (al) - (bl); \
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(sh) = (ah) - (bh) - ((al) < (bl)); \
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(sl) = __x; \
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} while (0)
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#define gmp_umul_ppmm(w1, w0, u, v) \
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do { \
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int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \
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if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \
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{ \
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unsigned int __ww = (unsigned int) (u) * (v); \
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w0 = (mp_limb_t) __ww; \
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w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
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} \
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else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \
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{ \
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uintptr_t __ww = (uintptr_t) (u) * (v); \
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w0 = (mp_limb_t) __ww; \
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w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \
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} \
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else { \
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mp_limb_t __x0, __x1, __x2, __x3; \
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unsigned __ul, __vl, __uh, __vh; \
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mp_limb_t __u = (u), __v = (v); \
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\
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__ul = __u & GMP_LLIMB_MASK; \
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__uh = __u >> (GMP_LIMB_BITS / 2); \
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__vl = __v & GMP_LLIMB_MASK; \
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__vh = __v >> (GMP_LIMB_BITS / 2); \
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\
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__x0 = (mp_limb_t) __ul * __vl; \
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__x1 = (mp_limb_t) __ul * __vh; \
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__x2 = (mp_limb_t) __uh * __vl; \
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__x3 = (mp_limb_t) __uh * __vh; \
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\
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__x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \
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__x1 += __x2; /* but this indeed can */ \
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if (__x1 < __x2) /* did we get it? */ \
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__x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \
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\
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(w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \
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(w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \
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} \
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} while (0)
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#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
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do { \
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mp_limb_t _qh, _ql, _r, _mask; \
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gmp_umul_ppmm (_qh, _ql, (nh), (di)); \
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gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \
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_r = (nl) - _qh * (d); \
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_mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \
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_qh += _mask; \
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_r += _mask & (d); \
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if (_r >= (d)) \
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{ \
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_r -= (d); \
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_qh++; \
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} \
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\
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(r) = _r; \
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(q) = _qh; \
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} while (0)
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#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \
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do { \
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mp_limb_t _q0, _t1, _t0, _mask; \
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gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \
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gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \
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\
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/* Compute the two most significant limbs of n - q'd */ \
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(r1) = (n1) - (d1) * (q); \
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gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \
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gmp_umul_ppmm (_t1, _t0, (d0), (q)); \
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gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \
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(q)++; \
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\
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/* Conditionally adjust q and the remainders */ \
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_mask = - (mp_limb_t) ((r1) >= _q0); \
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(q) += _mask; \
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gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \
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if ((r1) >= (d1)) \
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{ \
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if ((r1) > (d1) || (r0) >= (d0)) \
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{ \
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(q)++; \
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gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \
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} \
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} \
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} while (0)
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/* Swap macros. */
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#define MP_LIMB_T_SWAP(x, y) \
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do { \
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mp_limb_t __mp_limb_t_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_limb_t_swap__tmp; \
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} while (0)
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#define MP_SIZE_T_SWAP(x, y) \
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do { \
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mp_size_t __mp_size_t_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_size_t_swap__tmp; \
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} while (0)
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#define MP_BITCNT_T_SWAP(x,y) \
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do { \
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mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_bitcnt_t_swap__tmp; \
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} while (0)
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#define MP_PTR_SWAP(x, y) \
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do { \
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mp_ptr __mp_ptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_ptr_swap__tmp; \
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} while (0)
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#define MP_SRCPTR_SWAP(x, y) \
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do { \
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mp_srcptr __mp_srcptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mp_srcptr_swap__tmp; \
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} while (0)
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#define MPN_PTR_SWAP(xp,xs, yp,ys) \
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do { \
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MP_PTR_SWAP (xp, yp); \
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MP_SIZE_T_SWAP (xs, ys); \
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} while(0)
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#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \
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do { \
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MP_SRCPTR_SWAP (xp, yp); \
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MP_SIZE_T_SWAP (xs, ys); \
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} while(0)
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#define MPZ_PTR_SWAP(x, y) \
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do { \
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mpz_ptr __mpz_ptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mpz_ptr_swap__tmp; \
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} while (0)
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#define MPZ_SRCPTR_SWAP(x, y) \
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do { \
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mpz_srcptr __mpz_srcptr_swap__tmp = (x); \
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(x) = (y); \
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(y) = __mpz_srcptr_swap__tmp; \
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} while (0)
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const int mp_bits_per_limb = GMP_LIMB_BITS;
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/* Memory allocation and other helper functions. */
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static void
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gmp_die (const char *msg)
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{
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fprintf (stderr, "%s\n", msg);
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abort();
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}
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static void *
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gmp_default_alloc (size_t size)
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{
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void *p;
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assert (size > 0);
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p = malloc (size);
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if (!p)
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gmp_die("gmp_default_alloc: Virtual memory exhausted.");
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return p;
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}
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static void *
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gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size)
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{
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void * p;
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p = realloc (old, new_size);
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if (!p)
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gmp_die("gmp_default_realloc: Virtual memory exhausted.");
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return p;
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}
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static void
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gmp_default_free (void *p, size_t unused_size)
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{
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free (p);
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}
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static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc;
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static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc;
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static void (*gmp_free_func) (void *, size_t) = gmp_default_free;
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void
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mp_get_memory_functions (void *(**alloc_func) (size_t),
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void *(**realloc_func) (void *, size_t, size_t),
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void (**free_func) (void *, size_t))
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{
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if (alloc_func)
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*alloc_func = gmp_allocate_func;
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if (realloc_func)
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*realloc_func = gmp_reallocate_func;
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if (free_func)
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*free_func = gmp_free_func;
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}
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void
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mp_set_memory_functions (void *(*alloc_func) (size_t),
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void *(*realloc_func) (void *, size_t, size_t),
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void (*free_func) (void *, size_t))
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{
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if (!alloc_func)
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alloc_func = gmp_default_alloc;
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if (!realloc_func)
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realloc_func = gmp_default_realloc;
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if (!free_func)
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free_func = gmp_default_free;
|
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|
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gmp_allocate_func = alloc_func;
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gmp_reallocate_func = realloc_func;
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gmp_free_func = free_func;
|
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}
|
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|
||
#define gmp_xalloc(size) ((*gmp_allocate_func)((size)))
|
||
#define gmp_free(p) ((*gmp_free_func) ((p), 0))
|
||
|
||
static mp_ptr
|
||
gmp_xalloc_limbs (mp_size_t size)
|
||
{
|
||
return (mp_ptr) gmp_xalloc (size * sizeof (mp_limb_t));
|
||
}
|
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|
||
static mp_ptr
|
||
gmp_xrealloc_limbs (mp_ptr old, mp_size_t size)
|
||
{
|
||
assert (size > 0);
|
||
return (mp_ptr) (*gmp_reallocate_func) (old, 0, size * sizeof (mp_limb_t));
|
||
}
|
||
|
||
|
||
/* MPN interface */
|
||
|
||
void
|
||
mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
|
||
{
|
||
mp_size_t i;
|
||
for (i = 0; i < n; i++)
|
||
d[i] = s[i];
|
||
}
|
||
|
||
void
|
||
mpn_copyd (mp_ptr d, mp_srcptr s, mp_size_t n)
|
||
{
|
||
while (--n >= 0)
|
||
d[n] = s[n];
|
||
}
|
||
|
||
int
|
||
mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
|
||
{
|
||
while (--n >= 0)
|
||
{
|
||
if (ap[n] != bp[n])
|
||
return ap[n] > bp[n] ? 1 : -1;
|
||
}
|
||
return 0;
|
||
}
|
||
|
||
static int
|
||
mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
|
||
{
|
||
if (an != bn)
|
||
return an < bn ? -1 : 1;
|
||
else
|
||
return mpn_cmp (ap, bp, an);
|
||
}
|
||
|
||
static mp_size_t
|
||
mpn_normalized_size (mp_srcptr xp, mp_size_t n)
|
||
{
|
||
while (n > 0 && xp[n-1] == 0)
|
||
--n;
|
||
return n;
|
||
}
|
||
|
||
int
|
||
mpn_zero_p(mp_srcptr rp, mp_size_t n)
|
||
{
|
||
return mpn_normalized_size (rp, n) == 0;
|
||
}
|
||
|
||
void
|
||
mpn_zero (mp_ptr rp, mp_size_t n)
|
||
{
|
||
while (--n >= 0)
|
||
rp[n] = 0;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
|
||
{
|
||
mp_size_t i;
|
||
|
||
assert (n > 0);
|
||
i = 0;
|
||
do
|
||
{
|
||
mp_limb_t r = ap[i] + b;
|
||
/* Carry out */
|
||
b = (r < b);
|
||
rp[i] = r;
|
||
}
|
||
while (++i < n);
|
||
|
||
return b;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
|
||
{
|
||
mp_size_t i;
|
||
mp_limb_t cy;
|
||
|
||
for (i = 0, cy = 0; i < n; i++)
|
||
{
|
||
mp_limb_t a, b, r;
|
||
a = ap[i]; b = bp[i];
|
||
r = a + cy;
|
||
cy = (r < cy);
|
||
r += b;
|
||
cy += (r < b);
|
||
rp[i] = r;
|
||
}
|
||
return cy;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
|
||
{
|
||
mp_limb_t cy;
|
||
|
||
assert (an >= bn);
|
||
|
||
cy = mpn_add_n (rp, ap, bp, bn);
|
||
if (an > bn)
|
||
cy = mpn_add_1 (rp + bn, ap + bn, an - bn, cy);
|
||
return cy;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
|
||
{
|
||
mp_size_t i;
|
||
|
||
assert (n > 0);
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
mp_limb_t a = ap[i];
|
||
/* Carry out */
|
||
mp_limb_t cy = a < b;
|
||
rp[i] = a - b;
|
||
b = cy;
|
||
}
|
||
while (++i < n);
|
||
|
||
return b;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
|
||
{
|
||
mp_size_t i;
|
||
mp_limb_t cy;
|
||
|
||
for (i = 0, cy = 0; i < n; i++)
|
||
{
|
||
mp_limb_t a, b;
|
||
a = ap[i]; b = bp[i];
|
||
b += cy;
|
||
cy = (b < cy);
|
||
cy += (a < b);
|
||
rp[i] = a - b;
|
||
}
|
||
return cy;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
|
||
{
|
||
mp_limb_t cy;
|
||
|
||
assert (an >= bn);
|
||
|
||
cy = mpn_sub_n (rp, ap, bp, bn);
|
||
if (an > bn)
|
||
cy = mpn_sub_1 (rp + bn, ap + bn, an - bn, cy);
|
||
return cy;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_mul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
|
||
{
|
||
mp_limb_t ul, cl, hpl, lpl;
|
||
|
||
assert (n >= 1);
|
||
|
||
cl = 0;
|
||
do
|
||
{
|
||
ul = *up++;
|
||
gmp_umul_ppmm (hpl, lpl, ul, vl);
|
||
|
||
lpl += cl;
|
||
cl = (lpl < cl) + hpl;
|
||
|
||
*rp++ = lpl;
|
||
}
|
||
while (--n != 0);
|
||
|
||
return cl;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_addmul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
|
||
{
|
||
mp_limb_t ul, cl, hpl, lpl, rl;
|
||
|
||
assert (n >= 1);
|
||
|
||
cl = 0;
|
||
do
|
||
{
|
||
ul = *up++;
|
||
gmp_umul_ppmm (hpl, lpl, ul, vl);
|
||
|
||
lpl += cl;
|
||
cl = (lpl < cl) + hpl;
|
||
|
||
rl = *rp;
|
||
lpl = rl + lpl;
|
||
cl += lpl < rl;
|
||
*rp++ = lpl;
|
||
}
|
||
while (--n != 0);
|
||
|
||
return cl;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_submul_1 (mp_ptr rp, mp_srcptr up, mp_size_t n, mp_limb_t vl)
|
||
{
|
||
mp_limb_t ul, cl, hpl, lpl, rl;
|
||
|
||
assert (n >= 1);
|
||
|
||
cl = 0;
|
||
do
|
||
{
|
||
ul = *up++;
|
||
gmp_umul_ppmm (hpl, lpl, ul, vl);
|
||
|
||
lpl += cl;
|
||
cl = (lpl < cl) + hpl;
|
||
|
||
rl = *rp;
|
||
lpl = rl - lpl;
|
||
cl += lpl > rl;
|
||
*rp++ = lpl;
|
||
}
|
||
while (--n != 0);
|
||
|
||
return cl;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_mul (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_srcptr vp, mp_size_t vn)
|
||
{
|
||
assert (un >= vn);
|
||
assert (vn >= 1);
|
||
assert (!GMP_MPN_OVERLAP_P(rp, un + vn, up, un));
|
||
assert (!GMP_MPN_OVERLAP_P(rp, un + vn, vp, vn));
|
||
|
||
/* We first multiply by the low order limb. This result can be
|
||
stored, not added, to rp. We also avoid a loop for zeroing this
|
||
way. */
|
||
|
||
rp[un] = mpn_mul_1 (rp, up, un, vp[0]);
|
||
|
||
/* Now accumulate the product of up[] and the next higher limb from
|
||
vp[]. */
|
||
|
||
while (--vn >= 1)
|
||
{
|
||
rp += 1, vp += 1;
|
||
rp[un] = mpn_addmul_1 (rp, up, un, vp[0]);
|
||
}
|
||
return rp[un];
|
||
}
|
||
|
||
void
|
||
mpn_mul_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
|
||
{
|
||
mpn_mul (rp, ap, n, bp, n);
|
||
}
|
||
|
||
void
|
||
mpn_sqr (mp_ptr rp, mp_srcptr ap, mp_size_t n)
|
||
{
|
||
mpn_mul (rp, ap, n, ap, n);
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_lshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
|
||
{
|
||
mp_limb_t high_limb, low_limb;
|
||
unsigned int tnc;
|
||
mp_limb_t retval;
|
||
|
||
assert (n >= 1);
|
||
assert (cnt >= 1);
|
||
assert (cnt < GMP_LIMB_BITS);
|
||
|
||
up += n;
|
||
rp += n;
|
||
|
||
tnc = GMP_LIMB_BITS - cnt;
|
||
low_limb = *--up;
|
||
retval = low_limb >> tnc;
|
||
high_limb = (low_limb << cnt);
|
||
|
||
while (--n != 0)
|
||
{
|
||
low_limb = *--up;
|
||
*--rp = high_limb | (low_limb >> tnc);
|
||
high_limb = (low_limb << cnt);
|
||
}
|
||
*--rp = high_limb;
|
||
|
||
return retval;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_rshift (mp_ptr rp, mp_srcptr up, mp_size_t n, unsigned int cnt)
|
||
{
|
||
mp_limb_t high_limb, low_limb;
|
||
unsigned int tnc;
|
||
mp_limb_t retval;
|
||
|
||
assert (n >= 1);
|
||
assert (cnt >= 1);
|
||
assert (cnt < GMP_LIMB_BITS);
|
||
|
||
tnc = GMP_LIMB_BITS - cnt;
|
||
high_limb = *up++;
|
||
retval = (high_limb << tnc);
|
||
low_limb = high_limb >> cnt;
|
||
|
||
while (--n != 0)
|
||
{
|
||
high_limb = *up++;
|
||
*rp++ = low_limb | (high_limb << tnc);
|
||
low_limb = high_limb >> cnt;
|
||
}
|
||
*rp = low_limb;
|
||
|
||
return retval;
|
||
}
|
||
|
||
static mp_bitcnt_t
|
||
mpn_common_scan (mp_limb_t limb, mp_size_t i, mp_srcptr up, mp_size_t un,
|
||
mp_limb_t ux)
|
||
{
|
||
unsigned cnt;
|
||
|
||
assert (ux == 0 || ux == GMP_LIMB_MAX);
|
||
assert (0 <= i && i <= un );
|
||
|
||
while (limb == 0)
|
||
{
|
||
i++;
|
||
if (i == un)
|
||
return (ux == 0 ? ~(mp_bitcnt_t) 0 : un * GMP_LIMB_BITS);
|
||
limb = ux ^ up[i];
|
||
}
|
||
gmp_ctz (cnt, limb);
|
||
return (mp_bitcnt_t) i * GMP_LIMB_BITS + cnt;
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpn_scan1 (mp_srcptr ptr, mp_bitcnt_t bit)
|
||
{
|
||
mp_size_t i;
|
||
i = bit / GMP_LIMB_BITS;
|
||
|
||
return mpn_common_scan ( ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
|
||
i, ptr, i, 0);
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpn_scan0 (mp_srcptr ptr, mp_bitcnt_t bit)
|
||
{
|
||
mp_size_t i;
|
||
i = bit / GMP_LIMB_BITS;
|
||
|
||
return mpn_common_scan (~ptr[i] & (GMP_LIMB_MAX << (bit % GMP_LIMB_BITS)),
|
||
i, ptr, i, GMP_LIMB_MAX);
|
||
}
|
||
|
||
void
|
||
mpn_com (mp_ptr rp, mp_srcptr up, mp_size_t n)
|
||
{
|
||
while (--n >= 0)
|
||
*rp++ = ~ *up++;
|
||
}
|
||
|
||
mp_limb_t
|
||
mpn_neg (mp_ptr rp, mp_srcptr up, mp_size_t n)
|
||
{
|
||
while (*up == 0)
|
||
{
|
||
*rp = 0;
|
||
if (!--n)
|
||
return 0;
|
||
++up; ++rp;
|
||
}
|
||
*rp = - *up;
|
||
mpn_com (++rp, ++up, --n);
|
||
return 1;
|
||
}
|
||
|
||
|
||
/* MPN division interface. */
|
||
|
||
/* The 3/2 inverse is defined as
|
||
|
||
m = floor( (B^3-1) / (B u1 + u0)) - B
|
||
*/
|
||
mp_limb_t
|
||
mpn_invert_3by2 (mp_limb_t u1, mp_limb_t u0)
|
||
{
|
||
mp_limb_t r, m;
|
||
|
||
{
|
||
mp_limb_t p, ql;
|
||
unsigned ul, uh, qh;
|
||
|
||
/* For notation, let b denote the half-limb base, so that B = b^2.
|
||
Split u1 = b uh + ul. */
|
||
ul = u1 & GMP_LLIMB_MASK;
|
||
uh = u1 >> (GMP_LIMB_BITS / 2);
|
||
|
||
/* Approximation of the high half of quotient. Differs from the 2/1
|
||
inverse of the half limb uh, since we have already subtracted
|
||
u0. */
|
||
qh = (u1 ^ GMP_LIMB_MAX) / uh;
|
||
|
||
/* Adjust to get a half-limb 3/2 inverse, i.e., we want
|
||
|
||
qh' = floor( (b^3 - 1) / u) - b = floor ((b^3 - b u - 1) / u
|
||
= floor( (b (~u) + b-1) / u),
|
||
|
||
and the remainder
|
||
|
||
r = b (~u) + b-1 - qh (b uh + ul)
|
||
= b (~u - qh uh) + b-1 - qh ul
|
||
|
||
Subtraction of qh ul may underflow, which implies adjustments.
|
||
But by normalization, 2 u >= B > qh ul, so we need to adjust by
|
||
at most 2.
|
||
*/
|
||
|
||
r = ((~u1 - (mp_limb_t) qh * uh) << (GMP_LIMB_BITS / 2)) | GMP_LLIMB_MASK;
|
||
|
||
p = (mp_limb_t) qh * ul;
|
||
/* Adjustment steps taken from udiv_qrnnd_c */
|
||
if (r < p)
|
||
{
|
||
qh--;
|
||
r += u1;
|
||
if (r >= u1) /* i.e. we didn't get carry when adding to r */
|
||
if (r < p)
|
||
{
|
||
qh--;
|
||
r += u1;
|
||
}
|
||
}
|
||
r -= p;
|
||
|
||
/* Low half of the quotient is
|
||
|
||
ql = floor ( (b r + b-1) / u1).
|
||
|
||
This is a 3/2 division (on half-limbs), for which qh is a
|
||
suitable inverse. */
|
||
|
||
p = (r >> (GMP_LIMB_BITS / 2)) * qh + r;
|
||
/* Unlike full-limb 3/2, we can add 1 without overflow. For this to
|
||
work, it is essential that ql is a full mp_limb_t. */
|
||
ql = (p >> (GMP_LIMB_BITS / 2)) + 1;
|
||
|
||
/* By the 3/2 trick, we don't need the high half limb. */
|
||
r = (r << (GMP_LIMB_BITS / 2)) + GMP_LLIMB_MASK - ql * u1;
|
||
|
||
if (r >= (GMP_LIMB_MAX & (p << (GMP_LIMB_BITS / 2))))
|
||
{
|
||
ql--;
|
||
r += u1;
|
||
}
|
||
m = ((mp_limb_t) qh << (GMP_LIMB_BITS / 2)) + ql;
|
||
if (r >= u1)
|
||
{
|
||
m++;
|
||
r -= u1;
|
||
}
|
||
}
|
||
|
||
/* Now m is the 2/1 inverse of u1. If u0 > 0, adjust it to become a
|
||
3/2 inverse. */
|
||
if (u0 > 0)
|
||
{
|
||
mp_limb_t th, tl;
|
||
r = ~r;
|
||
r += u0;
|
||
if (r < u0)
|
||
{
|
||
m--;
|
||
if (r >= u1)
|
||
{
|
||
m--;
|
||
r -= u1;
|
||
}
|
||
r -= u1;
|
||
}
|
||
gmp_umul_ppmm (th, tl, u0, m);
|
||
r += th;
|
||
if (r < th)
|
||
{
|
||
m--;
|
||
m -= ((r > u1) | ((r == u1) & (tl > u0)));
|
||
}
|
||
}
|
||
|
||
return m;
|
||
}
|
||
|
||
struct gmp_div_inverse
|
||
{
|
||
/* Normalization shift count. */
|
||
unsigned shift;
|
||
/* Normalized divisor (d0 unused for mpn_div_qr_1) */
|
||
mp_limb_t d1, d0;
|
||
/* Inverse, for 2/1 or 3/2. */
|
||
mp_limb_t di;
|
||
};
|
||
|
||
static void
|
||
mpn_div_qr_1_invert (struct gmp_div_inverse *inv, mp_limb_t d)
|
||
{
|
||
unsigned shift;
|
||
|
||
assert (d > 0);
|
||
gmp_clz (shift, d);
|
||
inv->shift = shift;
|
||
inv->d1 = d << shift;
|
||
inv->di = mpn_invert_limb (inv->d1);
|
||
}
|
||
|
||
static void
|
||
mpn_div_qr_2_invert (struct gmp_div_inverse *inv,
|
||
mp_limb_t d1, mp_limb_t d0)
|
||
{
|
||
unsigned shift;
|
||
|
||
assert (d1 > 0);
|
||
gmp_clz (shift, d1);
|
||
inv->shift = shift;
|
||
if (shift > 0)
|
||
{
|
||
d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
|
||
d0 <<= shift;
|
||
}
|
||
inv->d1 = d1;
|
||
inv->d0 = d0;
|
||
inv->di = mpn_invert_3by2 (d1, d0);
|
||
}
|
||
|
||
static void
|
||
mpn_div_qr_invert (struct gmp_div_inverse *inv,
|
||
mp_srcptr dp, mp_size_t dn)
|
||
{
|
||
assert (dn > 0);
|
||
|
||
if (dn == 1)
|
||
mpn_div_qr_1_invert (inv, dp[0]);
|
||
else if (dn == 2)
|
||
mpn_div_qr_2_invert (inv, dp[1], dp[0]);
|
||
else
|
||
{
|
||
unsigned shift;
|
||
mp_limb_t d1, d0;
|
||
|
||
d1 = dp[dn-1];
|
||
d0 = dp[dn-2];
|
||
assert (d1 > 0);
|
||
gmp_clz (shift, d1);
|
||
inv->shift = shift;
|
||
if (shift > 0)
|
||
{
|
||
d1 = (d1 << shift) | (d0 >> (GMP_LIMB_BITS - shift));
|
||
d0 = (d0 << shift) | (dp[dn-3] >> (GMP_LIMB_BITS - shift));
|
||
}
|
||
inv->d1 = d1;
|
||
inv->d0 = d0;
|
||
inv->di = mpn_invert_3by2 (d1, d0);
|
||
}
|
||
}
|
||
|
||
/* Not matching current public gmp interface, rather corresponding to
|
||
the sbpi1_div_* functions. */
|
||
static mp_limb_t
|
||
mpn_div_qr_1_preinv (mp_ptr qp, mp_srcptr np, mp_size_t nn,
|
||
const struct gmp_div_inverse *inv)
|
||
{
|
||
mp_limb_t d, di;
|
||
mp_limb_t r;
|
||
mp_ptr tp = NULL;
|
||
|
||
if (inv->shift > 0)
|
||
{
|
||
/* Shift, reusing qp area if possible. In-place shift if qp == np. */
|
||
tp = qp ? qp : gmp_xalloc_limbs (nn);
|
||
r = mpn_lshift (tp, np, nn, inv->shift);
|
||
np = tp;
|
||
}
|
||
else
|
||
r = 0;
|
||
|
||
d = inv->d1;
|
||
di = inv->di;
|
||
while (--nn >= 0)
|
||
{
|
||
mp_limb_t q;
|
||
|
||
gmp_udiv_qrnnd_preinv (q, r, r, np[nn], d, di);
|
||
if (qp)
|
||
qp[nn] = q;
|
||
}
|
||
if ((inv->shift > 0) && (tp != qp))
|
||
gmp_free (tp);
|
||
|
||
return r >> inv->shift;
|
||
}
|
||
|
||
static void
|
||
mpn_div_qr_2_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
|
||
const struct gmp_div_inverse *inv)
|
||
{
|
||
unsigned shift;
|
||
mp_size_t i;
|
||
mp_limb_t d1, d0, di, r1, r0;
|
||
|
||
assert (nn >= 2);
|
||
shift = inv->shift;
|
||
d1 = inv->d1;
|
||
d0 = inv->d0;
|
||
di = inv->di;
|
||
|
||
if (shift > 0)
|
||
r1 = mpn_lshift (np, np, nn, shift);
|
||
else
|
||
r1 = 0;
|
||
|
||
r0 = np[nn - 1];
|
||
|
||
i = nn - 2;
|
||
do
|
||
{
|
||
mp_limb_t n0, q;
|
||
n0 = np[i];
|
||
gmp_udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di);
|
||
|
||
if (qp)
|
||
qp[i] = q;
|
||
}
|
||
while (--i >= 0);
|
||
|
||
if (shift > 0)
|
||
{
|
||
assert ((r0 & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - shift))) == 0);
|
||
r0 = (r0 >> shift) | (r1 << (GMP_LIMB_BITS - shift));
|
||
r1 >>= shift;
|
||
}
|
||
|
||
np[1] = r1;
|
||
np[0] = r0;
|
||
}
|
||
|
||
static void
|
||
mpn_div_qr_pi1 (mp_ptr qp,
|
||
mp_ptr np, mp_size_t nn, mp_limb_t n1,
|
||
mp_srcptr dp, mp_size_t dn,
|
||
mp_limb_t dinv)
|
||
{
|
||
mp_size_t i;
|
||
|
||
mp_limb_t d1, d0;
|
||
mp_limb_t cy, cy1;
|
||
mp_limb_t q;
|
||
|
||
assert (dn > 2);
|
||
assert (nn >= dn);
|
||
|
||
d1 = dp[dn - 1];
|
||
d0 = dp[dn - 2];
|
||
|
||
assert ((d1 & GMP_LIMB_HIGHBIT) != 0);
|
||
/* Iteration variable is the index of the q limb.
|
||
*
|
||
* We divide <n1, np[dn-1+i], np[dn-2+i], np[dn-3+i],..., np[i]>
|
||
* by <d1, d0, dp[dn-3], ..., dp[0] >
|
||
*/
|
||
|
||
i = nn - dn;
|
||
do
|
||
{
|
||
mp_limb_t n0 = np[dn-1+i];
|
||
|
||
if (n1 == d1 && n0 == d0)
|
||
{
|
||
q = GMP_LIMB_MAX;
|
||
mpn_submul_1 (np+i, dp, dn, q);
|
||
n1 = np[dn-1+i]; /* update n1, last loop's value will now be invalid */
|
||
}
|
||
else
|
||
{
|
||
gmp_udiv_qr_3by2 (q, n1, n0, n1, n0, np[dn-2+i], d1, d0, dinv);
|
||
|
||
cy = mpn_submul_1 (np + i, dp, dn-2, q);
|
||
|
||
cy1 = n0 < cy;
|
||
n0 = n0 - cy;
|
||
cy = n1 < cy1;
|
||
n1 = n1 - cy1;
|
||
np[dn-2+i] = n0;
|
||
|
||
if (cy != 0)
|
||
{
|
||
n1 += d1 + mpn_add_n (np + i, np + i, dp, dn - 1);
|
||
q--;
|
||
}
|
||
}
|
||
|
||
if (qp)
|
||
qp[i] = q;
|
||
}
|
||
while (--i >= 0);
|
||
|
||
np[dn - 1] = n1;
|
||
}
|
||
|
||
static void
|
||
mpn_div_qr_preinv (mp_ptr qp, mp_ptr np, mp_size_t nn,
|
||
mp_srcptr dp, mp_size_t dn,
|
||
const struct gmp_div_inverse *inv)
|
||
{
|
||
assert (dn > 0);
|
||
assert (nn >= dn);
|
||
|
||
if (dn == 1)
|
||
np[0] = mpn_div_qr_1_preinv (qp, np, nn, inv);
|
||
else if (dn == 2)
|
||
mpn_div_qr_2_preinv (qp, np, nn, inv);
|
||
else
|
||
{
|
||
mp_limb_t nh;
|
||
unsigned shift;
|
||
|
||
assert (inv->d1 == dp[dn-1]);
|
||
assert (inv->d0 == dp[dn-2]);
|
||
assert ((inv->d1 & GMP_LIMB_HIGHBIT) != 0);
|
||
|
||
shift = inv->shift;
|
||
if (shift > 0)
|
||
nh = mpn_lshift (np, np, nn, shift);
|
||
else
|
||
nh = 0;
|
||
|
||
mpn_div_qr_pi1 (qp, np, nn, nh, dp, dn, inv->di);
|
||
|
||
if (shift > 0)
|
||
gmp_assert_nocarry (mpn_rshift (np, np, dn, shift));
|
||
}
|
||
}
|
||
|
||
static void
|
||
mpn_div_qr (mp_ptr qp, mp_ptr np, mp_size_t nn, mp_srcptr dp, mp_size_t dn)
|
||
{
|
||
struct gmp_div_inverse inv;
|
||
mp_ptr tp = NULL;
|
||
|
||
assert (dn > 0);
|
||
assert (nn >= dn);
|
||
|
||
mpn_div_qr_invert (&inv, dp, dn);
|
||
if (dn > 2 && inv.shift > 0)
|
||
{
|
||
tp = gmp_xalloc_limbs (dn);
|
||
gmp_assert_nocarry (mpn_lshift (tp, dp, dn, inv.shift));
|
||
dp = tp;
|
||
}
|
||
mpn_div_qr_preinv (qp, np, nn, dp, dn, &inv);
|
||
if (tp)
|
||
gmp_free (tp);
|
||
}
|
||
|
||
|
||
/* MPN base conversion. */
|
||
static unsigned
|
||
mpn_base_power_of_two_p (unsigned b)
|
||
{
|
||
switch (b)
|
||
{
|
||
case 2: return 1;
|
||
case 4: return 2;
|
||
case 8: return 3;
|
||
case 16: return 4;
|
||
case 32: return 5;
|
||
case 64: return 6;
|
||
case 128: return 7;
|
||
case 256: return 8;
|
||
default: return 0;
|
||
}
|
||
}
|
||
|
||
struct mpn_base_info
|
||
{
|
||
/* bb is the largest power of the base which fits in one limb, and
|
||
exp is the corresponding exponent. */
|
||
unsigned exp;
|
||
mp_limb_t bb;
|
||
};
|
||
|
||
static void
|
||
mpn_get_base_info (struct mpn_base_info *info, mp_limb_t b)
|
||
{
|
||
mp_limb_t m;
|
||
mp_limb_t p;
|
||
unsigned exp;
|
||
|
||
m = GMP_LIMB_MAX / b;
|
||
for (exp = 1, p = b; p <= m; exp++)
|
||
p *= b;
|
||
|
||
info->exp = exp;
|
||
info->bb = p;
|
||
}
|
||
|
||
static mp_bitcnt_t
|
||
mpn_limb_size_in_base_2 (mp_limb_t u)
|
||
{
|
||
unsigned shift;
|
||
|
||
assert (u > 0);
|
||
gmp_clz (shift, u);
|
||
return GMP_LIMB_BITS - shift;
|
||
}
|
||
|
||
static size_t
|
||
mpn_get_str_bits (unsigned char *sp, unsigned bits, mp_srcptr up, mp_size_t un)
|
||
{
|
||
unsigned char mask;
|
||
size_t sn, j;
|
||
mp_size_t i;
|
||
unsigned shift;
|
||
|
||
sn = ((un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1])
|
||
+ bits - 1) / bits;
|
||
|
||
mask = (1U << bits) - 1;
|
||
|
||
for (i = 0, j = sn, shift = 0; j-- > 0;)
|
||
{
|
||
unsigned char digit = up[i] >> shift;
|
||
|
||
shift += bits;
|
||
|
||
if (shift >= GMP_LIMB_BITS && ++i < un)
|
||
{
|
||
shift -= GMP_LIMB_BITS;
|
||
digit |= up[i] << (bits - shift);
|
||
}
|
||
sp[j] = digit & mask;
|
||
}
|
||
return sn;
|
||
}
|
||
|
||
/* We generate digits from the least significant end, and reverse at
|
||
the end. */
|
||
static size_t
|
||
mpn_limb_get_str (unsigned char *sp, mp_limb_t w,
|
||
const struct gmp_div_inverse *binv)
|
||
{
|
||
mp_size_t i;
|
||
for (i = 0; w > 0; i++)
|
||
{
|
||
mp_limb_t h, l, r;
|
||
|
||
h = w >> (GMP_LIMB_BITS - binv->shift);
|
||
l = w << binv->shift;
|
||
|
||
gmp_udiv_qrnnd_preinv (w, r, h, l, binv->d1, binv->di);
|
||
assert ((r & (GMP_LIMB_MAX >> (GMP_LIMB_BITS - binv->shift))) == 0);
|
||
r >>= binv->shift;
|
||
|
||
sp[i] = r;
|
||
}
|
||
return i;
|
||
}
|
||
|
||
static size_t
|
||
mpn_get_str_other (unsigned char *sp,
|
||
int base, const struct mpn_base_info *info,
|
||
mp_ptr up, mp_size_t un)
|
||
{
|
||
struct gmp_div_inverse binv;
|
||
size_t sn;
|
||
size_t i;
|
||
|
||
mpn_div_qr_1_invert (&binv, base);
|
||
|
||
sn = 0;
|
||
|
||
if (un > 1)
|
||
{
|
||
struct gmp_div_inverse bbinv;
|
||
mpn_div_qr_1_invert (&bbinv, info->bb);
|
||
|
||
do
|
||
{
|
||
mp_limb_t w;
|
||
size_t done;
|
||
w = mpn_div_qr_1_preinv (up, up, un, &bbinv);
|
||
un -= (up[un-1] == 0);
|
||
done = mpn_limb_get_str (sp + sn, w, &binv);
|
||
|
||
for (sn += done; done < info->exp; done++)
|
||
sp[sn++] = 0;
|
||
}
|
||
while (un > 1);
|
||
}
|
||
sn += mpn_limb_get_str (sp + sn, up[0], &binv);
|
||
|
||
/* Reverse order */
|
||
for (i = 0; 2*i + 1 < sn; i++)
|
||
{
|
||
unsigned char t = sp[i];
|
||
sp[i] = sp[sn - i - 1];
|
||
sp[sn - i - 1] = t;
|
||
}
|
||
|
||
return sn;
|
||
}
|
||
|
||
size_t
|
||
mpn_get_str (unsigned char *sp, int base, mp_ptr up, mp_size_t un)
|
||
{
|
||
unsigned bits;
|
||
|
||
assert (un > 0);
|
||
assert (up[un-1] > 0);
|
||
|
||
bits = mpn_base_power_of_two_p (base);
|
||
if (bits)
|
||
return mpn_get_str_bits (sp, bits, up, un);
|
||
else
|
||
{
|
||
struct mpn_base_info info;
|
||
|
||
mpn_get_base_info (&info, base);
|
||
return mpn_get_str_other (sp, base, &info, up, un);
|
||
}
|
||
}
|
||
|
||
static mp_size_t
|
||
mpn_set_str_bits (mp_ptr rp, const unsigned char *sp, size_t sn,
|
||
unsigned bits)
|
||
{
|
||
mp_size_t rn;
|
||
size_t j;
|
||
unsigned shift;
|
||
|
||
for (j = sn, rn = 0, shift = 0; j-- > 0; )
|
||
{
|
||
if (shift == 0)
|
||
{
|
||
rp[rn++] = sp[j];
|
||
shift += bits;
|
||
}
|
||
else
|
||
{
|
||
rp[rn-1] |= (mp_limb_t) sp[j] << shift;
|
||
shift += bits;
|
||
if (shift >= GMP_LIMB_BITS)
|
||
{
|
||
shift -= GMP_LIMB_BITS;
|
||
if (shift > 0)
|
||
rp[rn++] = (mp_limb_t) sp[j] >> (bits - shift);
|
||
}
|
||
}
|
||
}
|
||
rn = mpn_normalized_size (rp, rn);
|
||
return rn;
|
||
}
|
||
|
||
/* Result is usually normalized, except for all-zero input, in which
|
||
case a single zero limb is written at *RP, and 1 is returned. */
|
||
static mp_size_t
|
||
mpn_set_str_other (mp_ptr rp, const unsigned char *sp, size_t sn,
|
||
mp_limb_t b, const struct mpn_base_info *info)
|
||
{
|
||
mp_size_t rn;
|
||
mp_limb_t w;
|
||
unsigned k;
|
||
size_t j;
|
||
|
||
assert (sn > 0);
|
||
|
||
k = 1 + (sn - 1) % info->exp;
|
||
|
||
j = 0;
|
||
w = sp[j++];
|
||
while (--k != 0)
|
||
w = w * b + sp[j++];
|
||
|
||
rp[0] = w;
|
||
|
||
for (rn = 1; j < sn;)
|
||
{
|
||
mp_limb_t cy;
|
||
|
||
w = sp[j++];
|
||
for (k = 1; k < info->exp; k++)
|
||
w = w * b + sp[j++];
|
||
|
||
cy = mpn_mul_1 (rp, rp, rn, info->bb);
|
||
cy += mpn_add_1 (rp, rp, rn, w);
|
||
if (cy > 0)
|
||
rp[rn++] = cy;
|
||
}
|
||
assert (j == sn);
|
||
|
||
return rn;
|
||
}
|
||
|
||
mp_size_t
|
||
mpn_set_str (mp_ptr rp, const unsigned char *sp, size_t sn, int base)
|
||
{
|
||
unsigned bits;
|
||
|
||
if (sn == 0)
|
||
return 0;
|
||
|
||
bits = mpn_base_power_of_two_p (base);
|
||
if (bits)
|
||
return mpn_set_str_bits (rp, sp, sn, bits);
|
||
else
|
||
{
|
||
struct mpn_base_info info;
|
||
|
||
mpn_get_base_info (&info, base);
|
||
return mpn_set_str_other (rp, sp, sn, base, &info);
|
||
}
|
||
}
|
||
|
||
|
||
/* MPZ interface */
|
||
void
|
||
mpz_init (mpz_t r)
|
||
{
|
||
static const mp_limb_t dummy_limb = GMP_LIMB_MAX & 0xc1a0;
|
||
|
||
r->_mp_alloc = 0;
|
||
r->_mp_size = 0;
|
||
r->_mp_d = (mp_ptr) &dummy_limb;
|
||
}
|
||
|
||
/* The utility of this function is a bit limited, since many functions
|
||
assigns the result variable using mpz_swap. */
|
||
void
|
||
mpz_init2 (mpz_t r, mp_bitcnt_t bits)
|
||
{
|
||
mp_size_t rn;
|
||
|
||
bits -= (bits != 0); /* Round down, except if 0 */
|
||
rn = 1 + bits / GMP_LIMB_BITS;
|
||
|
||
r->_mp_alloc = rn;
|
||
r->_mp_size = 0;
|
||
r->_mp_d = gmp_xalloc_limbs (rn);
|
||
}
|
||
|
||
void
|
||
mpz_clear (mpz_t r)
|
||
{
|
||
if (r->_mp_alloc)
|
||
gmp_free (r->_mp_d);
|
||
}
|
||
|
||
static mp_ptr
|
||
mpz_realloc (mpz_t r, mp_size_t size)
|
||
{
|
||
size = GMP_MAX (size, 1);
|
||
|
||
if (r->_mp_alloc)
|
||
r->_mp_d = gmp_xrealloc_limbs (r->_mp_d, size);
|
||
else
|
||
r->_mp_d = gmp_xalloc_limbs (size);
|
||
r->_mp_alloc = size;
|
||
|
||
if (GMP_ABS (r->_mp_size) > size)
|
||
r->_mp_size = 0;
|
||
|
||
return r->_mp_d;
|
||
}
|
||
|
||
/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
|
||
#define MPZ_REALLOC(z,n) ((n) > (z)->_mp_alloc \
|
||
? mpz_realloc(z,n) \
|
||
: (z)->_mp_d)
|
||
|
||
/* MPZ assignment and basic conversions. */
|
||
void
|
||
mpz_set_si (mpz_t r, intptr_t x)
|
||
{
|
||
if (x >= 0)
|
||
mpz_set_ui (r, x);
|
||
else /* (x < 0) */
|
||
if (GMP_LIMB_BITS < GMP_ULONG_BITS)
|
||
{
|
||
mpz_set_ui (r, GMP_NEG_CAST (uintptr_t, x));
|
||
mpz_neg (r, r);
|
||
}
|
||
else
|
||
{
|
||
r->_mp_size = -1;
|
||
MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (uintptr_t, x);
|
||
}
|
||
}
|
||
|
||
void
|
||
mpz_set_ui (mpz_t r, uintptr_t x)
|
||
{
|
||
if (x > 0)
|
||
{
|
||
r->_mp_size = 1;
|
||
MPZ_REALLOC (r, 1)[0] = x;
|
||
if (GMP_LIMB_BITS < GMP_ULONG_BITS)
|
||
{
|
||
int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
|
||
while (x >>= LOCAL_GMP_LIMB_BITS)
|
||
{
|
||
++ r->_mp_size;
|
||
MPZ_REALLOC (r, r->_mp_size)[r->_mp_size - 1] = x;
|
||
}
|
||
}
|
||
}
|
||
else
|
||
r->_mp_size = 0;
|
||
}
|
||
|
||
void
|
||
mpz_set (mpz_t r, const mpz_t x)
|
||
{
|
||
/* Allow the NOP r == x */
|
||
if (r != x)
|
||
{
|
||
mp_size_t n;
|
||
mp_ptr rp;
|
||
|
||
n = GMP_ABS (x->_mp_size);
|
||
rp = MPZ_REALLOC (r, n);
|
||
|
||
mpn_copyi (rp, x->_mp_d, n);
|
||
r->_mp_size = x->_mp_size;
|
||
}
|
||
}
|
||
|
||
void
|
||
mpz_init_set_si (mpz_t r, intptr_t x)
|
||
{
|
||
mpz_init (r);
|
||
mpz_set_si (r, x);
|
||
}
|
||
|
||
void
|
||
mpz_init_set_ui (mpz_t r, uintptr_t x)
|
||
{
|
||
mpz_init (r);
|
||
mpz_set_ui (r, x);
|
||
}
|
||
|
||
void
|
||
mpz_init_set (mpz_t r, const mpz_t x)
|
||
{
|
||
mpz_init (r);
|
||
mpz_set (r, x);
|
||
}
|
||
|
||
int
|
||
mpz_fits_slong_p (const mpz_t u)
|
||
{
|
||
return (INTPTR_MAX + INTPTR_MIN == 0 || mpz_cmp_ui (u, INTPTR_MAX) <= 0) &&
|
||
mpz_cmpabs_ui (u, GMP_NEG_CAST (uintptr_t, INTPTR_MIN)) <= 0;
|
||
}
|
||
|
||
static int
|
||
mpn_absfits_ulong_p (mp_srcptr up, mp_size_t un)
|
||
{
|
||
int ulongsize = GMP_ULONG_BITS / GMP_LIMB_BITS;
|
||
mp_limb_t ulongrem = 0;
|
||
|
||
if (GMP_ULONG_BITS % GMP_LIMB_BITS != 0)
|
||
ulongrem = (mp_limb_t) (ULONG_MAX >> GMP_LIMB_BITS * ulongsize) + 1;
|
||
|
||
return un <= ulongsize || (up[ulongsize] < ulongrem && un == ulongsize + 1);
|
||
}
|
||
|
||
int
|
||
mpz_fits_ulong_p (const mpz_t u)
|
||
{
|
||
mp_size_t us = u->_mp_size;
|
||
|
||
return us >= 0 && mpn_absfits_ulong_p (u->_mp_d, us);
|
||
}
|
||
|
||
intptr_t
|
||
mpz_get_si (const mpz_t u)
|
||
{
|
||
uintptr_t r = mpz_get_ui (u);
|
||
uintptr_t c = -INTPTR_MAX - INTPTR_MIN;
|
||
|
||
if (u->_mp_size < 0)
|
||
/* This expression is necessary to properly handle -INTPTR_MIN */
|
||
return -(intptr_t) c - (intptr_t) ((r - c) & INTPTR_MAX);
|
||
else
|
||
return (intptr_t) (r & INTPTR_MAX);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_get_ui (const mpz_t u)
|
||
{
|
||
if (GMP_LIMB_BITS < GMP_ULONG_BITS)
|
||
{
|
||
int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS;
|
||
uintptr_t r = 0;
|
||
mp_size_t n = GMP_ABS (u->_mp_size);
|
||
n = GMP_MIN (n, 1 + (mp_size_t) (GMP_ULONG_BITS - 1) / GMP_LIMB_BITS);
|
||
while (--n >= 0)
|
||
r = (r << LOCAL_GMP_LIMB_BITS) + u->_mp_d[n];
|
||
return r;
|
||
}
|
||
|
||
return u->_mp_size == 0 ? 0 : u->_mp_d[0];
|
||
}
|
||
|
||
size_t
|
||
mpz_size (const mpz_t u)
|
||
{
|
||
return GMP_ABS (u->_mp_size);
|
||
}
|
||
|
||
mp_limb_t
|
||
mpz_getlimbn (const mpz_t u, mp_size_t n)
|
||
{
|
||
if (n >= 0 && n < GMP_ABS (u->_mp_size))
|
||
return u->_mp_d[n];
|
||
else
|
||
return 0;
|
||
}
|
||
|
||
void
|
||
mpz_realloc2 (mpz_t x, mp_bitcnt_t n)
|
||
{
|
||
mpz_realloc (x, 1 + (n - (n != 0)) / GMP_LIMB_BITS);
|
||
}
|
||
|
||
mp_srcptr
|
||
mpz_limbs_read (mpz_srcptr x)
|
||
{
|
||
return x->_mp_d;
|
||
}
|
||
|
||
mp_ptr
|
||
mpz_limbs_modify (mpz_t x, mp_size_t n)
|
||
{
|
||
assert (n > 0);
|
||
return MPZ_REALLOC (x, n);
|
||
}
|
||
|
||
mp_ptr
|
||
mpz_limbs_write (mpz_t x, mp_size_t n)
|
||
{
|
||
return mpz_limbs_modify (x, n);
|
||
}
|
||
|
||
void
|
||
mpz_limbs_finish (mpz_t x, mp_size_t xs)
|
||
{
|
||
mp_size_t xn;
|
||
xn = mpn_normalized_size (x->_mp_d, GMP_ABS (xs));
|
||
x->_mp_size = xs < 0 ? -xn : xn;
|
||
}
|
||
|
||
static mpz_srcptr
|
||
mpz_roinit_normal_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
|
||
{
|
||
x->_mp_alloc = 0;
|
||
x->_mp_d = (mp_ptr) xp;
|
||
x->_mp_size = xs;
|
||
return x;
|
||
}
|
||
|
||
mpz_srcptr
|
||
mpz_roinit_n (mpz_t x, mp_srcptr xp, mp_size_t xs)
|
||
{
|
||
mpz_roinit_normal_n (x, xp, xs);
|
||
mpz_limbs_finish (x, xs);
|
||
return x;
|
||
}
|
||
|
||
|
||
/* Conversions and comparison to double. */
|
||
void
|
||
mpz_set_d (mpz_t r, double x)
|
||
{
|
||
int sign;
|
||
mp_ptr rp;
|
||
mp_size_t rn, i;
|
||
double B;
|
||
double Bi;
|
||
mp_limb_t f;
|
||
|
||
/* x != x is true when x is a NaN, and x == x * 0.5 is true when x is
|
||
zero or infinity. */
|
||
if (x != x || x == x * 0.5)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
sign = x < 0.0 ;
|
||
if (sign)
|
||
x = - x;
|
||
|
||
if (x < 1.0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
|
||
Bi = 1.0 / B;
|
||
for (rn = 1; x >= B; rn++)
|
||
x *= Bi;
|
||
|
||
rp = MPZ_REALLOC (r, rn);
|
||
|
||
f = (mp_limb_t) x;
|
||
x -= f;
|
||
assert (x < 1.0);
|
||
i = rn-1;
|
||
rp[i] = f;
|
||
while (--i >= 0)
|
||
{
|
||
x = B * x;
|
||
f = (mp_limb_t) x;
|
||
x -= f;
|
||
assert (x < 1.0);
|
||
rp[i] = f;
|
||
}
|
||
|
||
r->_mp_size = sign ? - rn : rn;
|
||
}
|
||
|
||
void
|
||
mpz_init_set_d (mpz_t r, double x)
|
||
{
|
||
mpz_init (r);
|
||
mpz_set_d (r, x);
|
||
}
|
||
|
||
double
|
||
mpz_get_d (const mpz_t u)
|
||
{
|
||
int m;
|
||
mp_limb_t l;
|
||
mp_size_t un;
|
||
double x;
|
||
double B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
|
||
if (un == 0)
|
||
return 0.0;
|
||
|
||
l = u->_mp_d[--un];
|
||
gmp_clz (m, l);
|
||
m = m + GMP_DBL_MANT_BITS - GMP_LIMB_BITS;
|
||
if (m < 0)
|
||
l &= GMP_LIMB_MAX << -m;
|
||
|
||
for (x = l; --un >= 0;)
|
||
{
|
||
x = B*x;
|
||
if (m > 0) {
|
||
l = u->_mp_d[un];
|
||
m -= GMP_LIMB_BITS;
|
||
if (m < 0)
|
||
l &= GMP_LIMB_MAX << -m;
|
||
x += l;
|
||
}
|
||
}
|
||
|
||
if (u->_mp_size < 0)
|
||
x = -x;
|
||
|
||
return x;
|
||
}
|
||
|
||
int
|
||
mpz_cmpabs_d (const mpz_t x, double d)
|
||
{
|
||
mp_size_t xn;
|
||
double B, Bi;
|
||
mp_size_t i;
|
||
|
||
xn = x->_mp_size;
|
||
d = GMP_ABS (d);
|
||
|
||
if (xn != 0)
|
||
{
|
||
xn = GMP_ABS (xn);
|
||
|
||
B = 4.0 * (double) (GMP_LIMB_HIGHBIT >> 1);
|
||
Bi = 1.0 / B;
|
||
|
||
/* Scale d so it can be compared with the top limb. */
|
||
for (i = 1; i < xn; i++)
|
||
d *= Bi;
|
||
|
||
if (d >= B)
|
||
return -1;
|
||
|
||
/* Compare floor(d) to top limb, subtract and cancel when equal. */
|
||
for (i = xn; i-- > 0;)
|
||
{
|
||
mp_limb_t f, xl;
|
||
|
||
f = (mp_limb_t) d;
|
||
xl = x->_mp_d[i];
|
||
if (xl > f)
|
||
return 1;
|
||
else if (xl < f)
|
||
return -1;
|
||
d = B * (d - f);
|
||
}
|
||
}
|
||
return - (d > 0.0);
|
||
}
|
||
|
||
int
|
||
mpz_cmp_d (const mpz_t x, double d)
|
||
{
|
||
if (x->_mp_size < 0)
|
||
{
|
||
if (d >= 0.0)
|
||
return -1;
|
||
else
|
||
return -mpz_cmpabs_d (x, d);
|
||
}
|
||
else
|
||
{
|
||
if (d < 0.0)
|
||
return 1;
|
||
else
|
||
return mpz_cmpabs_d (x, d);
|
||
}
|
||
}
|
||
|
||
|
||
/* MPZ comparisons and the like. */
|
||
int
|
||
mpz_sgn (const mpz_t u)
|
||
{
|
||
return GMP_CMP (u->_mp_size, 0);
|
||
}
|
||
|
||
int
|
||
mpz_cmp_si (const mpz_t u, intptr_t v)
|
||
{
|
||
mp_size_t usize = u->_mp_size;
|
||
|
||
if (v >= 0)
|
||
return mpz_cmp_ui (u, v);
|
||
else if (usize >= 0)
|
||
return 1;
|
||
else
|
||
return - mpz_cmpabs_ui (u, GMP_NEG_CAST (uintptr_t, v));
|
||
}
|
||
|
||
int
|
||
mpz_cmp_ui (const mpz_t u, uintptr_t v)
|
||
{
|
||
mp_size_t usize = u->_mp_size;
|
||
|
||
if (usize < 0)
|
||
return -1;
|
||
else
|
||
return mpz_cmpabs_ui (u, v);
|
||
}
|
||
|
||
int
|
||
mpz_cmp (const mpz_t a, const mpz_t b)
|
||
{
|
||
mp_size_t asize = a->_mp_size;
|
||
mp_size_t bsize = b->_mp_size;
|
||
|
||
if (asize != bsize)
|
||
return (asize < bsize) ? -1 : 1;
|
||
else if (asize >= 0)
|
||
return mpn_cmp (a->_mp_d, b->_mp_d, asize);
|
||
else
|
||
return mpn_cmp (b->_mp_d, a->_mp_d, -asize);
|
||
}
|
||
|
||
int
|
||
mpz_cmpabs_ui (const mpz_t u, uintptr_t v)
|
||
{
|
||
mp_size_t un = GMP_ABS (u->_mp_size);
|
||
|
||
if (! mpn_absfits_ulong_p (u->_mp_d, un))
|
||
return 1;
|
||
else
|
||
{
|
||
uintptr_t uu = mpz_get_ui (u);
|
||
return GMP_CMP(uu, v);
|
||
}
|
||
}
|
||
|
||
int
|
||
mpz_cmpabs (const mpz_t u, const mpz_t v)
|
||
{
|
||
return mpn_cmp4 (u->_mp_d, GMP_ABS (u->_mp_size),
|
||
v->_mp_d, GMP_ABS (v->_mp_size));
|
||
}
|
||
|
||
void
|
||
mpz_abs (mpz_t r, const mpz_t u)
|
||
{
|
||
mpz_set (r, u);
|
||
r->_mp_size = GMP_ABS (r->_mp_size);
|
||
}
|
||
|
||
void
|
||
mpz_neg (mpz_t r, const mpz_t u)
|
||
{
|
||
mpz_set (r, u);
|
||
r->_mp_size = -r->_mp_size;
|
||
}
|
||
|
||
void
|
||
mpz_swap (mpz_t u, mpz_t v)
|
||
{
|
||
MP_SIZE_T_SWAP (u->_mp_size, v->_mp_size);
|
||
MP_SIZE_T_SWAP (u->_mp_alloc, v->_mp_alloc);
|
||
MP_PTR_SWAP (u->_mp_d, v->_mp_d);
|
||
}
|
||
|
||
|
||
/* MPZ addition and subtraction */
|
||
|
||
|
||
void
|
||
mpz_add_ui (mpz_t r, const mpz_t a, uintptr_t b)
|
||
{
|
||
mpz_t bb;
|
||
mpz_init_set_ui (bb, b);
|
||
mpz_add (r, a, bb);
|
||
mpz_clear (bb);
|
||
}
|
||
|
||
void
|
||
mpz_sub_ui (mpz_t r, const mpz_t a, uintptr_t b)
|
||
{
|
||
mpz_ui_sub (r, b, a);
|
||
mpz_neg (r, r);
|
||
}
|
||
|
||
void
|
||
mpz_ui_sub (mpz_t r, uintptr_t a, const mpz_t b)
|
||
{
|
||
mpz_neg (r, b);
|
||
mpz_add_ui (r, r, a);
|
||
}
|
||
|
||
static mp_size_t
|
||
mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
|
||
{
|
||
mp_size_t an = GMP_ABS (a->_mp_size);
|
||
mp_size_t bn = GMP_ABS (b->_mp_size);
|
||
mp_ptr rp;
|
||
mp_limb_t cy;
|
||
|
||
if (an < bn)
|
||
{
|
||
MPZ_SRCPTR_SWAP (a, b);
|
||
MP_SIZE_T_SWAP (an, bn);
|
||
}
|
||
|
||
rp = MPZ_REALLOC (r, an + 1);
|
||
cy = mpn_add (rp, a->_mp_d, an, b->_mp_d, bn);
|
||
|
||
rp[an] = cy;
|
||
|
||
return an + cy;
|
||
}
|
||
|
||
static mp_size_t
|
||
mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
|
||
{
|
||
mp_size_t an = GMP_ABS (a->_mp_size);
|
||
mp_size_t bn = GMP_ABS (b->_mp_size);
|
||
int cmp;
|
||
mp_ptr rp;
|
||
|
||
cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
|
||
if (cmp > 0)
|
||
{
|
||
rp = MPZ_REALLOC (r, an);
|
||
gmp_assert_nocarry (mpn_sub (rp, a->_mp_d, an, b->_mp_d, bn));
|
||
return mpn_normalized_size (rp, an);
|
||
}
|
||
else if (cmp < 0)
|
||
{
|
||
rp = MPZ_REALLOC (r, bn);
|
||
gmp_assert_nocarry (mpn_sub (rp, b->_mp_d, bn, a->_mp_d, an));
|
||
return -mpn_normalized_size (rp, bn);
|
||
}
|
||
else
|
||
return 0;
|
||
}
|
||
|
||
void
|
||
mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
|
||
{
|
||
mp_size_t rn;
|
||
|
||
if ( (a->_mp_size ^ b->_mp_size) >= 0)
|
||
rn = mpz_abs_add (r, a, b);
|
||
else
|
||
rn = mpz_abs_sub (r, a, b);
|
||
|
||
r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
|
||
}
|
||
|
||
void
|
||
mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
|
||
{
|
||
mp_size_t rn;
|
||
|
||
if ( (a->_mp_size ^ b->_mp_size) >= 0)
|
||
rn = mpz_abs_sub (r, a, b);
|
||
else
|
||
rn = mpz_abs_add (r, a, b);
|
||
|
||
r->_mp_size = a->_mp_size >= 0 ? rn : - rn;
|
||
}
|
||
|
||
|
||
/* MPZ multiplication */
|
||
void
|
||
mpz_mul_si (mpz_t r, const mpz_t u, intptr_t v)
|
||
{
|
||
if (v < 0)
|
||
{
|
||
mpz_mul_ui (r, u, GMP_NEG_CAST (uintptr_t, v));
|
||
mpz_neg (r, r);
|
||
}
|
||
else
|
||
mpz_mul_ui (r, u, v);
|
||
}
|
||
|
||
void
|
||
mpz_mul_ui (mpz_t r, const mpz_t u, uintptr_t v)
|
||
{
|
||
mpz_t vv;
|
||
mpz_init_set_ui (vv, v);
|
||
mpz_mul (r, u, vv);
|
||
mpz_clear (vv);
|
||
return;
|
||
}
|
||
|
||
void
|
||
mpz_mul (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
int sign;
|
||
mp_size_t un, vn, rn;
|
||
mpz_t t;
|
||
mp_ptr tp;
|
||
|
||
un = u->_mp_size;
|
||
vn = v->_mp_size;
|
||
|
||
if (un == 0 || vn == 0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
sign = (un ^ vn) < 0;
|
||
|
||
un = GMP_ABS (un);
|
||
vn = GMP_ABS (vn);
|
||
|
||
mpz_init2 (t, (un + vn) * GMP_LIMB_BITS);
|
||
|
||
tp = t->_mp_d;
|
||
if (un >= vn)
|
||
mpn_mul (tp, u->_mp_d, un, v->_mp_d, vn);
|
||
else
|
||
mpn_mul (tp, v->_mp_d, vn, u->_mp_d, un);
|
||
|
||
rn = un + vn;
|
||
rn -= tp[rn-1] == 0;
|
||
|
||
t->_mp_size = sign ? - rn : rn;
|
||
mpz_swap (r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
void
|
||
mpz_mul_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bits)
|
||
{
|
||
mp_size_t un, rn;
|
||
mp_size_t limbs;
|
||
unsigned shift;
|
||
mp_ptr rp;
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
if (un == 0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
limbs = bits / GMP_LIMB_BITS;
|
||
shift = bits % GMP_LIMB_BITS;
|
||
|
||
rn = un + limbs + (shift > 0);
|
||
rp = MPZ_REALLOC (r, rn);
|
||
if (shift > 0)
|
||
{
|
||
mp_limb_t cy = mpn_lshift (rp + limbs, u->_mp_d, un, shift);
|
||
rp[rn-1] = cy;
|
||
rn -= (cy == 0);
|
||
}
|
||
else
|
||
mpn_copyd (rp + limbs, u->_mp_d, un);
|
||
|
||
mpn_zero (rp, limbs);
|
||
|
||
r->_mp_size = (u->_mp_size < 0) ? - rn : rn;
|
||
}
|
||
|
||
void
|
||
mpz_addmul_ui (mpz_t r, const mpz_t u, uintptr_t v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init_set_ui (t, v);
|
||
mpz_mul (t, u, t);
|
||
mpz_add (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
void
|
||
mpz_submul_ui (mpz_t r, const mpz_t u, uintptr_t v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init_set_ui (t, v);
|
||
mpz_mul (t, u, t);
|
||
mpz_sub (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
void
|
||
mpz_addmul (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init (t);
|
||
mpz_mul (t, u, v);
|
||
mpz_add (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
void
|
||
mpz_submul (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init (t);
|
||
mpz_mul (t, u, v);
|
||
mpz_sub (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
|
||
/* MPZ division */
|
||
enum mpz_div_round_mode { GMP_DIV_FLOOR, GMP_DIV_CEIL, GMP_DIV_TRUNC };
|
||
|
||
/* Allows q or r to be zero. Returns 1 iff remainder is non-zero. */
|
||
static int
|
||
mpz_div_qr (mpz_t q, mpz_t r,
|
||
const mpz_t n, const mpz_t d, enum mpz_div_round_mode mode)
|
||
{
|
||
mp_size_t ns, ds, nn, dn, qs;
|
||
ns = n->_mp_size;
|
||
ds = d->_mp_size;
|
||
|
||
if (ds == 0)
|
||
gmp_die("mpz_div_qr: Divide by zero.");
|
||
|
||
if (ns == 0)
|
||
{
|
||
if (q)
|
||
q->_mp_size = 0;
|
||
if (r)
|
||
r->_mp_size = 0;
|
||
return 0;
|
||
}
|
||
|
||
nn = GMP_ABS (ns);
|
||
dn = GMP_ABS (ds);
|
||
|
||
qs = ds ^ ns;
|
||
|
||
if (nn < dn)
|
||
{
|
||
if (mode == GMP_DIV_CEIL && qs >= 0)
|
||
{
|
||
/* q = 1, r = n - d */
|
||
if (r)
|
||
mpz_sub (r, n, d);
|
||
if (q)
|
||
mpz_set_ui (q, 1);
|
||
}
|
||
else if (mode == GMP_DIV_FLOOR && qs < 0)
|
||
{
|
||
/* q = -1, r = n + d */
|
||
if (r)
|
||
mpz_add (r, n, d);
|
||
if (q)
|
||
mpz_set_si (q, -1);
|
||
}
|
||
else
|
||
{
|
||
/* q = 0, r = d */
|
||
if (r)
|
||
mpz_set (r, n);
|
||
if (q)
|
||
q->_mp_size = 0;
|
||
}
|
||
return 1;
|
||
}
|
||
else
|
||
{
|
||
mp_ptr np, qp;
|
||
mp_size_t qn, rn;
|
||
mpz_t tq, tr;
|
||
|
||
mpz_init_set (tr, n);
|
||
np = tr->_mp_d;
|
||
|
||
qn = nn - dn + 1;
|
||
|
||
if (q)
|
||
{
|
||
mpz_init2 (tq, qn * GMP_LIMB_BITS);
|
||
qp = tq->_mp_d;
|
||
}
|
||
else
|
||
qp = NULL;
|
||
|
||
mpn_div_qr (qp, np, nn, d->_mp_d, dn);
|
||
|
||
if (qp)
|
||
{
|
||
qn -= (qp[qn-1] == 0);
|
||
|
||
tq->_mp_size = qs < 0 ? -qn : qn;
|
||
}
|
||
rn = mpn_normalized_size (np, dn);
|
||
tr->_mp_size = ns < 0 ? - rn : rn;
|
||
|
||
if (mode == GMP_DIV_FLOOR && qs < 0 && rn != 0)
|
||
{
|
||
if (q)
|
||
mpz_sub_ui (tq, tq, 1);
|
||
if (r)
|
||
mpz_add (tr, tr, d);
|
||
}
|
||
else if (mode == GMP_DIV_CEIL && qs >= 0 && rn != 0)
|
||
{
|
||
if (q)
|
||
mpz_add_ui (tq, tq, 1);
|
||
if (r)
|
||
mpz_sub (tr, tr, d);
|
||
}
|
||
|
||
if (q)
|
||
{
|
||
mpz_swap (tq, q);
|
||
mpz_clear (tq);
|
||
}
|
||
if (r)
|
||
mpz_swap (tr, r);
|
||
|
||
mpz_clear (tr);
|
||
|
||
return rn != 0;
|
||
}
|
||
}
|
||
|
||
void
|
||
mpz_cdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (q, r, n, d, GMP_DIV_CEIL);
|
||
}
|
||
|
||
void
|
||
mpz_fdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (q, r, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
void
|
||
mpz_tdiv_qr (mpz_t q, mpz_t r, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (q, r, n, d, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
void
|
||
mpz_cdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (q, NULL, n, d, GMP_DIV_CEIL);
|
||
}
|
||
|
||
void
|
||
mpz_fdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (q, NULL, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
void
|
||
mpz_tdiv_q (mpz_t q, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
void
|
||
mpz_cdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (NULL, r, n, d, GMP_DIV_CEIL);
|
||
}
|
||
|
||
void
|
||
mpz_fdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (NULL, r, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
void
|
||
mpz_tdiv_r (mpz_t r, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (NULL, r, n, d, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
void
|
||
mpz_mod (mpz_t r, const mpz_t n, const mpz_t d)
|
||
{
|
||
mpz_div_qr (NULL, r, n, d, d->_mp_size >= 0 ? GMP_DIV_FLOOR : GMP_DIV_CEIL);
|
||
}
|
||
|
||
static void
|
||
mpz_div_q_2exp (mpz_t q, const mpz_t u, mp_bitcnt_t bit_index,
|
||
enum mpz_div_round_mode mode)
|
||
{
|
||
mp_size_t un, qn;
|
||
mp_size_t limb_cnt;
|
||
mp_ptr qp;
|
||
int adjust;
|
||
|
||
un = u->_mp_size;
|
||
if (un == 0)
|
||
{
|
||
q->_mp_size = 0;
|
||
return;
|
||
}
|
||
limb_cnt = bit_index / GMP_LIMB_BITS;
|
||
qn = GMP_ABS (un) - limb_cnt;
|
||
bit_index %= GMP_LIMB_BITS;
|
||
|
||
if (mode == ((un > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* un != 0 here. */
|
||
/* Note: Below, the final indexing at limb_cnt is valid because at
|
||
that point we have qn > 0. */
|
||
adjust = (qn <= 0
|
||
|| !mpn_zero_p (u->_mp_d, limb_cnt)
|
||
|| (u->_mp_d[limb_cnt]
|
||
& (((mp_limb_t) 1 << bit_index) - 1)));
|
||
else
|
||
adjust = 0;
|
||
|
||
if (qn <= 0)
|
||
qn = 0;
|
||
else
|
||
{
|
||
qp = MPZ_REALLOC (q, qn);
|
||
|
||
if (bit_index != 0)
|
||
{
|
||
mpn_rshift (qp, u->_mp_d + limb_cnt, qn, bit_index);
|
||
qn -= qp[qn - 1] == 0;
|
||
}
|
||
else
|
||
{
|
||
mpn_copyi (qp, u->_mp_d + limb_cnt, qn);
|
||
}
|
||
}
|
||
|
||
q->_mp_size = qn;
|
||
|
||
if (adjust)
|
||
mpz_add_ui (q, q, 1);
|
||
if (un < 0)
|
||
mpz_neg (q, q);
|
||
}
|
||
|
||
static void
|
||
mpz_div_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t bit_index,
|
||
enum mpz_div_round_mode mode)
|
||
{
|
||
mp_size_t us, un, rn;
|
||
mp_ptr rp;
|
||
mp_limb_t mask;
|
||
|
||
us = u->_mp_size;
|
||
if (us == 0 || bit_index == 0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
rn = (bit_index + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
|
||
assert (rn > 0);
|
||
|
||
rp = MPZ_REALLOC (r, rn);
|
||
un = GMP_ABS (us);
|
||
|
||
mask = GMP_LIMB_MAX >> (rn * GMP_LIMB_BITS - bit_index);
|
||
|
||
if (rn > un)
|
||
{
|
||
/* Quotient (with truncation) is zero, and remainder is
|
||
non-zero */
|
||
if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
|
||
{
|
||
/* Have to negate and sign extend. */
|
||
mp_size_t i;
|
||
|
||
gmp_assert_nocarry (! mpn_neg (rp, u->_mp_d, un));
|
||
for (i = un; i < rn - 1; i++)
|
||
rp[i] = GMP_LIMB_MAX;
|
||
|
||
rp[rn-1] = mask;
|
||
us = -us;
|
||
}
|
||
else
|
||
{
|
||
/* Just copy */
|
||
if (r != u)
|
||
mpn_copyi (rp, u->_mp_d, un);
|
||
|
||
rn = un;
|
||
}
|
||
}
|
||
else
|
||
{
|
||
if (r != u)
|
||
mpn_copyi (rp, u->_mp_d, rn - 1);
|
||
|
||
rp[rn-1] = u->_mp_d[rn-1] & mask;
|
||
|
||
if (mode == ((us > 0) ? GMP_DIV_CEIL : GMP_DIV_FLOOR)) /* us != 0 here. */
|
||
{
|
||
/* If r != 0, compute 2^{bit_count} - r. */
|
||
mpn_neg (rp, rp, rn);
|
||
|
||
rp[rn-1] &= mask;
|
||
|
||
/* us is not used for anything else, so we can modify it
|
||
here to indicate flipped sign. */
|
||
us = -us;
|
||
}
|
||
}
|
||
rn = mpn_normalized_size (rp, rn);
|
||
r->_mp_size = us < 0 ? -rn : rn;
|
||
}
|
||
|
||
void
|
||
mpz_cdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
||
{
|
||
mpz_div_q_2exp (r, u, cnt, GMP_DIV_CEIL);
|
||
}
|
||
|
||
void
|
||
mpz_fdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
||
{
|
||
mpz_div_q_2exp (r, u, cnt, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
void
|
||
mpz_tdiv_q_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
||
{
|
||
mpz_div_q_2exp (r, u, cnt, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
void
|
||
mpz_cdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
||
{
|
||
mpz_div_r_2exp (r, u, cnt, GMP_DIV_CEIL);
|
||
}
|
||
|
||
void
|
||
mpz_fdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
||
{
|
||
mpz_div_r_2exp (r, u, cnt, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
void
|
||
mpz_tdiv_r_2exp (mpz_t r, const mpz_t u, mp_bitcnt_t cnt)
|
||
{
|
||
mpz_div_r_2exp (r, u, cnt, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
void
|
||
mpz_divexact (mpz_t q, const mpz_t n, const mpz_t d)
|
||
{
|
||
gmp_assert_nocarry (mpz_div_qr (q, NULL, n, d, GMP_DIV_TRUNC));
|
||
}
|
||
|
||
int
|
||
mpz_divisible_p (const mpz_t n, const mpz_t d)
|
||
{
|
||
return mpz_div_qr (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
|
||
}
|
||
|
||
int
|
||
mpz_congruent_p (const mpz_t a, const mpz_t b, const mpz_t m)
|
||
{
|
||
mpz_t t;
|
||
int res;
|
||
|
||
/* a == b (mod 0) iff a == b */
|
||
if (mpz_sgn (m) == 0)
|
||
return (mpz_cmp (a, b) == 0);
|
||
|
||
mpz_init (t);
|
||
mpz_sub (t, a, b);
|
||
res = mpz_divisible_p (t, m);
|
||
mpz_clear (t);
|
||
|
||
return res;
|
||
}
|
||
|
||
static uintptr_t
|
||
mpz_div_qr_ui (mpz_t q, mpz_t r,
|
||
const mpz_t n, uintptr_t d, enum mpz_div_round_mode mode)
|
||
{
|
||
uintptr_t ret;
|
||
mpz_t rr, dd;
|
||
|
||
mpz_init (rr);
|
||
mpz_init_set_ui (dd, d);
|
||
mpz_div_qr (q, rr, n, dd, mode);
|
||
mpz_clear (dd);
|
||
ret = mpz_get_ui (rr);
|
||
|
||
if (r)
|
||
mpz_swap (r, rr);
|
||
mpz_clear (rr);
|
||
|
||
return ret;
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_cdiv_q_ui (mpz_t q, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_fdiv_q_ui (mpz_t q, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_tdiv_q_ui (mpz_t q, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_cdiv_r_ui (mpz_t r, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL);
|
||
}
|
||
uintptr_t
|
||
mpz_fdiv_r_ui (mpz_t r, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
uintptr_t
|
||
mpz_tdiv_r_ui (mpz_t r, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_cdiv_ui (const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_fdiv_ui (const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_tdiv_ui (const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC);
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_mod_ui (mpz_t r, const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR);
|
||
}
|
||
|
||
void
|
||
mpz_divexact_ui (mpz_t q, const mpz_t n, uintptr_t d)
|
||
{
|
||
gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC));
|
||
}
|
||
|
||
int
|
||
mpz_divisible_ui_p (const mpz_t n, uintptr_t d)
|
||
{
|
||
return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC) == 0;
|
||
}
|
||
|
||
|
||
/* GCD */
|
||
static mp_limb_t
|
||
mpn_gcd_11 (mp_limb_t u, mp_limb_t v)
|
||
{
|
||
unsigned shift;
|
||
|
||
assert ( (u | v) > 0);
|
||
|
||
if (u == 0)
|
||
return v;
|
||
else if (v == 0)
|
||
return u;
|
||
|
||
gmp_ctz (shift, u | v);
|
||
|
||
u >>= shift;
|
||
v >>= shift;
|
||
|
||
if ( (u & 1) == 0)
|
||
MP_LIMB_T_SWAP (u, v);
|
||
|
||
while ( (v & 1) == 0)
|
||
v >>= 1;
|
||
|
||
while (u != v)
|
||
{
|
||
if (u > v)
|
||
{
|
||
u -= v;
|
||
do
|
||
u >>= 1;
|
||
while ( (u & 1) == 0);
|
||
}
|
||
else
|
||
{
|
||
v -= u;
|
||
do
|
||
v >>= 1;
|
||
while ( (v & 1) == 0);
|
||
}
|
||
}
|
||
return u << shift;
|
||
}
|
||
|
||
uintptr_t
|
||
mpz_gcd_ui (mpz_t g, const mpz_t u, uintptr_t v)
|
||
{
|
||
mpz_t t;
|
||
mpz_init_set_ui(t, v);
|
||
mpz_gcd (t, u, t);
|
||
if (v > 0)
|
||
v = mpz_get_ui (t);
|
||
|
||
if (g)
|
||
mpz_swap (t, g);
|
||
|
||
mpz_clear (t);
|
||
|
||
return v;
|
||
}
|
||
|
||
static mp_bitcnt_t
|
||
mpz_make_odd (mpz_t r)
|
||
{
|
||
mp_bitcnt_t shift;
|
||
|
||
assert (r->_mp_size > 0);
|
||
/* Count trailing zeros, equivalent to mpn_scan1, because we know that there is a 1 */
|
||
shift = mpn_common_scan (r->_mp_d[0], 0, r->_mp_d, 0, 0);
|
||
mpz_tdiv_q_2exp (r, r, shift);
|
||
|
||
return shift;
|
||
}
|
||
|
||
void
|
||
mpz_gcd (mpz_t g, const mpz_t u, const mpz_t v)
|
||
{
|
||
mpz_t tu, tv;
|
||
mp_bitcnt_t uz, vz, gz;
|
||
|
||
if (u->_mp_size == 0)
|
||
{
|
||
mpz_abs (g, v);
|
||
return;
|
||
}
|
||
if (v->_mp_size == 0)
|
||
{
|
||
mpz_abs (g, u);
|
||
return;
|
||
}
|
||
|
||
mpz_init (tu);
|
||
mpz_init (tv);
|
||
|
||
mpz_abs (tu, u);
|
||
uz = mpz_make_odd (tu);
|
||
mpz_abs (tv, v);
|
||
vz = mpz_make_odd (tv);
|
||
gz = GMP_MIN (uz, vz);
|
||
|
||
if (tu->_mp_size < tv->_mp_size)
|
||
mpz_swap (tu, tv);
|
||
|
||
mpz_tdiv_r (tu, tu, tv);
|
||
if (tu->_mp_size == 0)
|
||
{
|
||
mpz_swap (g, tv);
|
||
}
|
||
else
|
||
for (;;)
|
||
{
|
||
int c;
|
||
|
||
mpz_make_odd (tu);
|
||
c = mpz_cmp (tu, tv);
|
||
if (c == 0)
|
||
{
|
||
mpz_swap (g, tu);
|
||
break;
|
||
}
|
||
if (c < 0)
|
||
mpz_swap (tu, tv);
|
||
|
||
if (tv->_mp_size == 1)
|
||
{
|
||
mp_limb_t vl = tv->_mp_d[0];
|
||
mp_limb_t ul = mpz_tdiv_ui (tu, vl);
|
||
mpz_set_ui (g, mpn_gcd_11 (ul, vl));
|
||
break;
|
||
}
|
||
mpz_sub (tu, tu, tv);
|
||
}
|
||
mpz_clear (tu);
|
||
mpz_clear (tv);
|
||
mpz_mul_2exp (g, g, gz);
|
||
}
|
||
|
||
void
|
||
mpz_gcdext (mpz_t g, mpz_t s, mpz_t t, const mpz_t u, const mpz_t v)
|
||
{
|
||
mpz_t tu, tv, s0, s1, t0, t1;
|
||
mp_bitcnt_t uz, vz, gz;
|
||
mp_bitcnt_t power;
|
||
|
||
if (u->_mp_size == 0)
|
||
{
|
||
/* g = 0 u + sgn(v) v */
|
||
intptr_t sign = mpz_sgn (v);
|
||
mpz_abs (g, v);
|
||
if (s)
|
||
s->_mp_size = 0;
|
||
if (t)
|
||
mpz_set_si (t, sign);
|
||
return;
|
||
}
|
||
|
||
if (v->_mp_size == 0)
|
||
{
|
||
/* g = sgn(u) u + 0 v */
|
||
intptr_t sign = mpz_sgn (u);
|
||
mpz_abs (g, u);
|
||
if (s)
|
||
mpz_set_si (s, sign);
|
||
if (t)
|
||
t->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
mpz_init (tu);
|
||
mpz_init (tv);
|
||
mpz_init (s0);
|
||
mpz_init (s1);
|
||
mpz_init (t0);
|
||
mpz_init (t1);
|
||
|
||
mpz_abs (tu, u);
|
||
uz = mpz_make_odd (tu);
|
||
mpz_abs (tv, v);
|
||
vz = mpz_make_odd (tv);
|
||
gz = GMP_MIN (uz, vz);
|
||
|
||
uz -= gz;
|
||
vz -= gz;
|
||
|
||
/* Cofactors corresponding to odd gcd. gz handled later. */
|
||
if (tu->_mp_size < tv->_mp_size)
|
||
{
|
||
mpz_swap (tu, tv);
|
||
MPZ_SRCPTR_SWAP (u, v);
|
||
MPZ_PTR_SWAP (s, t);
|
||
MP_BITCNT_T_SWAP (uz, vz);
|
||
}
|
||
|
||
/* Maintain
|
||
*
|
||
* u = t0 tu + t1 tv
|
||
* v = s0 tu + s1 tv
|
||
*
|
||
* where u and v denote the inputs with common factors of two
|
||
* eliminated, and det (s0, t0; s1, t1) = 2^p. Then
|
||
*
|
||
* 2^p tu = s1 u - t1 v
|
||
* 2^p tv = -s0 u + t0 v
|
||
*/
|
||
|
||
/* After initial division, tu = q tv + tu', we have
|
||
*
|
||
* u = 2^uz (tu' + q tv)
|
||
* v = 2^vz tv
|
||
*
|
||
* or
|
||
*
|
||
* t0 = 2^uz, t1 = 2^uz q
|
||
* s0 = 0, s1 = 2^vz
|
||
*/
|
||
|
||
mpz_setbit (t0, uz);
|
||
mpz_tdiv_qr (t1, tu, tu, tv);
|
||
mpz_mul_2exp (t1, t1, uz);
|
||
|
||
mpz_setbit (s1, vz);
|
||
power = uz + vz;
|
||
|
||
if (tu->_mp_size > 0)
|
||
{
|
||
mp_bitcnt_t shift;
|
||
shift = mpz_make_odd (tu);
|
||
mpz_mul_2exp (t0, t0, shift);
|
||
mpz_mul_2exp (s0, s0, shift);
|
||
power += shift;
|
||
|
||
for (;;)
|
||
{
|
||
int c;
|
||
c = mpz_cmp (tu, tv);
|
||
if (c == 0)
|
||
break;
|
||
|
||
if (c < 0)
|
||
{
|
||
/* tv = tv' + tu
|
||
*
|
||
* u = t0 tu + t1 (tv' + tu) = (t0 + t1) tu + t1 tv'
|
||
* v = s0 tu + s1 (tv' + tu) = (s0 + s1) tu + s1 tv' */
|
||
|
||
mpz_sub (tv, tv, tu);
|
||
mpz_add (t0, t0, t1);
|
||
mpz_add (s0, s0, s1);
|
||
|
||
shift = mpz_make_odd (tv);
|
||
mpz_mul_2exp (t1, t1, shift);
|
||
mpz_mul_2exp (s1, s1, shift);
|
||
}
|
||
else
|
||
{
|
||
mpz_sub (tu, tu, tv);
|
||
mpz_add (t1, t0, t1);
|
||
mpz_add (s1, s0, s1);
|
||
|
||
shift = mpz_make_odd (tu);
|
||
mpz_mul_2exp (t0, t0, shift);
|
||
mpz_mul_2exp (s0, s0, shift);
|
||
}
|
||
power += shift;
|
||
}
|
||
}
|
||
|
||
/* Now tv = odd part of gcd, and -s0 and t0 are corresponding
|
||
cofactors. */
|
||
|
||
mpz_mul_2exp (tv, tv, gz);
|
||
mpz_neg (s0, s0);
|
||
|
||
/* 2^p g = s0 u + t0 v. Eliminate one factor of two at a time. To
|
||
adjust cofactors, we need u / g and v / g */
|
||
|
||
mpz_divexact (s1, v, tv);
|
||
mpz_abs (s1, s1);
|
||
mpz_divexact (t1, u, tv);
|
||
mpz_abs (t1, t1);
|
||
|
||
while (power-- > 0)
|
||
{
|
||
/* s0 u + t0 v = (s0 - v/g) u - (t0 + u/g) v */
|
||
if (mpz_odd_p (s0) || mpz_odd_p (t0))
|
||
{
|
||
mpz_sub (s0, s0, s1);
|
||
mpz_add (t0, t0, t1);
|
||
}
|
||
assert (mpz_even_p (t0) && mpz_even_p (s0));
|
||
mpz_tdiv_q_2exp (s0, s0, 1);
|
||
mpz_tdiv_q_2exp (t0, t0, 1);
|
||
}
|
||
|
||
/* Arrange so that |s| < |u| / 2g */
|
||
mpz_add (s1, s0, s1);
|
||
if (mpz_cmpabs (s0, s1) > 0)
|
||
{
|
||
mpz_swap (s0, s1);
|
||
mpz_sub (t0, t0, t1);
|
||
}
|
||
if (u->_mp_size < 0)
|
||
mpz_neg (s0, s0);
|
||
if (v->_mp_size < 0)
|
||
mpz_neg (t0, t0);
|
||
|
||
mpz_swap (g, tv);
|
||
if (s)
|
||
mpz_swap (s, s0);
|
||
if (t)
|
||
mpz_swap (t, t0);
|
||
|
||
mpz_clear (tu);
|
||
mpz_clear (tv);
|
||
mpz_clear (s0);
|
||
mpz_clear (s1);
|
||
mpz_clear (t0);
|
||
mpz_clear (t1);
|
||
}
|
||
|
||
void
|
||
mpz_lcm (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mpz_t g;
|
||
|
||
if (u->_mp_size == 0 || v->_mp_size == 0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
mpz_init (g);
|
||
|
||
mpz_gcd (g, u, v);
|
||
mpz_divexact (g, u, g);
|
||
mpz_mul (r, g, v);
|
||
|
||
mpz_clear (g);
|
||
mpz_abs (r, r);
|
||
}
|
||
|
||
void
|
||
mpz_lcm_ui (mpz_t r, const mpz_t u, uintptr_t v)
|
||
{
|
||
if (v == 0 || u->_mp_size == 0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
v /= mpz_gcd_ui (NULL, u, v);
|
||
mpz_mul_ui (r, u, v);
|
||
|
||
mpz_abs (r, r);
|
||
}
|
||
|
||
int
|
||
mpz_invert (mpz_t r, const mpz_t u, const mpz_t m)
|
||
{
|
||
mpz_t g, tr;
|
||
int invertible;
|
||
|
||
if (u->_mp_size == 0 || mpz_cmpabs_ui (m, 1) <= 0)
|
||
return 0;
|
||
|
||
mpz_init (g);
|
||
mpz_init (tr);
|
||
|
||
mpz_gcdext (g, tr, NULL, u, m);
|
||
invertible = (mpz_cmp_ui (g, 1) == 0);
|
||
|
||
if (invertible)
|
||
{
|
||
if (tr->_mp_size < 0)
|
||
{
|
||
if (m->_mp_size >= 0)
|
||
mpz_add (tr, tr, m);
|
||
else
|
||
mpz_sub (tr, tr, m);
|
||
}
|
||
mpz_swap (r, tr);
|
||
}
|
||
|
||
mpz_clear (g);
|
||
mpz_clear (tr);
|
||
return invertible;
|
||
}
|
||
|
||
|
||
/* Higher level operations (sqrt, pow and root) */
|
||
|
||
void
|
||
mpz_pow_ui (mpz_t r, const mpz_t b, uintptr_t e)
|
||
{
|
||
uintptr_t bit;
|
||
mpz_t tr;
|
||
mpz_init_set_ui (tr, 1);
|
||
|
||
bit = GMP_ULONG_HIGHBIT;
|
||
do
|
||
{
|
||
mpz_mul (tr, tr, tr);
|
||
if (e & bit)
|
||
mpz_mul (tr, tr, b);
|
||
bit >>= 1;
|
||
}
|
||
while (bit > 0);
|
||
|
||
mpz_swap (r, tr);
|
||
mpz_clear (tr);
|
||
}
|
||
|
||
void
|
||
mpz_ui_pow_ui (mpz_t r, uintptr_t blimb, uintptr_t e)
|
||
{
|
||
mpz_t b;
|
||
|
||
mpz_init_set_ui (b, blimb);
|
||
mpz_pow_ui (r, b, e);
|
||
mpz_clear (b);
|
||
}
|
||
|
||
void
|
||
mpz_powm (mpz_t r, const mpz_t b, const mpz_t e, const mpz_t m)
|
||
{
|
||
mpz_t tr;
|
||
mpz_t base;
|
||
mp_size_t en, mn;
|
||
mp_srcptr mp;
|
||
struct gmp_div_inverse minv;
|
||
unsigned shift;
|
||
mp_ptr tp = NULL;
|
||
|
||
en = GMP_ABS (e->_mp_size);
|
||
mn = GMP_ABS (m->_mp_size);
|
||
if (mn == 0)
|
||
gmp_die ("mpz_powm: Zero modulo.");
|
||
|
||
if (en == 0)
|
||
{
|
||
mpz_set_ui (r, 1);
|
||
return;
|
||
}
|
||
|
||
mp = m->_mp_d;
|
||
mpn_div_qr_invert (&minv, mp, mn);
|
||
shift = minv.shift;
|
||
|
||
if (shift > 0)
|
||
{
|
||
/* To avoid shifts, we do all our reductions, except the final
|
||
one, using a *normalized* m. */
|
||
minv.shift = 0;
|
||
|
||
tp = gmp_xalloc_limbs (mn);
|
||
gmp_assert_nocarry (mpn_lshift (tp, mp, mn, shift));
|
||
mp = tp;
|
||
}
|
||
|
||
mpz_init (base);
|
||
|
||
if (e->_mp_size < 0)
|
||
{
|
||
if (!mpz_invert (base, b, m))
|
||
gmp_die ("mpz_powm: Negative exponent and non-invertible base.");
|
||
}
|
||
else
|
||
{
|
||
mp_size_t bn;
|
||
mpz_abs (base, b);
|
||
|
||
bn = base->_mp_size;
|
||
if (bn >= mn)
|
||
{
|
||
mpn_div_qr_preinv (NULL, base->_mp_d, base->_mp_size, mp, mn, &minv);
|
||
bn = mn;
|
||
}
|
||
|
||
/* We have reduced the absolute value. Now take care of the
|
||
sign. Note that we get zero represented non-canonically as
|
||
m. */
|
||
if (b->_mp_size < 0)
|
||
{
|
||
mp_ptr bp = MPZ_REALLOC (base, mn);
|
||
gmp_assert_nocarry (mpn_sub (bp, mp, mn, bp, bn));
|
||
bn = mn;
|
||
}
|
||
base->_mp_size = mpn_normalized_size (base->_mp_d, bn);
|
||
}
|
||
mpz_init_set_ui (tr, 1);
|
||
|
||
while (--en >= 0)
|
||
{
|
||
mp_limb_t w = e->_mp_d[en];
|
||
mp_limb_t bit;
|
||
|
||
bit = GMP_LIMB_HIGHBIT;
|
||
do
|
||
{
|
||
mpz_mul (tr, tr, tr);
|
||
if (w & bit)
|
||
mpz_mul (tr, tr, base);
|
||
if (tr->_mp_size > mn)
|
||
{
|
||
mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
|
||
tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
|
||
}
|
||
bit >>= 1;
|
||
}
|
||
while (bit > 0);
|
||
}
|
||
|
||
/* Final reduction */
|
||
if (tr->_mp_size >= mn)
|
||
{
|
||
minv.shift = shift;
|
||
mpn_div_qr_preinv (NULL, tr->_mp_d, tr->_mp_size, mp, mn, &minv);
|
||
tr->_mp_size = mpn_normalized_size (tr->_mp_d, mn);
|
||
}
|
||
if (tp)
|
||
gmp_free (tp);
|
||
|
||
mpz_swap (r, tr);
|
||
mpz_clear (tr);
|
||
mpz_clear (base);
|
||
}
|
||
|
||
void
|
||
mpz_powm_ui (mpz_t r, const mpz_t b, uintptr_t elimb, const mpz_t m)
|
||
{
|
||
mpz_t e;
|
||
|
||
mpz_init_set_ui (e, elimb);
|
||
mpz_powm (r, b, e, m);
|
||
mpz_clear (e);
|
||
}
|
||
|
||
/* x=trunc(y^(1/z)), r=y-x^z */
|
||
void
|
||
mpz_rootrem (mpz_t x, mpz_t r, const mpz_t y, uintptr_t z)
|
||
{
|
||
int sgn;
|
||
mpz_t t, u;
|
||
|
||
sgn = y->_mp_size < 0;
|
||
if ((~z & sgn) != 0)
|
||
gmp_die ("mpz_rootrem: Negative argument, with even root.");
|
||
if (z == 0)
|
||
gmp_die ("mpz_rootrem: Zeroth root.");
|
||
|
||
if (mpz_cmpabs_ui (y, 1) <= 0) {
|
||
if (x)
|
||
mpz_set (x, y);
|
||
if (r)
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
mpz_init (u);
|
||
mpz_init (t);
|
||
mpz_setbit (t, mpz_sizeinbase (y, 2) / z + 1);
|
||
|
||
if (z == 2) /* simplify sqrt loop: z-1 == 1 */
|
||
do {
|
||
mpz_swap (u, t); /* u = x */
|
||
mpz_tdiv_q (t, y, u); /* t = y/x */
|
||
mpz_add (t, t, u); /* t = y/x + x */
|
||
mpz_tdiv_q_2exp (t, t, 1); /* x'= (y/x + x)/2 */
|
||
} while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
|
||
else /* z != 2 */ {
|
||
mpz_t v;
|
||
|
||
mpz_init (v);
|
||
if (sgn)
|
||
mpz_neg (t, t);
|
||
|
||
do {
|
||
mpz_swap (u, t); /* u = x */
|
||
mpz_pow_ui (t, u, z - 1); /* t = x^(z-1) */
|
||
mpz_tdiv_q (t, y, t); /* t = y/x^(z-1) */
|
||
mpz_mul_ui (v, u, z - 1); /* v = x*(z-1) */
|
||
mpz_add (t, t, v); /* t = y/x^(z-1) + x*(z-1) */
|
||
mpz_tdiv_q_ui (t, t, z); /* x'=(y/x^(z-1) + x*(z-1))/z */
|
||
} while (mpz_cmpabs (t, u) < 0); /* |x'| < |x| */
|
||
|
||
mpz_clear (v);
|
||
}
|
||
|
||
if (r) {
|
||
mpz_pow_ui (t, u, z);
|
||
mpz_sub (r, y, t);
|
||
}
|
||
if (x)
|
||
mpz_swap (x, u);
|
||
mpz_clear (u);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
int
|
||
mpz_root (mpz_t x, const mpz_t y, uintptr_t z)
|
||
{
|
||
int res;
|
||
mpz_t r;
|
||
|
||
mpz_init (r);
|
||
mpz_rootrem (x, r, y, z);
|
||
res = r->_mp_size == 0;
|
||
mpz_clear (r);
|
||
|
||
return res;
|
||
}
|
||
|
||
/* Compute s = floor(sqrt(u)) and r = u - s^2. Allows r == NULL */
|
||
void
|
||
mpz_sqrtrem (mpz_t s, mpz_t r, const mpz_t u)
|
||
{
|
||
mpz_rootrem (s, r, u, 2);
|
||
}
|
||
|
||
void
|
||
mpz_sqrt (mpz_t s, const mpz_t u)
|
||
{
|
||
mpz_rootrem (s, NULL, u, 2);
|
||
}
|
||
|
||
int
|
||
mpz_perfect_square_p (const mpz_t u)
|
||
{
|
||
if (u->_mp_size <= 0)
|
||
return (u->_mp_size == 0);
|
||
else
|
||
return mpz_root (NULL, u, 2);
|
||
}
|
||
|
||
int
|
||
mpn_perfect_square_p (mp_srcptr p, mp_size_t n)
|
||
{
|
||
mpz_t t;
|
||
|
||
assert (n > 0);
|
||
assert (p [n-1] != 0);
|
||
return mpz_root (NULL, mpz_roinit_normal_n (t, p, n), 2);
|
||
}
|
||
|
||
mp_size_t
|
||
mpn_sqrtrem (mp_ptr sp, mp_ptr rp, mp_srcptr p, mp_size_t n)
|
||
{
|
||
mpz_t s, r, u;
|
||
mp_size_t res;
|
||
|
||
assert (n > 0);
|
||
assert (p [n-1] != 0);
|
||
|
||
mpz_init (r);
|
||
mpz_init (s);
|
||
mpz_rootrem (s, r, mpz_roinit_normal_n (u, p, n), 2);
|
||
|
||
assert (s->_mp_size == (n+1)/2);
|
||
mpn_copyd (sp, s->_mp_d, s->_mp_size);
|
||
mpz_clear (s);
|
||
res = r->_mp_size;
|
||
if (rp)
|
||
mpn_copyd (rp, r->_mp_d, res);
|
||
mpz_clear (r);
|
||
return res;
|
||
}
|
||
|
||
/* Combinatorics */
|
||
|
||
void
|
||
mpz_mfac_uiui (mpz_t x, uintptr_t n, uintptr_t m)
|
||
{
|
||
mpz_set_ui (x, n + (n == 0));
|
||
if (m + 1 < 2) return;
|
||
while (n > m + 1)
|
||
mpz_mul_ui (x, x, n -= m);
|
||
}
|
||
|
||
void
|
||
mpz_2fac_ui (mpz_t x, uintptr_t n)
|
||
{
|
||
mpz_mfac_uiui (x, n, 2);
|
||
}
|
||
|
||
void
|
||
mpz_fac_ui (mpz_t x, uintptr_t n)
|
||
{
|
||
mpz_mfac_uiui (x, n, 1);
|
||
}
|
||
|
||
void
|
||
mpz_bin_uiui (mpz_t r, uintptr_t n, uintptr_t k)
|
||
{
|
||
mpz_t t;
|
||
|
||
mpz_set_ui (r, k <= n);
|
||
|
||
if (k > (n >> 1))
|
||
k = (k <= n) ? n - k : 0;
|
||
|
||
mpz_init (t);
|
||
mpz_fac_ui (t, k);
|
||
|
||
for (; k > 0; --k)
|
||
mpz_mul_ui (r, r, n--);
|
||
|
||
mpz_divexact (r, r, t);
|
||
mpz_clear (t);
|
||
}
|
||
|
||
|
||
/* Primality testing */
|
||
|
||
/* Computes Kronecker (a/b) with odd b, a!=0 and GCD(a,b) = 1 */
|
||
/* Adapted from JACOBI_BASE_METHOD==4 in mpn/generic/jacbase.c */
|
||
static int
|
||
gmp_jacobi_coprime (mp_limb_t a, mp_limb_t b)
|
||
{
|
||
int c, bit = 0;
|
||
|
||
assert (b & 1);
|
||
assert (a != 0);
|
||
/* assert (mpn_gcd_11 (a, b) == 1); */
|
||
|
||
/* Below, we represent a and b shifted right so that the least
|
||
significant one bit is implicit. */
|
||
b >>= 1;
|
||
|
||
gmp_ctz(c, a);
|
||
a >>= 1;
|
||
|
||
do
|
||
{
|
||
a >>= c;
|
||
/* (2/b) = -1 if b = 3 or 5 mod 8 */
|
||
bit ^= c & (b ^ (b >> 1));
|
||
if (a < b)
|
||
{
|
||
bit ^= a & b;
|
||
a = b - a;
|
||
b -= a;
|
||
}
|
||
else
|
||
{
|
||
a -= b;
|
||
assert (a != 0);
|
||
}
|
||
|
||
gmp_ctz(c, a);
|
||
++c;
|
||
}
|
||
while (b > 0);
|
||
|
||
return bit & 1 ? -1 : 1;
|
||
}
|
||
|
||
static void
|
||
gmp_lucas_step_k_2k (mpz_t V, mpz_t Qk, const mpz_t n)
|
||
{
|
||
mpz_mod (Qk, Qk, n);
|
||
/* V_{2k} <- V_k ^ 2 - 2Q^k */
|
||
mpz_mul (V, V, V);
|
||
mpz_submul_ui (V, Qk, 2);
|
||
mpz_tdiv_r (V, V, n);
|
||
/* Q^{2k} = (Q^k)^2 */
|
||
mpz_mul (Qk, Qk, Qk);
|
||
}
|
||
|
||
/* Computes V_k, Q^k (mod n) for the Lucas' sequence */
|
||
/* with P=1, Q=Q; k = (n>>b0)|1. */
|
||
/* Requires an odd n > 4; b0 > 0; -2*Q must not overflow a intptr_t */
|
||
/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */
|
||
static int
|
||
gmp_lucas_mod (mpz_t V, mpz_t Qk, intptr_t Q,
|
||
mp_bitcnt_t b0, const mpz_t n)
|
||
{
|
||
mp_bitcnt_t bs;
|
||
mpz_t U;
|
||
int res;
|
||
|
||
assert (b0 > 0);
|
||
assert (Q <= - (INTPTR_MIN / 2));
|
||
assert (Q >= - (INTPTR_MAX / 2));
|
||
assert (mpz_cmp_ui (n, 4) > 0);
|
||
assert (mpz_odd_p (n));
|
||
|
||
mpz_init_set_ui (U, 1); /* U1 = 1 */
|
||
mpz_set_ui (V, 1); /* V1 = 1 */
|
||
mpz_set_si (Qk, Q);
|
||
|
||
for (bs = mpz_sizeinbase (n, 2) - 1; --bs >= b0;)
|
||
{
|
||
/* U_{2k} <- U_k * V_k */
|
||
mpz_mul (U, U, V);
|
||
/* V_{2k} <- V_k ^ 2 - 2Q^k */
|
||
/* Q^{2k} = (Q^k)^2 */
|
||
gmp_lucas_step_k_2k (V, Qk, n);
|
||
|
||
/* A step k->k+1 is performed if the bit in $n$ is 1 */
|
||
/* mpz_tstbit(n,bs) or the bit is 0 in $n$ but */
|
||
/* should be 1 in $n+1$ (bs == b0) */
|
||
if (b0 == bs || mpz_tstbit (n, bs))
|
||
{
|
||
/* Q^{k+1} <- Q^k * Q */
|
||
mpz_mul_si (Qk, Qk, Q);
|
||
/* U_{k+1} <- (U_k + V_k) / 2 */
|
||
mpz_swap (U, V); /* Keep in V the old value of U_k */
|
||
mpz_add (U, U, V);
|
||
/* We have to compute U/2, so we need an even value, */
|
||
/* equivalent (mod n) */
|
||
if (mpz_odd_p (U))
|
||
mpz_add (U, U, n);
|
||
mpz_tdiv_q_2exp (U, U, 1);
|
||
/* V_{k+1} <-(D*U_k + V_k) / 2 =
|
||
U_{k+1} + (D-1)/2*U_k = U_{k+1} - 2Q*U_k */
|
||
mpz_mul_si (V, V, -2*Q);
|
||
mpz_add (V, U, V);
|
||
mpz_tdiv_r (V, V, n);
|
||
}
|
||
mpz_tdiv_r (U, U, n);
|
||
}
|
||
|
||
res = U->_mp_size == 0;
|
||
mpz_clear (U);
|
||
return res;
|
||
}
|
||
|
||
/* Performs strong Lucas' test on x, with parameters suggested */
|
||
/* for the BPSW test. Qk is only passed to recycle a variable. */
|
||
/* Requires GCD (x,6) = 1.*/
|
||
static int
|
||
gmp_stronglucas (const mpz_t x, mpz_t Qk)
|
||
{
|
||
mp_bitcnt_t b0;
|
||
mpz_t V, n;
|
||
mp_limb_t maxD, D; /* The absolute value is stored. */
|
||
intptr_t Q;
|
||
mp_limb_t tl;
|
||
|
||
/* Test on the absolute value. */
|
||
mpz_roinit_normal_n (n, x->_mp_d, GMP_ABS (x->_mp_size));
|
||
|
||
assert (mpz_odd_p (n));
|
||
/* assert (mpz_gcd_ui (NULL, n, 6) == 1); */
|
||
if (mpz_root (Qk, n, 2))
|
||
return 0; /* A square is composite. */
|
||
|
||
/* Check Ds up to square root (in case, n is prime)
|
||
or avoid overflows */
|
||
maxD = (Qk->_mp_size == 1) ? Qk->_mp_d [0] - 1 : GMP_LIMB_MAX;
|
||
|
||
D = 3;
|
||
/* Search a D such that (D/n) = -1 in the sequence 5,-7,9,-11,.. */
|
||
/* For those Ds we have (D/n) = (n/|D|) */
|
||
do
|
||
{
|
||
if (D >= maxD)
|
||
return 1 + (D != GMP_LIMB_MAX); /* (1 + ! ~ D) */
|
||
D += 2;
|
||
tl = mpz_tdiv_ui (n, D);
|
||
if (tl == 0)
|
||
return 0;
|
||
}
|
||
while (gmp_jacobi_coprime (tl, D) == 1);
|
||
|
||
mpz_init (V);
|
||
|
||
/* n-(D/n) = n+1 = d*2^{b0}, with d = (n>>b0) | 1 */
|
||
b0 = mpz_scan0 (n, 0);
|
||
|
||
/* D= P^2 - 4Q; P = 1; Q = (1-D)/4 */
|
||
Q = (D & 2) ? (intptr_t) (D >> 2) + 1 : -(intptr_t) (D >> 2);
|
||
|
||
if (! gmp_lucas_mod (V, Qk, Q, b0, n)) /* If Ud != 0 */
|
||
while (V->_mp_size != 0 && --b0 != 0) /* while Vk != 0 */
|
||
/* V <- V ^ 2 - 2Q^k */
|
||
/* Q^{2k} = (Q^k)^2 */
|
||
gmp_lucas_step_k_2k (V, Qk, n);
|
||
|
||
mpz_clear (V);
|
||
return (b0 != 0);
|
||
}
|
||
|
||
static int
|
||
gmp_millerrabin (const mpz_t n, const mpz_t nm1, mpz_t y,
|
||
const mpz_t q, mp_bitcnt_t k)
|
||
{
|
||
assert (k > 0);
|
||
|
||
/* Caller must initialize y to the base. */
|
||
mpz_powm (y, y, q, n);
|
||
|
||
if (mpz_cmp_ui (y, 1) == 0 || mpz_cmp (y, nm1) == 0)
|
||
return 1;
|
||
|
||
while (--k > 0)
|
||
{
|
||
mpz_powm_ui (y, y, 2, n);
|
||
if (mpz_cmp (y, nm1) == 0)
|
||
return 1;
|
||
/* y == 1 means that the previous y was a non-trivial square root
|
||
of 1 (mod n). y == 0 means that n is a power of the base.
|
||
In either case, n is not prime. */
|
||
if (mpz_cmp_ui (y, 1) <= 0)
|
||
return 0;
|
||
}
|
||
return 0;
|
||
}
|
||
|
||
/* This product is 0xc0cfd797, and fits in 32 bits. */
|
||
#define GMP_PRIME_PRODUCT \
|
||
(3UL*5UL*7UL*11UL*13UL*17UL*19UL*23UL*29UL)
|
||
|
||
/* Bit (p+1)/2 is set, for each odd prime <= 61 */
|
||
#define GMP_PRIME_MASK 0xc96996dcUL
|
||
|
||
int
|
||
mpz_probab_prime_p (const mpz_t n, int reps)
|
||
{
|
||
mpz_t nm1;
|
||
mpz_t q;
|
||
mpz_t y;
|
||
mp_bitcnt_t k;
|
||
int is_prime;
|
||
int j;
|
||
|
||
/* Note that we use the absolute value of n only, for compatibility
|
||
with the real GMP. */
|
||
if (mpz_even_p (n))
|
||
return (mpz_cmpabs_ui (n, 2) == 0) ? 2 : 0;
|
||
|
||
/* Above test excludes n == 0 */
|
||
assert (n->_mp_size != 0);
|
||
|
||
if (mpz_cmpabs_ui (n, 64) < 0)
|
||
return (GMP_PRIME_MASK >> (n->_mp_d[0] >> 1)) & 2;
|
||
|
||
if (mpz_gcd_ui (NULL, n, GMP_PRIME_PRODUCT) != 1)
|
||
return 0;
|
||
|
||
/* All prime factors are >= 31. */
|
||
if (mpz_cmpabs_ui (n, 31*31) < 0)
|
||
return 2;
|
||
|
||
mpz_init (nm1);
|
||
mpz_init (q);
|
||
|
||
/* Find q and k, where q is odd and n = 1 + 2**k * q. */
|
||
mpz_abs (nm1, n);
|
||
nm1->_mp_d[0] -= 1;
|
||
k = mpz_scan1 (nm1, 0);
|
||
mpz_tdiv_q_2exp (q, nm1, k);
|
||
|
||
/* BPSW test */
|
||
mpz_init_set_ui (y, 2);
|
||
is_prime = gmp_millerrabin (n, nm1, y, q, k) && gmp_stronglucas (n, y);
|
||
reps -= 24; /* skip the first 24 repetitions */
|
||
|
||
/* Use Miller-Rabin, with a deterministic sequence of bases, a[j] =
|
||
j^2 + j + 41 using Euler's polynomial. We potentially stop early,
|
||
if a[j] >= n - 1. Since n >= 31*31, this can happen only if reps >
|
||
30 (a[30] == 971 > 31*31 == 961). */
|
||
|
||
for (j = 0; is_prime & (j < reps); j++)
|
||
{
|
||
mpz_set_ui (y, (uintptr_t) j*j+j+41);
|
||
if (mpz_cmp (y, nm1) >= 0)
|
||
{
|
||
/* Don't try any further bases. This "early" break does not affect
|
||
the result for any reasonable reps value (<=5000 was tested) */
|
||
assert (j >= 30);
|
||
break;
|
||
}
|
||
is_prime = gmp_millerrabin (n, nm1, y, q, k);
|
||
}
|
||
mpz_clear (nm1);
|
||
mpz_clear (q);
|
||
mpz_clear (y);
|
||
|
||
return is_prime;
|
||
}
|
||
|
||
|
||
/* Logical operations and bit manipulation. */
|
||
|
||
/* Numbers are treated as if represented in two's complement (and
|
||
infinitely sign extended). For a negative values we get the two's
|
||
complement from -x = ~x + 1, where ~ is bitwise complement.
|
||
Negation transforms
|
||
|
||
xxxx10...0
|
||
|
||
into
|
||
|
||
yyyy10...0
|
||
|
||
where yyyy is the bitwise complement of xxxx. So least significant
|
||
bits, up to and including the first one bit, are unchanged, and
|
||
the more significant bits are all complemented.
|
||
|
||
To change a bit from zero to one in a negative number, subtract the
|
||
corresponding power of two from the absolute value. This can never
|
||
underflow. To change a bit from one to zero, add the corresponding
|
||
power of two, and this might overflow. E.g., if x = -001111, the
|
||
two's complement is 110001. Clearing the least significant bit, we
|
||
get two's complement 110000, and -010000. */
|
||
|
||
int
|
||
mpz_tstbit (const mpz_t d, mp_bitcnt_t bit_index)
|
||
{
|
||
mp_size_t limb_index;
|
||
unsigned shift;
|
||
mp_size_t ds;
|
||
mp_size_t dn;
|
||
mp_limb_t w;
|
||
int bit;
|
||
|
||
ds = d->_mp_size;
|
||
dn = GMP_ABS (ds);
|
||
limb_index = bit_index / GMP_LIMB_BITS;
|
||
if (limb_index >= dn)
|
||
return ds < 0;
|
||
|
||
shift = bit_index % GMP_LIMB_BITS;
|
||
w = d->_mp_d[limb_index];
|
||
bit = (w >> shift) & 1;
|
||
|
||
if (ds < 0)
|
||
{
|
||
/* d < 0. Check if any of the bits below is set: If so, our bit
|
||
must be complemented. */
|
||
if (shift > 0 && (mp_limb_t) (w << (GMP_LIMB_BITS - shift)) > 0)
|
||
return bit ^ 1;
|
||
while (--limb_index >= 0)
|
||
if (d->_mp_d[limb_index] > 0)
|
||
return bit ^ 1;
|
||
}
|
||
return bit;
|
||
}
|
||
|
||
static void
|
||
mpz_abs_add_bit (mpz_t d, mp_bitcnt_t bit_index)
|
||
{
|
||
mp_size_t dn, limb_index;
|
||
mp_limb_t bit;
|
||
mp_ptr dp;
|
||
|
||
dn = GMP_ABS (d->_mp_size);
|
||
|
||
limb_index = bit_index / GMP_LIMB_BITS;
|
||
bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
|
||
|
||
if (limb_index >= dn)
|
||
{
|
||
mp_size_t i;
|
||
/* The bit should be set outside of the end of the number.
|
||
We have to increase the size of the number. */
|
||
dp = MPZ_REALLOC (d, limb_index + 1);
|
||
|
||
dp[limb_index] = bit;
|
||
for (i = dn; i < limb_index; i++)
|
||
dp[i] = 0;
|
||
dn = limb_index + 1;
|
||
}
|
||
else
|
||
{
|
||
mp_limb_t cy;
|
||
|
||
dp = d->_mp_d;
|
||
|
||
cy = mpn_add_1 (dp + limb_index, dp + limb_index, dn - limb_index, bit);
|
||
if (cy > 0)
|
||
{
|
||
dp = MPZ_REALLOC (d, dn + 1);
|
||
dp[dn++] = cy;
|
||
}
|
||
}
|
||
|
||
d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
|
||
}
|
||
|
||
static void
|
||
mpz_abs_sub_bit (mpz_t d, mp_bitcnt_t bit_index)
|
||
{
|
||
mp_size_t dn, limb_index;
|
||
mp_ptr dp;
|
||
mp_limb_t bit;
|
||
|
||
dn = GMP_ABS (d->_mp_size);
|
||
dp = d->_mp_d;
|
||
|
||
limb_index = bit_index / GMP_LIMB_BITS;
|
||
bit = (mp_limb_t) 1 << (bit_index % GMP_LIMB_BITS);
|
||
|
||
assert (limb_index < dn);
|
||
|
||
gmp_assert_nocarry (mpn_sub_1 (dp + limb_index, dp + limb_index,
|
||
dn - limb_index, bit));
|
||
dn = mpn_normalized_size (dp, dn);
|
||
d->_mp_size = (d->_mp_size < 0) ? - dn : dn;
|
||
}
|
||
|
||
void
|
||
mpz_setbit (mpz_t d, mp_bitcnt_t bit_index)
|
||
{
|
||
if (!mpz_tstbit (d, bit_index))
|
||
{
|
||
if (d->_mp_size >= 0)
|
||
mpz_abs_add_bit (d, bit_index);
|
||
else
|
||
mpz_abs_sub_bit (d, bit_index);
|
||
}
|
||
}
|
||
|
||
void
|
||
mpz_clrbit (mpz_t d, mp_bitcnt_t bit_index)
|
||
{
|
||
if (mpz_tstbit (d, bit_index))
|
||
{
|
||
if (d->_mp_size >= 0)
|
||
mpz_abs_sub_bit (d, bit_index);
|
||
else
|
||
mpz_abs_add_bit (d, bit_index);
|
||
}
|
||
}
|
||
|
||
void
|
||
mpz_combit (mpz_t d, mp_bitcnt_t bit_index)
|
||
{
|
||
if (mpz_tstbit (d, bit_index) ^ (d->_mp_size < 0))
|
||
mpz_abs_sub_bit (d, bit_index);
|
||
else
|
||
mpz_abs_add_bit (d, bit_index);
|
||
}
|
||
|
||
void
|
||
mpz_com (mpz_t r, const mpz_t u)
|
||
{
|
||
mpz_add_ui (r, u, 1);
|
||
mpz_neg (r, r);
|
||
}
|
||
|
||
void
|
||
mpz_and (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mp_size_t un, vn, rn, i;
|
||
mp_ptr up, vp, rp;
|
||
|
||
mp_limb_t ux, vx, rx;
|
||
mp_limb_t uc, vc, rc;
|
||
mp_limb_t ul, vl, rl;
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
vn = GMP_ABS (v->_mp_size);
|
||
if (un < vn)
|
||
{
|
||
MPZ_SRCPTR_SWAP (u, v);
|
||
MP_SIZE_T_SWAP (un, vn);
|
||
}
|
||
if (vn == 0)
|
||
{
|
||
r->_mp_size = 0;
|
||
return;
|
||
}
|
||
|
||
uc = u->_mp_size < 0;
|
||
vc = v->_mp_size < 0;
|
||
rc = uc & vc;
|
||
|
||
ux = -uc;
|
||
vx = -vc;
|
||
rx = -rc;
|
||
|
||
/* If the smaller input is positive, higher limbs don't matter. */
|
||
rn = vx ? un : vn;
|
||
|
||
rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
|
||
|
||
up = u->_mp_d;
|
||
vp = v->_mp_d;
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
ul = (up[i] ^ ux) + uc;
|
||
uc = ul < uc;
|
||
|
||
vl = (vp[i] ^ vx) + vc;
|
||
vc = vl < vc;
|
||
|
||
rl = ( (ul & vl) ^ rx) + rc;
|
||
rc = rl < rc;
|
||
rp[i] = rl;
|
||
}
|
||
while (++i < vn);
|
||
assert (vc == 0);
|
||
|
||
for (; i < rn; i++)
|
||
{
|
||
ul = (up[i] ^ ux) + uc;
|
||
uc = ul < uc;
|
||
|
||
rl = ( (ul & vx) ^ rx) + rc;
|
||
rc = rl < rc;
|
||
rp[i] = rl;
|
||
}
|
||
if (rc)
|
||
rp[rn++] = rc;
|
||
else
|
||
rn = mpn_normalized_size (rp, rn);
|
||
|
||
r->_mp_size = rx ? -rn : rn;
|
||
}
|
||
|
||
void
|
||
mpz_ior (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mp_size_t un, vn, rn, i;
|
||
mp_ptr up, vp, rp;
|
||
|
||
mp_limb_t ux, vx, rx;
|
||
mp_limb_t uc, vc, rc;
|
||
mp_limb_t ul, vl, rl;
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
vn = GMP_ABS (v->_mp_size);
|
||
if (un < vn)
|
||
{
|
||
MPZ_SRCPTR_SWAP (u, v);
|
||
MP_SIZE_T_SWAP (un, vn);
|
||
}
|
||
if (vn == 0)
|
||
{
|
||
mpz_set (r, u);
|
||
return;
|
||
}
|
||
|
||
uc = u->_mp_size < 0;
|
||
vc = v->_mp_size < 0;
|
||
rc = uc | vc;
|
||
|
||
ux = -uc;
|
||
vx = -vc;
|
||
rx = -rc;
|
||
|
||
/* If the smaller input is negative, by sign extension higher limbs
|
||
don't matter. */
|
||
rn = vx ? vn : un;
|
||
|
||
rp = MPZ_REALLOC (r, rn + (mp_size_t) rc);
|
||
|
||
up = u->_mp_d;
|
||
vp = v->_mp_d;
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
ul = (up[i] ^ ux) + uc;
|
||
uc = ul < uc;
|
||
|
||
vl = (vp[i] ^ vx) + vc;
|
||
vc = vl < vc;
|
||
|
||
rl = ( (ul | vl) ^ rx) + rc;
|
||
rc = rl < rc;
|
||
rp[i] = rl;
|
||
}
|
||
while (++i < vn);
|
||
assert (vc == 0);
|
||
|
||
for (; i < rn; i++)
|
||
{
|
||
ul = (up[i] ^ ux) + uc;
|
||
uc = ul < uc;
|
||
|
||
rl = ( (ul | vx) ^ rx) + rc;
|
||
rc = rl < rc;
|
||
rp[i] = rl;
|
||
}
|
||
if (rc)
|
||
rp[rn++] = rc;
|
||
else
|
||
rn = mpn_normalized_size (rp, rn);
|
||
|
||
r->_mp_size = rx ? -rn : rn;
|
||
}
|
||
|
||
void
|
||
mpz_xor (mpz_t r, const mpz_t u, const mpz_t v)
|
||
{
|
||
mp_size_t un, vn, i;
|
||
mp_ptr up, vp, rp;
|
||
|
||
mp_limb_t ux, vx, rx;
|
||
mp_limb_t uc, vc, rc;
|
||
mp_limb_t ul, vl, rl;
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
vn = GMP_ABS (v->_mp_size);
|
||
if (un < vn)
|
||
{
|
||
MPZ_SRCPTR_SWAP (u, v);
|
||
MP_SIZE_T_SWAP (un, vn);
|
||
}
|
||
if (vn == 0)
|
||
{
|
||
mpz_set (r, u);
|
||
return;
|
||
}
|
||
|
||
uc = u->_mp_size < 0;
|
||
vc = v->_mp_size < 0;
|
||
rc = uc ^ vc;
|
||
|
||
ux = -uc;
|
||
vx = -vc;
|
||
rx = -rc;
|
||
|
||
rp = MPZ_REALLOC (r, un + (mp_size_t) rc);
|
||
|
||
up = u->_mp_d;
|
||
vp = v->_mp_d;
|
||
|
||
i = 0;
|
||
do
|
||
{
|
||
ul = (up[i] ^ ux) + uc;
|
||
uc = ul < uc;
|
||
|
||
vl = (vp[i] ^ vx) + vc;
|
||
vc = vl < vc;
|
||
|
||
rl = (ul ^ vl ^ rx) + rc;
|
||
rc = rl < rc;
|
||
rp[i] = rl;
|
||
}
|
||
while (++i < vn);
|
||
assert (vc == 0);
|
||
|
||
for (; i < un; i++)
|
||
{
|
||
ul = (up[i] ^ ux) + uc;
|
||
uc = ul < uc;
|
||
|
||
rl = (ul ^ ux) + rc;
|
||
rc = rl < rc;
|
||
rp[i] = rl;
|
||
}
|
||
if (rc)
|
||
rp[un++] = rc;
|
||
else
|
||
un = mpn_normalized_size (rp, un);
|
||
|
||
r->_mp_size = rx ? -un : un;
|
||
}
|
||
|
||
static unsigned
|
||
gmp_popcount_limb (mp_limb_t x)
|
||
{
|
||
unsigned c;
|
||
|
||
/* Do 16 bits at a time, to avoid limb-sized constants. */
|
||
int LOCAL_SHIFT_BITS = 16;
|
||
for (c = 0; x > 0;)
|
||
{
|
||
unsigned w = x - ((x >> 1) & 0x5555);
|
||
w = ((w >> 2) & 0x3333) + (w & 0x3333);
|
||
w = (w >> 4) + w;
|
||
w = ((w >> 8) & 0x000f) + (w & 0x000f);
|
||
c += w;
|
||
if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS)
|
||
x >>= LOCAL_SHIFT_BITS;
|
||
else
|
||
x = 0;
|
||
}
|
||
return c;
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpn_popcount (mp_srcptr p, mp_size_t n)
|
||
{
|
||
mp_size_t i;
|
||
mp_bitcnt_t c;
|
||
|
||
for (c = 0, i = 0; i < n; i++)
|
||
c += gmp_popcount_limb (p[i]);
|
||
|
||
return c;
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpz_popcount (const mpz_t u)
|
||
{
|
||
mp_size_t un;
|
||
|
||
un = u->_mp_size;
|
||
|
||
if (un < 0)
|
||
return ~(mp_bitcnt_t) 0;
|
||
|
||
return mpn_popcount (u->_mp_d, un);
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpz_hamdist (const mpz_t u, const mpz_t v)
|
||
{
|
||
mp_size_t un, vn, i;
|
||
mp_limb_t uc, vc, ul, vl, comp;
|
||
mp_srcptr up, vp;
|
||
mp_bitcnt_t c;
|
||
|
||
un = u->_mp_size;
|
||
vn = v->_mp_size;
|
||
|
||
if ( (un ^ vn) < 0)
|
||
return ~(mp_bitcnt_t) 0;
|
||
|
||
comp = - (uc = vc = (un < 0));
|
||
if (uc)
|
||
{
|
||
assert (vn < 0);
|
||
un = -un;
|
||
vn = -vn;
|
||
}
|
||
|
||
up = u->_mp_d;
|
||
vp = v->_mp_d;
|
||
|
||
if (un < vn)
|
||
MPN_SRCPTR_SWAP (up, un, vp, vn);
|
||
|
||
for (i = 0, c = 0; i < vn; i++)
|
||
{
|
||
ul = (up[i] ^ comp) + uc;
|
||
uc = ul < uc;
|
||
|
||
vl = (vp[i] ^ comp) + vc;
|
||
vc = vl < vc;
|
||
|
||
c += gmp_popcount_limb (ul ^ vl);
|
||
}
|
||
assert (vc == 0);
|
||
|
||
for (; i < un; i++)
|
||
{
|
||
ul = (up[i] ^ comp) + uc;
|
||
uc = ul < uc;
|
||
|
||
c += gmp_popcount_limb (ul ^ comp);
|
||
}
|
||
|
||
return c;
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpz_scan1 (const mpz_t u, mp_bitcnt_t starting_bit)
|
||
{
|
||
mp_ptr up;
|
||
mp_size_t us, un, i;
|
||
mp_limb_t limb, ux;
|
||
|
||
us = u->_mp_size;
|
||
un = GMP_ABS (us);
|
||
i = starting_bit / GMP_LIMB_BITS;
|
||
|
||
/* Past the end there's no 1 bits for u>=0, or an immediate 1 bit
|
||
for u<0. Notice this test picks up any u==0 too. */
|
||
if (i >= un)
|
||
return (us >= 0 ? ~(mp_bitcnt_t) 0 : starting_bit);
|
||
|
||
up = u->_mp_d;
|
||
ux = 0;
|
||
limb = up[i];
|
||
|
||
if (starting_bit != 0)
|
||
{
|
||
if (us < 0)
|
||
{
|
||
ux = mpn_zero_p (up, i);
|
||
limb = ~ limb + ux;
|
||
ux = - (mp_limb_t) (limb >= ux);
|
||
}
|
||
|
||
/* Mask to 0 all bits before starting_bit, thus ignoring them. */
|
||
limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
|
||
}
|
||
|
||
return mpn_common_scan (limb, i, up, un, ux);
|
||
}
|
||
|
||
mp_bitcnt_t
|
||
mpz_scan0 (const mpz_t u, mp_bitcnt_t starting_bit)
|
||
{
|
||
mp_ptr up;
|
||
mp_size_t us, un, i;
|
||
mp_limb_t limb, ux;
|
||
|
||
us = u->_mp_size;
|
||
ux = - (mp_limb_t) (us >= 0);
|
||
un = GMP_ABS (us);
|
||
i = starting_bit / GMP_LIMB_BITS;
|
||
|
||
/* When past end, there's an immediate 0 bit for u>=0, or no 0 bits for
|
||
u<0. Notice this test picks up all cases of u==0 too. */
|
||
if (i >= un)
|
||
return (ux ? starting_bit : ~(mp_bitcnt_t) 0);
|
||
|
||
up = u->_mp_d;
|
||
limb = up[i] ^ ux;
|
||
|
||
if (ux == 0)
|
||
limb -= mpn_zero_p (up, i); /* limb = ~(~limb + zero_p) */
|
||
|
||
/* Mask all bits before starting_bit, thus ignoring them. */
|
||
limb &= GMP_LIMB_MAX << (starting_bit % GMP_LIMB_BITS);
|
||
|
||
return mpn_common_scan (limb, i, up, un, ux);
|
||
}
|
||
|
||
|
||
/* MPZ base conversion. */
|
||
|
||
size_t
|
||
mpz_sizeinbase (const mpz_t u, int base)
|
||
{
|
||
mp_size_t un;
|
||
mp_srcptr up;
|
||
mp_ptr tp;
|
||
mp_bitcnt_t bits;
|
||
struct gmp_div_inverse bi;
|
||
size_t ndigits;
|
||
|
||
assert (base >= 2);
|
||
assert (base <= 62);
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
if (un == 0)
|
||
return 1;
|
||
|
||
up = u->_mp_d;
|
||
|
||
bits = (un - 1) * GMP_LIMB_BITS + mpn_limb_size_in_base_2 (up[un-1]);
|
||
switch (base)
|
||
{
|
||
case 2:
|
||
return bits;
|
||
case 4:
|
||
return (bits + 1) / 2;
|
||
case 8:
|
||
return (bits + 2) / 3;
|
||
case 16:
|
||
return (bits + 3) / 4;
|
||
case 32:
|
||
return (bits + 4) / 5;
|
||
/* FIXME: Do something more clever for the common case of base
|
||
10. */
|
||
}
|
||
|
||
tp = gmp_xalloc_limbs (un);
|
||
mpn_copyi (tp, up, un);
|
||
mpn_div_qr_1_invert (&bi, base);
|
||
|
||
ndigits = 0;
|
||
do
|
||
{
|
||
ndigits++;
|
||
mpn_div_qr_1_preinv (tp, tp, un, &bi);
|
||
un -= (tp[un-1] == 0);
|
||
}
|
||
while (un > 0);
|
||
|
||
gmp_free (tp);
|
||
return ndigits;
|
||
}
|
||
|
||
char *
|
||
mpz_get_str (char *sp, int base, const mpz_t u)
|
||
{
|
||
unsigned bits;
|
||
const char *digits;
|
||
mp_size_t un;
|
||
size_t i, sn;
|
||
|
||
digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
|
||
if (base > 1)
|
||
{
|
||
if (base <= 36)
|
||
digits = "0123456789abcdefghijklmnopqrstuvwxyz";
|
||
else if (base > 62)
|
||
return NULL;
|
||
}
|
||
else if (base >= -1)
|
||
base = 10;
|
||
else
|
||
{
|
||
base = -base;
|
||
if (base > 36)
|
||
return NULL;
|
||
}
|
||
|
||
sn = 1 + mpz_sizeinbase (u, base);
|
||
if (!sp)
|
||
sp = (char *) gmp_xalloc (1 + sn);
|
||
|
||
un = GMP_ABS (u->_mp_size);
|
||
|
||
if (un == 0)
|
||
{
|
||
sp[0] = '0';
|
||
sp[1] = '\0';
|
||
return sp;
|
||
}
|
||
|
||
i = 0;
|
||
|
||
if (u->_mp_size < 0)
|
||
sp[i++] = '-';
|
||
|
||
bits = mpn_base_power_of_two_p (base);
|
||
|
||
if (bits)
|
||
/* Not modified in this case. */
|
||
sn = i + mpn_get_str_bits ((unsigned char *) sp + i, bits, u->_mp_d, un);
|
||
else
|
||
{
|
||
struct mpn_base_info info;
|
||
mp_ptr tp;
|
||
|
||
mpn_get_base_info (&info, base);
|
||
tp = gmp_xalloc_limbs (un);
|
||
mpn_copyi (tp, u->_mp_d, un);
|
||
|
||
sn = i + mpn_get_str_other ((unsigned char *) sp + i, base, &info, tp, un);
|
||
gmp_free (tp);
|
||
}
|
||
|
||
for (; i < sn; i++)
|
||
sp[i] = digits[(unsigned char) sp[i]];
|
||
|
||
sp[sn] = '\0';
|
||
return sp;
|
||
}
|
||
|
||
int
|
||
mpz_set_str (mpz_t r, const char *sp, int base)
|
||
{
|
||
unsigned bits, value_of_a;
|
||
mp_size_t rn, alloc;
|
||
mp_ptr rp;
|
||
size_t dn;
|
||
int sign;
|
||
unsigned char *dp;
|
||
|
||
assert (base == 0 || (base >= 2 && base <= 62));
|
||
|
||
while (isspace( (unsigned char) *sp))
|
||
sp++;
|
||
|
||
sign = (*sp == '-');
|
||
sp += sign;
|
||
|
||
if (base == 0)
|
||
{
|
||
if (sp[0] == '0')
|
||
{
|
||
if (sp[1] == 'x' || sp[1] == 'X')
|
||
{
|
||
base = 16;
|
||
sp += 2;
|
||
}
|
||
else if (sp[1] == 'b' || sp[1] == 'B')
|
||
{
|
||
base = 2;
|
||
sp += 2;
|
||
}
|
||
else
|
||
base = 8;
|
||
}
|
||
else
|
||
base = 10;
|
||
}
|
||
|
||
if (!*sp)
|
||
{
|
||
r->_mp_size = 0;
|
||
return -1;
|
||
}
|
||
dp = (unsigned char *) gmp_xalloc (strlen (sp));
|
||
|
||
value_of_a = (base > 36) ? 36 : 10;
|
||
for (dn = 0; *sp; sp++)
|
||
{
|
||
unsigned digit;
|
||
|
||
if (isspace ((unsigned char) *sp))
|
||
continue;
|
||
else if (*sp >= '0' && *sp <= '9')
|
||
digit = *sp - '0';
|
||
else if (*sp >= 'a' && *sp <= 'z')
|
||
digit = *sp - 'a' + value_of_a;
|
||
else if (*sp >= 'A' && *sp <= 'Z')
|
||
digit = *sp - 'A' + 10;
|
||
else
|
||
digit = base; /* fail */
|
||
|
||
if (digit >= (unsigned) base)
|
||
{
|
||
gmp_free (dp);
|
||
r->_mp_size = 0;
|
||
return -1;
|
||
}
|
||
|
||
dp[dn++] = digit;
|
||
}
|
||
|
||
if (!dn)
|
||
{
|
||
gmp_free (dp);
|
||
r->_mp_size = 0;
|
||
return -1;
|
||
}
|
||
bits = mpn_base_power_of_two_p (base);
|
||
|
||
if (bits > 0)
|
||
{
|
||
alloc = (dn * bits + GMP_LIMB_BITS - 1) / GMP_LIMB_BITS;
|
||
rp = MPZ_REALLOC (r, alloc);
|
||
rn = mpn_set_str_bits (rp, dp, dn, bits);
|
||
}
|
||
else
|
||
{
|
||
struct mpn_base_info info;
|
||
mpn_get_base_info (&info, base);
|
||
alloc = (dn + info.exp - 1) / info.exp;
|
||
rp = MPZ_REALLOC (r, alloc);
|
||
rn = mpn_set_str_other (rp, dp, dn, base, &info);
|
||
/* Normalization, needed for all-zero input. */
|
||
assert (rn > 0);
|
||
rn -= rp[rn-1] == 0;
|
||
}
|
||
assert (rn <= alloc);
|
||
gmp_free (dp);
|
||
|
||
r->_mp_size = sign ? - rn : rn;
|
||
|
||
return 0;
|
||
}
|
||
|
||
int
|
||
mpz_init_set_str (mpz_t r, const char *sp, int base)
|
||
{
|
||
mpz_init (r);
|
||
return mpz_set_str (r, sp, base);
|
||
}
|
||
|
||
size_t
|
||
mpz_out_str (FILE *stream, int base, const mpz_t x)
|
||
{
|
||
char *str;
|
||
size_t len;
|
||
|
||
str = mpz_get_str (NULL, base, x);
|
||
if (!str)
|
||
return 0;
|
||
len = strlen (str);
|
||
len = fwrite (str, 1, len, stream);
|
||
gmp_free (str);
|
||
return len;
|
||
}
|
||
|
||
|
||
static int
|
||
gmp_detect_endian (void)
|
||
{
|
||
static const int i = 2;
|
||
const unsigned char *p = (const unsigned char *) &i;
|
||
return 1 - *p;
|
||
}
|
||
|
||
/* Import and export. Does not support nails. */
|
||
void
|
||
mpz_import (mpz_t r, size_t count, int order, size_t size, int endian,
|
||
size_t nails, const void *src)
|
||
{
|
||
const unsigned char *p;
|
||
ptrdiff_t word_step;
|
||
mp_ptr rp;
|
||
mp_size_t rn;
|
||
|
||
/* The current (partial) limb. */
|
||
mp_limb_t limb;
|
||
/* The number of bytes already copied to this limb (starting from
|
||
the low end). */
|
||
size_t bytes;
|
||
/* The index where the limb should be stored, when completed. */
|
||
mp_size_t i;
|
||
|
||
if (nails != 0)
|
||
gmp_die ("mpz_import: Nails not supported.");
|
||
|
||
assert (order == 1 || order == -1);
|
||
assert (endian >= -1 && endian <= 1);
|
||
|
||
if (endian == 0)
|
||
endian = gmp_detect_endian ();
|
||
|
||
p = (unsigned char *) src;
|
||
|
||
word_step = (order != endian) ? 2 * size : 0;
|
||
|
||
/* Process bytes from the least significant end, so point p at the
|
||
least significant word. */
|
||
if (order == 1)
|
||
{
|
||
p += size * (count - 1);
|
||
word_step = - word_step;
|
||
}
|
||
|
||
/* And at least significant byte of that word. */
|
||
if (endian == 1)
|
||
p += (size - 1);
|
||
|
||
rn = (size * count + sizeof(mp_limb_t) - 1) / sizeof(mp_limb_t);
|
||
rp = MPZ_REALLOC (r, rn);
|
||
|
||
for (limb = 0, bytes = 0, i = 0; count > 0; count--, p += word_step)
|
||
{
|
||
size_t j;
|
||
for (j = 0; j < size; j++, p -= (ptrdiff_t) endian)
|
||
{
|
||
limb |= (mp_limb_t) *p << (bytes++ * CHAR_BIT);
|
||
if (bytes == sizeof(mp_limb_t))
|
||
{
|
||
rp[i++] = limb;
|
||
bytes = 0;
|
||
limb = 0;
|
||
}
|
||
}
|
||
}
|
||
assert (i + (bytes > 0) == rn);
|
||
if (limb != 0)
|
||
rp[i++] = limb;
|
||
else
|
||
i = mpn_normalized_size (rp, i);
|
||
|
||
r->_mp_size = i;
|
||
}
|
||
|
||
void *
|
||
mpz_export (void *r, size_t *countp, int order, size_t size, int endian,
|
||
size_t nails, const mpz_t u)
|
||
{
|
||
size_t count;
|
||
mp_size_t un;
|
||
|
||
if (nails != 0)
|
||
gmp_die ("mpz_import: Nails not supported.");
|
||
|
||
assert (order == 1 || order == -1);
|
||
assert (endian >= -1 && endian <= 1);
|
||
assert (size > 0 || u->_mp_size == 0);
|
||
|
||
un = u->_mp_size;
|
||
count = 0;
|
||
if (un != 0)
|
||
{
|
||
size_t k;
|
||
unsigned char *p;
|
||
ptrdiff_t word_step;
|
||
/* The current (partial) limb. */
|
||
mp_limb_t limb;
|
||
/* The number of bytes left to do in this limb. */
|
||
size_t bytes;
|
||
/* The index where the limb was read. */
|
||
mp_size_t i;
|
||
|
||
un = GMP_ABS (un);
|
||
|
||
/* Count bytes in top limb. */
|
||
limb = u->_mp_d[un-1];
|
||
assert (limb != 0);
|
||
|
||
k = (GMP_LIMB_BITS <= CHAR_BIT);
|
||
if (!k)
|
||
{
|
||
do {
|
||
int LOCAL_CHAR_BIT = CHAR_BIT;
|
||
k++; limb >>= LOCAL_CHAR_BIT;
|
||
} while (limb != 0);
|
||
}
|
||
/* else limb = 0; */
|
||
|
||
count = (k + (un-1) * sizeof (mp_limb_t) + size - 1) / size;
|
||
|
||
if (!r)
|
||
r = gmp_xalloc (count * size);
|
||
|
||
if (endian == 0)
|
||
endian = gmp_detect_endian ();
|
||
|
||
p = (unsigned char *) r;
|
||
|
||
word_step = (order != endian) ? 2 * size : 0;
|
||
|
||
/* Process bytes from the least significant end, so point p at the
|
||
least significant word. */
|
||
if (order == 1)
|
||
{
|
||
p += size * (count - 1);
|
||
word_step = - word_step;
|
||
}
|
||
|
||
/* And at least significant byte of that word. */
|
||
if (endian == 1)
|
||
p += (size - 1);
|
||
|
||
for (bytes = 0, i = 0, k = 0; k < count; k++, p += word_step)
|
||
{
|
||
size_t j;
|
||
for (j = 0; j < size; ++j, p -= (ptrdiff_t) endian)
|
||
{
|
||
if (sizeof (mp_limb_t) == 1)
|
||
{
|
||
if (i < un)
|
||
*p = u->_mp_d[i++];
|
||
else
|
||
*p = 0;
|
||
}
|
||
else
|
||
{
|
||
int LOCAL_CHAR_BIT = CHAR_BIT;
|
||
if (bytes == 0)
|
||
{
|
||
if (i < un)
|
||
limb = u->_mp_d[i++];
|
||
bytes = sizeof (mp_limb_t);
|
||
}
|
||
*p = limb;
|
||
limb >>= LOCAL_CHAR_BIT;
|
||
bytes--;
|
||
}
|
||
}
|
||
}
|
||
assert (i == un);
|
||
assert (k == count);
|
||
}
|
||
|
||
if (countp)
|
||
*countp = count;
|
||
|
||
return r;
|
||
}
|