From: Paul Eggert Date: Thu, 9 Jul 2020 23:35:48 +0000 (-0700) Subject: Use Gnulib libgmp module X-Git-Tag: emacs-28.0.90~7033 X-Git-Url: http://git.eshelyaron.com/gitweb/?a=commitdiff_plain;h=c8b6006d82196f9063581e988ea12d6c99c95536;p=emacs.git Use Gnulib libgmp module Instead of doing GMP by hand, use the Gnulib libgmp module. * .gitignore: Add lib/gmp.h. * admin/merge-gnulib (GNULIB_MODULES): Add libgmp. * configure.ac (GMP_LIB, GMP_OBJ): Remove. Gnulib uses the name LIB_GMP, so all uses changed. All uses of GMP_OBJ removed. (HAVE_GMP): Set this from Gnulib’s variables. * lib/gnulib.mk.in, m4/gnulib-comp.m4: Regenerate. * lib/mini-gmp-gnulib.c, lib/mini-gmp.c, lib/mini-gmp.h, m4/libgmp.m4: New files, copied from Gnulib. * src/bignum.h, test/data/emacs-module/mod-test.c: Include gmp.h unconditionally. * src/mini-gmp-emacs.c, src/mini-gmp.c, src/mini-gmp.h: Remove. This moves these files from src to lib, and updates them to the current GMP version. * test/Makefile.in (GMP_H): New macro. ($(test_module)): Use it to decide whether to compile mini-gmp-gnulib.c too. --- diff --git a/.gitignore b/.gitignore index d4be6bb23eb..890e63a4318 100644 --- a/.gitignore +++ b/.gitignore @@ -60,6 +60,7 @@ lib/execinfo.h lib/fcntl.h lib/getopt.h lib/getopt-cdefs.h +lib/gmp.h lib/ieee754.h lib/inttypes.h lib/libgnu.a diff --git a/admin/merge-gnulib b/admin/merge-gnulib index 5a78b052b24..3f32536a629 100755 --- a/admin/merge-gnulib +++ b/admin/merge-gnulib @@ -36,7 +36,7 @@ GNULIB_MODULES=' fchmodat fcntl fcntl-h fdopendir filemode filename filevercmp flexmember fpieee fstatat fsusage fsync futimens getloadavg getopt-gnu getrandom gettime gettimeofday gitlog-to-changelog - ieee754-h ignore-value intprops largefile lstat + ieee754-h ignore-value intprops largefile libgmp lstat manywarnings memmem-simple mempcpy memrchr minmax mkostemp mktime nstrftime pathmax pipe2 pselect pthread_sigmask qcopy-acl readlink readlinkat regex diff --git a/configure.ac b/configure.ac index 9fe1a0d32c1..148c50e0b39 100644 --- a/configure.ac +++ b/configure.ac @@ -4507,32 +4507,6 @@ AC_SUBST(KRB5LIB) AC_SUBST(DESLIB) AC_SUBST(KRB4LIB) -AC_ARG_WITH([libgmp], - [AS_HELP_STRING([--without-libgmp], - [don't use the GNU Multiple Precision (GMP) library; - this is the default on systems lacking libgmp.])]) -GMP_LIB= -GMP_OBJ=mini-gmp-emacs.o -HAVE_GMP=no -case $with_libgmp in - no) ;; - yes) HAVE_GMP=yes GMP_LIB=-lgmp;; - *) AC_CHECK_HEADERS([gmp.h], - [OLIBS=$LIBS - AC_SEARCH_LIBS([__gmpz_roinit_n], [gmp]) - LIBS=$OLIBS - case $ac_cv_search___gmpz_roinit_n in - 'none needed') HAVE_GMP=yes;; - -*) HAVE_GMP=yes GMP_LIB=$ac_cv_search___gmpz_roinit_n;; - esac]);; -esac -if test "$HAVE_GMP" = yes; then - GMP_OBJ= - AC_DEFINE([HAVE_GMP], 1, [Define to 1 if you have recent-enough GMP.]) -fi -AC_SUBST([GMP_LIB]) -AC_SUBST([GMP_OBJ]) - AC_CHECK_HEADERS(valgrind/valgrind.h) AC_CHECK_MEMBERS([struct unipair.unicode], [], [], [[#include ]]) @@ -5700,6 +5674,11 @@ done AC_DEFINE_UNQUOTED(EMACS_CONFIG_FEATURES, "${emacs_config_features}", [Summary of some of the main features enabled by configure.]) +if test -z "$GMP_H"; then + HAVE_GMP=yes +else + HAVE_GMP=no +fi AS_ECHO([" Does Emacs use -lXaw3d? ${HAVE_XAW3D} Does Emacs use -lXpm? ${HAVE_XPM} Does Emacs use -ljpeg? ${HAVE_JPEG} @@ -5728,7 +5707,7 @@ AS_ECHO([" Does Emacs use -lXaw3d? ${HAVE_XAW3D Does Emacs use -lxft? ${HAVE_XFT} Does Emacs use -lsystemd? ${HAVE_LIBSYSTEMD} Does Emacs use -ljansson? ${HAVE_JSON} - Does Emacs use -lgmp? ${HAVE_GMP} + Does Emacs use the GMP library? ${HAVE_GMP} Does Emacs directly use zlib? ${HAVE_ZLIB} Does Emacs have dynamic modules support? ${HAVE_MODULES} Does Emacs use toolkit scroll bars? ${USE_TOOLKIT_SCROLL_BARS} diff --git a/lib/gnulib.mk.in b/lib/gnulib.mk.in index c249d626728..68cae8faf74 100644 --- a/lib/gnulib.mk.in +++ b/lib/gnulib.mk.in @@ -117,6 +117,7 @@ # ignore-value \ # intprops \ # largefile \ +# libgmp \ # lstat \ # manywarnings \ # memmem-simple \ @@ -245,14 +246,14 @@ GL_GENERATE_ALLOCA_H = @GL_GENERATE_ALLOCA_H@ GL_GENERATE_BYTESWAP_H = @GL_GENERATE_BYTESWAP_H@ GL_GENERATE_ERRNO_H = @GL_GENERATE_ERRNO_H@ GL_GENERATE_EXECINFO_H = @GL_GENERATE_EXECINFO_H@ +GL_GENERATE_GMP_H = @GL_GENERATE_GMP_H@ GL_GENERATE_IEEE754_H = @GL_GENERATE_IEEE754_H@ GL_GENERATE_LIMITS_H = @GL_GENERATE_LIMITS_H@ GL_GENERATE_STDALIGN_H = @GL_GENERATE_STDALIGN_H@ GL_GENERATE_STDDEF_H = @GL_GENERATE_STDDEF_H@ GL_GENERATE_STDINT_H = @GL_GENERATE_STDINT_H@ GMALLOC_OBJ = @GMALLOC_OBJ@ -GMP_LIB = @GMP_LIB@ -GMP_OBJ = @GMP_OBJ@ +GMP_H = @GMP_H@ GNULIB_ACCESS = @GNULIB_ACCESS@ GNULIB_ALPHASORT = @GNULIB_ALPHASORT@ GNULIB_ATOLL = @GNULIB_ATOLL@ @@ -760,6 +761,7 @@ LIB_CLOCK_GETTIME = @LIB_CLOCK_GETTIME@ LIB_EACCESS = @LIB_EACCESS@ LIB_EXECINFO = @LIB_EXECINFO@ LIB_GETRANDOM = @LIB_GETRANDOM@ +LIB_GMP = @LIB_GMP@ LIB_MATH = @LIB_MATH@ LIB_PTHREAD = @LIB_PTHREAD@ LIB_PTHREAD_SIGMASK = @LIB_PTHREAD_SIGMASK@ @@ -2014,6 +2016,29 @@ EXTRA_DIST += cdefs.h libc-config.h endif ## end gnulib module libc-config +## begin gnulib module libgmp +ifeq (,$(OMIT_GNULIB_MODULE_libgmp)) + +BUILT_SOURCES += $(GMP_H) + +# Build gmp.h as a wrapper for mini-gmp.h when using mini-gmp. +ifneq (,$(GL_GENERATE_GMP_H)) +gmp.h: $(top_builddir)/config.status + echo '#include "mini-gmp.h"' >$@-t + mv $@-t $@ +else +gmp.h: $(top_builddir)/config.status + rm -f $@ +endif +MOSTLYCLEANFILES += gmp.h gmp.h-t + +EXTRA_DIST += mini-gmp-gnulib.c mini-gmp.c mini-gmp.h + +EXTRA_libgnu_a_SOURCES += mini-gmp-gnulib.c mini-gmp.c + +endif +## end gnulib module libgmp + ## begin gnulib module limits-h ifeq (,$(OMIT_GNULIB_MODULE_limits-h)) diff --git a/lib/mini-gmp-gnulib.c b/lib/mini-gmp-gnulib.c new file mode 100644 index 00000000000..5019be5d52a --- /dev/null +++ b/lib/mini-gmp-gnulib.c @@ -0,0 +1,37 @@ +/* Tailor mini-gmp.c for Gnulib-using applications. + + Copyright 2018-2020 Free Software Foundation, Inc. + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation; either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . */ + +#include + +#include +#include + +#include "mini-gmp.h" + +/* Pacify GCC -Wsuggest-attribute=const, malloc, pure. */ +#if 4 < __GNUC__ + (6 <= __GNUC_MINOR__) +# pragma GCC diagnostic ignored "-Wsuggest-attribute=const" +# pragma GCC diagnostic ignored "-Wsuggest-attribute=malloc" +# pragma GCC diagnostic ignored "-Wsuggest-attribute=pure" +#endif + +/* Pacify GCC -Wunused-variable for variables used only in 'assert' calls. */ +#if defined NDEBUG && 4 < __GNUC__ + (6 <= __GNUC_MINOR__) +# pragma GCC diagnostic ignored "-Wunused-variable" +#endif + +#include "mini-gmp.c" diff --git a/lib/mini-gmp.c b/lib/mini-gmp.c new file mode 100644 index 00000000000..2e0301b0081 --- /dev/null +++ b/lib/mini-gmp.c @@ -0,0 +1,4615 @@ +/* mini-gmp, a minimalistic implementation of a GNU GMP subset. + + Contributed to the GNU project by Niels Möller + +Copyright 1991-1997, 1999-2020 Free Software Foundation, Inc. + +This file is part of the GNU MP Library. + +The GNU MP Library is free software; you can redistribute it and/or modify +it under the terms of either: + + * the GNU General Public License as published by the Free + Software Foundation; either version 3 of the License, or (at your + option) any later version. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 3 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +The GNU MP Library is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + +/* NOTE: All functions in this file which are not declared in + mini-gmp.h are internal, and are not intended to be compatible + neither with GMP nor with future versions of mini-gmp. */ + +/* Much of the material copied from GMP files, including: gmp-impl.h, + longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c, + mpn/generic/lshift.c, mpn/generic/mul_1.c, + mpn/generic/mul_basecase.c, mpn/generic/rshift.c, + mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c, + mpn/generic/submul_1.c. */ + +#include +#include +#include +#include +#include +#include + +#include "mini-gmp.h" + +#if !defined(MINI_GMP_DONT_USE_FLOAT_H) +#include +#endif + + +/* Macros */ +#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT) + +#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0) +#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1)) + +#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2)) +#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1) + +#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT) +#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1)) + +#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x)) +#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1)) + +#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b)) +#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b)) + +#define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b))) + +#if defined(DBL_MANT_DIG) && FLT_RADIX == 2 +#define GMP_DBL_MANT_BITS DBL_MANT_DIG +#else +#define GMP_DBL_MANT_BITS (53) +#endif + +/* Return non-zero if xp,xsize and yp,ysize overlap. + If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no + overlap. If both these are false, there's an overlap. */ +#define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize) \ + ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp)) + +#define gmp_assert_nocarry(x) do { \ + mp_limb_t __cy = (x); \ + assert (__cy == 0); \ + } while (0) + +#define gmp_clz(count, x) do { \ + mp_limb_t __clz_x = (x); \ + unsigned __clz_c = 0; \ + int LOCAL_SHIFT_BITS = 8; \ + if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS) \ + for (; \ + (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \ + __clz_c += 8) \ + { __clz_x <<= LOCAL_SHIFT_BITS; } \ + for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \ + __clz_x <<= 1; \ + (count) = __clz_c; \ + } while (0) + +#define gmp_ctz(count, x) do { \ + mp_limb_t __ctz_x = (x); \ + unsigned __ctz_c = 0; \ + gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \ + (count) = GMP_LIMB_BITS - 1 - __ctz_c; \ + } while (0) + +#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \ + do { \ + mp_limb_t __x; \ + __x = (al) + (bl); \ + (sh) = (ah) + (bh) + (__x < (al)); \ + (sl) = __x; \ + } while (0) + +#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \ + do { \ + mp_limb_t __x; \ + __x = (al) - (bl); \ + (sh) = (ah) - (bh) - ((al) < (bl)); \ + (sl) = __x; \ + } while (0) + +#define gmp_umul_ppmm(w1, w0, u, v) \ + do { \ + int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \ + if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \ + { \ + unsigned int __ww = (unsigned int) (u) * (v); \ + w0 = (mp_limb_t) __ww; \ + w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ + } \ + else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \ + { \ + unsigned long int __ww = (unsigned long int) (u) * (v); \ + w0 = (mp_limb_t) __ww; \ + w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ + } \ + else { \ + mp_limb_t __x0, __x1, __x2, __x3; \ + unsigned __ul, __vl, __uh, __vh; \ + mp_limb_t __u = (u), __v = (v); \ + \ + __ul = __u & GMP_LLIMB_MASK; \ + __uh = __u >> (GMP_LIMB_BITS / 2); \ + __vl = __v & GMP_LLIMB_MASK; \ + __vh = __v >> (GMP_LIMB_BITS / 2); \ + \ + __x0 = (mp_limb_t) __ul * __vl; \ + __x1 = (mp_limb_t) __ul * __vh; \ + __x2 = (mp_limb_t) __uh * __vl; \ + __x3 = (mp_limb_t) __uh * __vh; \ + \ + __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \ + __x1 += __x2; /* but this indeed can */ \ + if (__x1 < __x2) /* did we get it? */ \ + __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \ + \ + (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \ + (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \ + } \ + } while (0) + +#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \ + do { \ + mp_limb_t _qh, _ql, _r, _mask; \ + gmp_umul_ppmm (_qh, _ql, (nh), (di)); \ + gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \ + _r = (nl) - _qh * (d); \ + _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \ + _qh += _mask; \ + _r += _mask & (d); \ + if (_r >= (d)) \ + { \ + _r -= (d); \ + _qh++; \ + } \ + \ + (r) = _r; \ + (q) = _qh; \ + } while (0) + +#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \ + do { \ + mp_limb_t _q0, _t1, _t0, _mask; \ + gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \ + gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \ + \ + /* Compute the two most significant limbs of n - q'd */ \ + (r1) = (n1) - (d1) * (q); \ + gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \ + gmp_umul_ppmm (_t1, _t0, (d0), (q)); \ + gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \ + (q)++; \ + \ + /* Conditionally adjust q and the remainders */ \ + _mask = - (mp_limb_t) ((r1) >= _q0); \ + (q) += _mask; \ + gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \ + if ((r1) >= (d1)) \ + { \ + if ((r1) > (d1) || (r0) >= (d0)) \ + { \ + (q)++; \ + gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \ + } \ + } \ + } while (0) + +/* Swap macros. */ +#define MP_LIMB_T_SWAP(x, y) \ + do { \ + mp_limb_t __mp_limb_t_swap__tmp = (x); \ + (x) = (y); \ + (y) = __mp_limb_t_swap__tmp; \ + } while (0) +#define MP_SIZE_T_SWAP(x, y) \ + do { \ + mp_size_t __mp_size_t_swap__tmp = (x); \ + (x) = (y); \ + (y) = __mp_size_t_swap__tmp; \ + } while (0) +#define MP_BITCNT_T_SWAP(x,y) \ + do { \ + mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \ + (x) = (y); \ + (y) = __mp_bitcnt_t_swap__tmp; \ + } while (0) +#define MP_PTR_SWAP(x, y) \ + do { \ + mp_ptr __mp_ptr_swap__tmp = (x); \ + (x) = (y); \ + (y) = __mp_ptr_swap__tmp; \ + } while (0) +#define MP_SRCPTR_SWAP(x, y) \ + do { \ + mp_srcptr __mp_srcptr_swap__tmp = (x); \ + (x) = (y); \ + (y) = __mp_srcptr_swap__tmp; \ + } while (0) + +#define MPN_PTR_SWAP(xp,xs, yp,ys) \ + do { \ + MP_PTR_SWAP (xp, yp); \ + MP_SIZE_T_SWAP (xs, ys); \ + } while(0) +#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \ + do { \ + MP_SRCPTR_SWAP (xp, yp); \ + MP_SIZE_T_SWAP (xs, ys); \ + } while(0) + +#define MPZ_PTR_SWAP(x, y) \ + do { \ + mpz_ptr __mpz_ptr_swap__tmp = (x); \ + (x) = (y); \ + (y) = __mpz_ptr_swap__tmp; \ + } while (0) +#define MPZ_SRCPTR_SWAP(x, y) \ + do { \ + mpz_srcptr __mpz_srcptr_swap__tmp = (x); \ + (x) = (y); \ + (y) = __mpz_srcptr_swap__tmp; \ + } while (0) + +const int mp_bits_per_limb = GMP_LIMB_BITS; + + +/* Memory allocation and other helper functions. */ +static void +gmp_die (const char *msg) +{ + fprintf (stderr, "%s\n", msg); + abort(); +} + +static void * +gmp_default_alloc (size_t size) +{ + void *p; + + assert (size > 0); + + p = malloc (size); + if (!p) + gmp_die("gmp_default_alloc: Virtual memory exhausted."); + + return p; +} + +static void * +gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size) +{ + void * p; + + p = realloc (old, new_size); + + if (!p) + gmp_die("gmp_default_realloc: Virtual memory exhausted."); + + return p; +} + +static void +gmp_default_free (void *p, size_t unused_size) +{ + free (p); +} + +static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc; +static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc; +static void (*gmp_free_func) (void *, size_t) = gmp_default_free; + +void +mp_get_memory_functions (void *(**alloc_func) (size_t), + void *(**realloc_func) (void *, size_t, size_t), + void (**free_func) (void *, size_t)) +{ + if (alloc_func) + *alloc_func = gmp_allocate_func; + + if (realloc_func) + *realloc_func = gmp_reallocate_func; + + if (free_func) + *free_func = gmp_free_func; +} + +void +mp_set_memory_functions (void *(*alloc_func) (size_t), + void *(*realloc_func) (void *, size_t, size_t), + void (*free_func) (void *, size_t)) +{ + if (!alloc_func) + alloc_func = gmp_default_alloc; + if (!realloc_func) + realloc_func = gmp_default_realloc; + if (!free_func) + free_func = gmp_default_free; + + gmp_allocate_func = alloc_func; + gmp_reallocate_func = realloc_func; + gmp_free_func = free_func; +} + +#define gmp_alloc(size) ((*gmp_allocate_func)((size))) +#define gmp_free(p, size) ((*gmp_free_func) ((p), (size))) +#define gmp_realloc(ptr, old_size, size) ((*gmp_reallocate_func)(ptr, old_size, size)) + +static mp_ptr +gmp_alloc_limbs (mp_size_t size) +{ + return (mp_ptr) gmp_alloc (size * sizeof (mp_limb_t)); +} + +static mp_ptr +gmp_realloc_limbs (mp_ptr old, mp_size_t old_size, mp_size_t size) +{ + assert (size > 0); + return (mp_ptr) gmp_realloc (old, old_size * sizeof (mp_limb_t), size * sizeof (mp_limb_t)); +} + +static void +gmp_free_limbs (mp_ptr old, mp_size_t size) +{ + gmp_free (old, 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; + mp_size_t tn = 0; + + if (inv->shift > 0) + { + /* Shift, reusing qp area if possible. In-place shift if qp == np. */ + tp = qp; + if (!tp) + { + tn = nn; + tp = gmp_alloc_limbs (tn); + } + 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 (tn) + gmp_free_limbs (tp, tn); + + 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 + * by + */ + + 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_alloc_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_limbs (tp, dn); +} + + +/* 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_alloc_limbs (rn); +} + +void +mpz_clear (mpz_t r) +{ + if (r->_mp_alloc) + gmp_free_limbs (r->_mp_d, r->_mp_alloc); +} + +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_realloc_limbs (r->_mp_d, r->_mp_alloc, size); + else + r->_mp_d = gmp_alloc_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, signed long int 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 (unsigned long int, x)); + mpz_neg (r, r); + } + else + { + r->_mp_size = -1; + MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x); + } +} + +void +mpz_set_ui (mpz_t r, unsigned long int 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, signed long int x) +{ + mpz_init (r); + mpz_set_si (r, x); +} + +void +mpz_init_set_ui (mpz_t r, unsigned long int 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 mpz_cmp_si (u, LONG_MAX) <= 0 && mpz_cmp_si (u, LONG_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); +} + +int +mpz_fits_sint_p (const mpz_t u) +{ + return mpz_cmp_si (u, INT_MAX) <= 0 && mpz_cmp_si (u, INT_MIN) >= 0; +} + +int +mpz_fits_uint_p (const mpz_t u) +{ + return u->_mp_size >= 0 && mpz_cmpabs_ui (u, UINT_MAX) <= 0; +} + +int +mpz_fits_sshort_p (const mpz_t u) +{ + return mpz_cmp_si (u, SHRT_MAX) <= 0 && mpz_cmp_si (u, SHRT_MIN) >= 0; +} + +int +mpz_fits_ushort_p (const mpz_t u) +{ + return u->_mp_size >= 0 && mpz_cmpabs_ui (u, USHRT_MAX) <= 0; +} + +long int +mpz_get_si (const mpz_t u) +{ + unsigned long r = mpz_get_ui (u); + unsigned long c = -LONG_MAX - LONG_MIN; + + if (u->_mp_size < 0) + /* This expression is necessary to properly handle -LONG_MIN */ + return -(long) c - (long) ((r - c) & LONG_MAX); + else + return (long) (r & LONG_MAX); +} + +unsigned long int +mpz_get_ui (const mpz_t u) +{ + if (GMP_LIMB_BITS < GMP_ULONG_BITS) + { + int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; + unsigned long 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, long 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 (unsigned long int, v)); +} + +int +mpz_cmp_ui (const mpz_t u, unsigned long 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, unsigned long v) +{ + mp_size_t un = GMP_ABS (u->_mp_size); + + if (! mpn_absfits_ulong_p (u->_mp_d, un)) + return 1; + else + { + unsigned long 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, unsigned long 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, unsigned long b) +{ + mpz_ui_sub (r, b, a); + mpz_neg (r, r); +} + +void +mpz_ui_sub (mpz_t r, unsigned long 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, long int v) +{ + if (v < 0) + { + mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v)); + mpz_neg (r, r); + } + else + mpz_mul_ui (r, u, v); +} + +void +mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int 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, unsigned long int 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, unsigned long int 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 unsigned long +mpz_div_qr_ui (mpz_t q, mpz_t r, + const mpz_t n, unsigned long d, enum mpz_div_round_mode mode) +{ + unsigned long 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; +} + +unsigned long +mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL); +} + +unsigned long +mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR); +} + +unsigned long +mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC); +} + +unsigned long +mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL); +} + +unsigned long +mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR); +} + +unsigned long +mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC); +} + +unsigned long +mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL); +} +unsigned long +mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); +} +unsigned long +mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC); +} + +unsigned long +mpz_cdiv_ui (const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL); +} + +unsigned long +mpz_fdiv_ui (const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR); +} + +unsigned long +mpz_tdiv_ui (const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC); +} + +unsigned long +mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d) +{ + return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); +} + +void +mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d) +{ + gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC)); +} + +int +mpz_divisible_ui_p (const mpz_t n, unsigned long 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; +} + +unsigned long +mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long 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 */ + signed long 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 */ + signed long 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, unsigned long 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, unsigned long e) +{ + unsigned long 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, unsigned long blimb, unsigned long 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_alloc_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_limbs (tp, mn); + + mpz_swap (r, tr); + mpz_clear (tr); + mpz_clear (base); +} + +void +mpz_powm_ui (mpz_t r, const mpz_t b, unsigned long 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, unsigned long 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, unsigned long 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, unsigned long n, unsigned long 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, unsigned long n) +{ + mpz_mfac_uiui (x, n, 2); +} + +void +mpz_fac_ui (mpz_t x, unsigned long n) +{ + mpz_mfac_uiui (x, n, 1); +} + +void +mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long 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; + + for (;;) + { + a >>= c; + /* (2/b) = -1 if b = 3 or 5 mod 8 */ + bit ^= c & (b ^ (b >> 1)); + if (a < b) + { + if (a == 0) + return bit & 1 ? -1 : 1; + bit ^= a & b; + a = b - a; + b -= a; + } + else + { + a -= b; + assert (a != 0); + } + + gmp_ctz(c, a); + ++c; + } +} + +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 long */ +/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */ +static int +gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q, + mp_bitcnt_t b0, const mpz_t n) +{ + mp_bitcnt_t bs; + mpz_t U; + int res; + + assert (b0 > 0); + assert (Q <= - (LONG_MIN / 2)); + assert (Q >= - (LONG_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. */ + long 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) ? (long) (D >> 2) + 1 : -(long) (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, (unsigned long) 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, tn; + 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_alloc_limbs (un); + mpn_copyi (tp, up, un); + mpn_div_qr_1_invert (&bi, base); + + tn = un; + ndigits = 0; + do + { + ndigits++; + mpn_div_qr_1_preinv (tp, tp, tn, &bi); + tn -= (tp[tn-1] == 0); + } + while (tn > 0); + + gmp_free_limbs (tp, un); + 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, osn; + + 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) + { + osn = 1 + sn; + sp = (char *) gmp_alloc (osn); + } + else + osn = 0; + un = GMP_ABS (u->_mp_size); + + if (un == 0) + { + sp[0] = '0'; + sn = 1; + goto ret; + } + + 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_alloc_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_limbs (tp, un); + } + + for (; i < sn; i++) + sp[i] = digits[(unsigned char) sp[i]]; + +ret: + sp[sn] = '\0'; + if (osn && osn != sn + 1) + sp = gmp_realloc(sp, osn, sn + 1); + 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, sn; + 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; + } + sn = strlen(sp); + dp = (unsigned char *) gmp_alloc (sn); + + 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, sn); + r->_mp_size = 0; + return -1; + } + + dp[dn++] = digit; + } + + if (!dn) + { + gmp_free (dp, sn); + 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, sn); + + 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, n; + + str = mpz_get_str (NULL, base, x); + len = strlen (str); + n = fwrite (str, 1, len, stream); + gmp_free (str, len + 1); + return n; +} + + +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_alloc (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; +} diff --git a/lib/mini-gmp.h b/lib/mini-gmp.h new file mode 100644 index 00000000000..c00568c2568 --- /dev/null +++ b/lib/mini-gmp.h @@ -0,0 +1,308 @@ +/* mini-gmp, a minimalistic implementation of a GNU GMP subset. + +Copyright 2011-2015, 2017, 2019 Free Software Foundation, Inc. + +This file is part of the GNU MP Library. + +The GNU MP Library is free software; you can redistribute it and/or modify +it under the terms of either: + + * the GNU General Public License as published by the Free + Software Foundation; either version 3 of the License, or (at your + option) any later version. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 3 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +The GNU MP Library is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY +or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + +/* About mini-gmp: This is a minimal implementation of a subset of the + GMP interface. It is intended for inclusion into applications which + have modest bignums needs, as a fallback when the real GMP library + is not installed. + + This file defines the public interface. */ + +#ifndef __MINI_GMP_H__ +#define __MINI_GMP_H__ + +/* For size_t */ +#include + +#if defined (__cplusplus) +extern "C" { +#endif + +void mp_set_memory_functions (void *(*) (size_t), + void *(*) (void *, size_t, size_t), + void (*) (void *, size_t)); + +void mp_get_memory_functions (void *(**) (size_t), + void *(**) (void *, size_t, size_t), + void (**) (void *, size_t)); + +#ifndef MINI_GMP_LIMB_TYPE +#define MINI_GMP_LIMB_TYPE long +#endif + +typedef unsigned MINI_GMP_LIMB_TYPE mp_limb_t; +typedef long mp_size_t; +typedef unsigned long mp_bitcnt_t; + +typedef mp_limb_t *mp_ptr; +typedef const mp_limb_t *mp_srcptr; + +typedef struct +{ + int _mp_alloc; /* Number of *limbs* allocated and pointed + to by the _mp_d field. */ + int _mp_size; /* abs(_mp_size) is the number of limbs the + last field points to. If _mp_size is + negative this is a negative number. */ + mp_limb_t *_mp_d; /* Pointer to the limbs. */ +} __mpz_struct; + +typedef __mpz_struct mpz_t[1]; + +typedef __mpz_struct *mpz_ptr; +typedef const __mpz_struct *mpz_srcptr; + +extern const int mp_bits_per_limb; + +void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t); +void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t); +void mpn_zero (mp_ptr, mp_size_t); + +int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t); +int mpn_zero_p (mp_srcptr, mp_size_t); + +mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); +mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); +mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); + +mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); +mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); +mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); + +mp_limb_t mpn_mul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); +mp_limb_t mpn_addmul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); +mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); + +mp_limb_t mpn_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); +void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); +void mpn_sqr (mp_ptr, mp_srcptr, mp_size_t); +int mpn_perfect_square_p (mp_srcptr, mp_size_t); +mp_size_t mpn_sqrtrem (mp_ptr, mp_ptr, mp_srcptr, mp_size_t); + +mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int); +mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int); + +mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t); +mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t); + +void mpn_com (mp_ptr, mp_srcptr, mp_size_t); +mp_limb_t mpn_neg (mp_ptr, mp_srcptr, mp_size_t); + +mp_bitcnt_t mpn_popcount (mp_srcptr, mp_size_t); + +mp_limb_t mpn_invert_3by2 (mp_limb_t, mp_limb_t); +#define mpn_invert_limb(x) mpn_invert_3by2 ((x), 0) + +size_t mpn_get_str (unsigned char *, int, mp_ptr, mp_size_t); +mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int); + +void mpz_init (mpz_t); +void mpz_init2 (mpz_t, mp_bitcnt_t); +void mpz_clear (mpz_t); + +#define mpz_odd_p(z) (((z)->_mp_size != 0) & (int) (z)->_mp_d[0]) +#define mpz_even_p(z) (! mpz_odd_p (z)) + +int mpz_sgn (const mpz_t); +int mpz_cmp_si (const mpz_t, long); +int mpz_cmp_ui (const mpz_t, unsigned long); +int mpz_cmp (const mpz_t, const mpz_t); +int mpz_cmpabs_ui (const mpz_t, unsigned long); +int mpz_cmpabs (const mpz_t, const mpz_t); +int mpz_cmp_d (const mpz_t, double); +int mpz_cmpabs_d (const mpz_t, double); + +void mpz_abs (mpz_t, const mpz_t); +void mpz_neg (mpz_t, const mpz_t); +void mpz_swap (mpz_t, mpz_t); + +void mpz_add_ui (mpz_t, const mpz_t, unsigned long); +void mpz_add (mpz_t, const mpz_t, const mpz_t); +void mpz_sub_ui (mpz_t, const mpz_t, unsigned long); +void mpz_ui_sub (mpz_t, unsigned long, const mpz_t); +void mpz_sub (mpz_t, const mpz_t, const mpz_t); + +void mpz_mul_si (mpz_t, const mpz_t, long int); +void mpz_mul_ui (mpz_t, const mpz_t, unsigned long int); +void mpz_mul (mpz_t, const mpz_t, const mpz_t); +void mpz_mul_2exp (mpz_t, const mpz_t, mp_bitcnt_t); +void mpz_addmul_ui (mpz_t, const mpz_t, unsigned long int); +void mpz_addmul (mpz_t, const mpz_t, const mpz_t); +void mpz_submul_ui (mpz_t, const mpz_t, unsigned long int); +void mpz_submul (mpz_t, const mpz_t, const mpz_t); + +void mpz_cdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); +void mpz_fdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); +void mpz_tdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); +void mpz_cdiv_q (mpz_t, const mpz_t, const mpz_t); +void mpz_fdiv_q (mpz_t, const mpz_t, const mpz_t); +void mpz_tdiv_q (mpz_t, const mpz_t, const mpz_t); +void mpz_cdiv_r (mpz_t, const mpz_t, const mpz_t); +void mpz_fdiv_r (mpz_t, const mpz_t, const mpz_t); +void mpz_tdiv_r (mpz_t, const mpz_t, const mpz_t); + +void mpz_cdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); +void mpz_fdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); +void mpz_tdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); +void mpz_cdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); +void mpz_fdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); +void mpz_tdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); + +void mpz_mod (mpz_t, const mpz_t, const mpz_t); + +void mpz_divexact (mpz_t, const mpz_t, const mpz_t); + +int mpz_divisible_p (const mpz_t, const mpz_t); +int mpz_congruent_p (const mpz_t, const mpz_t, const mpz_t); + +unsigned long mpz_cdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); +unsigned long mpz_fdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); +unsigned long mpz_tdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); +unsigned long mpz_cdiv_q_ui (mpz_t, const mpz_t, unsigned long); +unsigned long mpz_fdiv_q_ui (mpz_t, const mpz_t, unsigned long); +unsigned long mpz_tdiv_q_ui (mpz_t, const mpz_t, unsigned long); +unsigned long mpz_cdiv_r_ui (mpz_t, const mpz_t, unsigned long); +unsigned long mpz_fdiv_r_ui (mpz_t, const mpz_t, unsigned long); +unsigned long mpz_tdiv_r_ui (mpz_t, const mpz_t, unsigned long); +unsigned long mpz_cdiv_ui (const mpz_t, unsigned long); +unsigned long mpz_fdiv_ui (const mpz_t, unsigned long); +unsigned long mpz_tdiv_ui (const mpz_t, unsigned long); + +unsigned long mpz_mod_ui (mpz_t, const mpz_t, unsigned long); + +void mpz_divexact_ui (mpz_t, const mpz_t, unsigned long); + +int mpz_divisible_ui_p (const mpz_t, unsigned long); + +unsigned long mpz_gcd_ui (mpz_t, const mpz_t, unsigned long); +void mpz_gcd (mpz_t, const mpz_t, const mpz_t); +void mpz_gcdext (mpz_t, mpz_t, mpz_t, const mpz_t, const mpz_t); +void mpz_lcm_ui (mpz_t, const mpz_t, unsigned long); +void mpz_lcm (mpz_t, const mpz_t, const mpz_t); +int mpz_invert (mpz_t, const mpz_t, const mpz_t); + +void mpz_sqrtrem (mpz_t, mpz_t, const mpz_t); +void mpz_sqrt (mpz_t, const mpz_t); +int mpz_perfect_square_p (const mpz_t); + +void mpz_pow_ui (mpz_t, const mpz_t, unsigned long); +void mpz_ui_pow_ui (mpz_t, unsigned long, unsigned long); +void mpz_powm (mpz_t, const mpz_t, const mpz_t, const mpz_t); +void mpz_powm_ui (mpz_t, const mpz_t, unsigned long, const mpz_t); + +void mpz_rootrem (mpz_t, mpz_t, const mpz_t, unsigned long); +int mpz_root (mpz_t, const mpz_t, unsigned long); + +void mpz_fac_ui (mpz_t, unsigned long); +void mpz_2fac_ui (mpz_t, unsigned long); +void mpz_mfac_uiui (mpz_t, unsigned long, unsigned long); +void mpz_bin_uiui (mpz_t, unsigned long, unsigned long); + +int mpz_probab_prime_p (const mpz_t, int); + +int mpz_tstbit (const mpz_t, mp_bitcnt_t); +void mpz_setbit (mpz_t, mp_bitcnt_t); +void mpz_clrbit (mpz_t, mp_bitcnt_t); +void mpz_combit (mpz_t, mp_bitcnt_t); + +void mpz_com (mpz_t, const mpz_t); +void mpz_and (mpz_t, const mpz_t, const mpz_t); +void mpz_ior (mpz_t, const mpz_t, const mpz_t); +void mpz_xor (mpz_t, const mpz_t, const mpz_t); + +mp_bitcnt_t mpz_popcount (const mpz_t); +mp_bitcnt_t mpz_hamdist (const mpz_t, const mpz_t); +mp_bitcnt_t mpz_scan0 (const mpz_t, mp_bitcnt_t); +mp_bitcnt_t mpz_scan1 (const mpz_t, mp_bitcnt_t); + +int mpz_fits_slong_p (const mpz_t); +int mpz_fits_ulong_p (const mpz_t); +int mpz_fits_sint_p (const mpz_t); +int mpz_fits_uint_p (const mpz_t); +int mpz_fits_sshort_p (const mpz_t); +int mpz_fits_ushort_p (const mpz_t); +long int mpz_get_si (const mpz_t); +unsigned long int mpz_get_ui (const mpz_t); +double mpz_get_d (const mpz_t); +size_t mpz_size (const mpz_t); +mp_limb_t mpz_getlimbn (const mpz_t, mp_size_t); + +void mpz_realloc2 (mpz_t, mp_bitcnt_t); +mp_srcptr mpz_limbs_read (mpz_srcptr); +mp_ptr mpz_limbs_modify (mpz_t, mp_size_t); +mp_ptr mpz_limbs_write (mpz_t, mp_size_t); +void mpz_limbs_finish (mpz_t, mp_size_t); +mpz_srcptr mpz_roinit_n (mpz_t, mp_srcptr, mp_size_t); + +#define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }} + +void mpz_set_si (mpz_t, signed long int); +void mpz_set_ui (mpz_t, unsigned long int); +void mpz_set (mpz_t, const mpz_t); +void mpz_set_d (mpz_t, double); + +void mpz_init_set_si (mpz_t, signed long int); +void mpz_init_set_ui (mpz_t, unsigned long int); +void mpz_init_set (mpz_t, const mpz_t); +void mpz_init_set_d (mpz_t, double); + +size_t mpz_sizeinbase (const mpz_t, int); +char *mpz_get_str (char *, int, const mpz_t); +int mpz_set_str (mpz_t, const char *, int); +int mpz_init_set_str (mpz_t, const char *, int); + +/* This long list taken from gmp.h. */ +/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4, + defines EOF but not FILE. */ +#if defined (FILE) \ + || defined (H_STDIO) \ + || defined (_H_STDIO) /* AIX */ \ + || defined (_STDIO_H) /* glibc, Sun, SCO */ \ + || defined (_STDIO_H_) /* BSD, OSF */ \ + || defined (__STDIO_H) /* Borland */ \ + || defined (__STDIO_H__) /* IRIX */ \ + || defined (_STDIO_INCLUDED) /* HPUX */ \ + || defined (__dj_include_stdio_h_) /* DJGPP */ \ + || defined (_FILE_DEFINED) /* Microsoft */ \ + || defined (__STDIO__) /* Apple MPW MrC */ \ + || defined (_MSL_STDIO_H) /* Metrowerks */ \ + || defined (_STDIO_H_INCLUDED) /* QNX4 */ \ + || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ \ + || defined (__STDIO_LOADED) /* VMS */ +size_t mpz_out_str (FILE *, int, const mpz_t); +#endif + +void mpz_import (mpz_t, size_t, int, size_t, int, size_t, const void *); +void *mpz_export (void *, size_t *, int, size_t, int, size_t, const mpz_t); + +#if defined (__cplusplus) +} +#endif +#endif /* __MINI_GMP_H__ */ diff --git a/m4/gnulib-comp.m4 b/m4/gnulib-comp.m4 index 3a0fae11c44..f577a6fa741 100644 --- a/m4/gnulib-comp.m4 +++ b/m4/gnulib-comp.m4 @@ -118,6 +118,7 @@ AC_DEFUN([gl_EARLY], AC_REQUIRE([AC_SYS_LARGEFILE]) # Code from module lchmod: # Code from module libc-config: + # Code from module libgmp: # Code from module limits-h: # Code from module localtime-buffer: # Code from module lstat: @@ -345,6 +346,10 @@ AC_DEFUN([gl_INIT], gl_INTTYPES_INCOMPLETE AC_REQUIRE([gl_LARGEFILE]) gl___INLINE + gl_LIBGMP + if test -n "$GMP_H"; then + AC_LIBOBJ([mini-gmp-gnulib]) + fi gl_LIMITS_H gl_FUNC_LSTAT if test $REPLACE_LSTAT = 1; then @@ -1035,6 +1040,9 @@ AC_DEFUN([gl_FILE_LIST], [ lib/memmem.c lib/mempcpy.c lib/memrchr.c + lib/mini-gmp-gnulib.c + lib/mini-gmp.c + lib/mini-gmp.h lib/minmax.h lib/mkostemp.c lib/mktime-internal.h @@ -1166,6 +1174,7 @@ AC_DEFUN([gl_FILE_LIST], [ m4/inttypes.m4 m4/largefile.m4 m4/lchmod.m4 + m4/libgmp.m4 m4/limits-h.m4 m4/localtime-buffer.m4 m4/lstat.m4 diff --git a/m4/libgmp.m4 b/m4/libgmp.m4 new file mode 100644 index 00000000000..b569bb73462 --- /dev/null +++ b/m4/libgmp.m4 @@ -0,0 +1,44 @@ +# Configure the GMP library or a replacement. + +dnl Copyright 2020 Free Software Foundation, Inc. +dnl This file is free software; the Free Software Foundation +dnl gives unlimited permission to copy and/or distribute it, +dnl with or without modifications, as long as this notice is preserved. + +AC_DEFUN([gl_LIBGMP], +[ + AC_ARG_WITH([libgmp], + [AS_HELP_STRING([--without-libgmp], + [do not use the GNU Multiple Precision (GMP) library; + this is the default on systems lacking libgmp.])]) + + AC_CHECK_HEADERS_ONCE([gmp.h]) + GMP_H=gmp.h + LIB_GMP= + + case $with_libgmp in + no) ;; + yes) GMP_H= LIB_GMP=-lgmp;; + *) if test "$ac_cv_header_gmp_h" = yes; then + gl_saved_LIBS=$LIBS + AC_SEARCH_LIBS([__gmpz_roinit_n], [gmp]) + LIBS=$gl_saved_LIBS + case $ac_cv_search___gmpz_roinit_n in + 'none needed') + GMP_H=;; + -*) + GMP_H= LIB_GMP=$ac_cv_search___gmpz_roinit_n;; + esac + fi;; + esac + + if test -z "$GMP_H"; then + AC_DEFINE([HAVE_GMP], 1, + [Define to 1 if you have the GMP library instead of just the + mini-gmp replacement.]) + fi + + AC_SUBST([LIB_GMP]) + AC_SUBST([GMP_H]) + AM_CONDITIONAL([GL_GENERATE_GMP_H], [test -n "$GMP_H"]) +]) diff --git a/src/Makefile.in b/src/Makefile.in index 552dd2e50ae..72d69fb7a3e 100644 --- a/src/Makefile.in +++ b/src/Makefile.in @@ -323,8 +323,7 @@ INTERVALS_H = dispextern.h intervals.h composite.h GETLOADAVG_LIBS = @GETLOADAVG_LIBS@ -GMP_LIB = @GMP_LIB@ -GMP_OBJ = @GMP_OBJ@ +LIB_GMP = @LIB_GMP@ RUN_TEMACS = ./temacs @@ -531,7 +530,7 @@ LIBES = $(LIBS) $(W32_LIBS) $(LIBS_GNUSTEP) $(LIBX_BASE) $(LIBIMAGE) \ $(FREETYPE_LIBS) $(FONTCONFIG_LIBS) $(HARFBUZZ_LIBS) $(LIBOTF_LIBS) $(M17N_FLT_LIBS) \ $(LIBGNUTLS_LIBS) $(LIB_PTHREAD) $(GETADDRINFO_A_LIBS) $(LCMS2_LIBS) \ $(NOTIFY_LIBS) $(LIB_MATH) $(LIBZ) $(LIBMODULES) $(LIBSYSTEMD_LIBS) \ - $(JSON_LIBS) $(GMP_LIB) + $(JSON_LIBS) $(LIB_GMP) ## FORCE it so that admin/unidata can decide whether this file is ## up-to-date. Although since charprop depends on bootstrap-emacs, diff --git a/src/bignum.h b/src/bignum.h index 4a906c3c0eb..251a19e338a 100644 --- a/src/bignum.h +++ b/src/bignum.h @@ -22,12 +22,7 @@ along with GNU Emacs. If not, see . */ #ifndef BIGNUM_H #define BIGNUM_H -#ifdef HAVE_GMP -# include -#else -# include "mini-gmp.h" -#endif - +#include #include "lisp.h" /* Number of data bits in a limb. */ diff --git a/src/mini-gmp-emacs.c b/src/mini-gmp-emacs.c deleted file mode 100644 index b8399b075e0..00000000000 --- a/src/mini-gmp-emacs.c +++ /dev/null @@ -1,32 +0,0 @@ -/* Tailor mini-gmp.c for GNU Emacs - -Copyright 2018-2020 Free Software Foundation, Inc. - -This file is part of GNU Emacs. - -GNU Emacs is free software: you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation, either version 3 of the License, or (at -your option) any later version. - -GNU Emacs is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -You should have received a copy of the GNU General Public License -along with GNU Emacs. If not, see . */ - -#include - -#include - -/* Pacify GCC -Wsuggest-attribute=malloc. */ -static void *gmp_default_alloc (size_t) ATTRIBUTE_MALLOC; - -/* Pacify GCC -Wunused-variable for variables used only in 'assert' calls. */ -#if defined NDEBUG && GNUC_PREREQ (4, 6, 0) -# pragma GCC diagnostic ignored "-Wunused-variable" -#endif - -#include "mini-gmp.c" diff --git a/src/mini-gmp.c b/src/mini-gmp.c deleted file mode 100644 index 2e789a2dfcc..00000000000 --- a/src/mini-gmp.c +++ /dev/null @@ -1,4571 +0,0 @@ -/* mini-gmp, a minimalistic implementation of a GNU GMP subset. - - Contributed to the GNU project by Niels Möller - -Copyright 1991-1997, 1999-2019 Free Software Foundation, Inc. - -This file is part of the GNU MP Library. - -The GNU MP Library is free software; you can redistribute it and/or modify -it under the terms of either: - - * the GNU Lesser General Public License as published by the Free - Software Foundation; either version 3 of the License, or (at your - option) any later version. - -or - - * the GNU General Public License as published by the Free Software - Foundation; either version 2 of the License, or (at your option) any - later version. - -or both in parallel, as here. - -The GNU MP Library is distributed in the hope that it will be useful, but -WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License -for more details. - -You should have received copies of the GNU General Public License and the -GNU Lesser General Public License along with the GNU MP Library. If not, -see https://www.gnu.org/licenses/. */ - -/* NOTE: All functions in this file which are not declared in - mini-gmp.h are internal, and are not intended to be compatible - neither with GMP nor with future versions of mini-gmp. */ - -/* Much of the material copied from GMP files, including: gmp-impl.h, - longlong.h, mpn/generic/add_n.c, mpn/generic/addmul_1.c, - mpn/generic/lshift.c, mpn/generic/mul_1.c, - mpn/generic/mul_basecase.c, mpn/generic/rshift.c, - mpn/generic/sbpi1_div_qr.c, mpn/generic/sub_n.c, - mpn/generic/submul_1.c. */ - -#include -#include -#include -#include -#include -#include - -#include "mini-gmp.h" - -#if !defined(MINI_GMP_DONT_USE_FLOAT_H) -#include -#endif - - -/* Macros */ -#define GMP_LIMB_BITS (sizeof(mp_limb_t) * CHAR_BIT) - -#define GMP_LIMB_MAX ((mp_limb_t) ~ (mp_limb_t) 0) -#define GMP_LIMB_HIGHBIT ((mp_limb_t) 1 << (GMP_LIMB_BITS - 1)) - -#define GMP_HLIMB_BIT ((mp_limb_t) 1 << (GMP_LIMB_BITS / 2)) -#define GMP_LLIMB_MASK (GMP_HLIMB_BIT - 1) - -#define GMP_ULONG_BITS (sizeof(unsigned long) * CHAR_BIT) -#define GMP_ULONG_HIGHBIT ((unsigned long) 1 << (GMP_ULONG_BITS - 1)) - -#define GMP_ABS(x) ((x) >= 0 ? (x) : -(x)) -#define GMP_NEG_CAST(T,x) (-((T)((x) + 1) - 1)) - -#define GMP_MIN(a, b) ((a) < (b) ? (a) : (b)) -#define GMP_MAX(a, b) ((a) > (b) ? (a) : (b)) - -#define GMP_CMP(a,b) (((a) > (b)) - ((a) < (b))) - -#if defined(DBL_MANT_DIG) && FLT_RADIX == 2 -#define GMP_DBL_MANT_BITS DBL_MANT_DIG -#else -#define GMP_DBL_MANT_BITS (53) -#endif - -/* Return non-zero if xp,xsize and yp,ysize overlap. - If xp+xsize<=yp there's no overlap, or if yp+ysize<=xp there's no - overlap. If both these are false, there's an overlap. */ -#define GMP_MPN_OVERLAP_P(xp, xsize, yp, ysize) \ - ((xp) + (xsize) > (yp) && (yp) + (ysize) > (xp)) - -#define gmp_assert_nocarry(x) do { \ - mp_limb_t __cy = (x); \ - assert (__cy == 0); \ - } while (0) - -#define gmp_clz(count, x) do { \ - mp_limb_t __clz_x = (x); \ - unsigned __clz_c = 0; \ - int LOCAL_SHIFT_BITS = 8; \ - if (GMP_LIMB_BITS > LOCAL_SHIFT_BITS) \ - for (; \ - (__clz_x & ((mp_limb_t) 0xff << (GMP_LIMB_BITS - 8))) == 0; \ - __clz_c += 8) \ - { __clz_x <<= LOCAL_SHIFT_BITS; } \ - for (; (__clz_x & GMP_LIMB_HIGHBIT) == 0; __clz_c++) \ - __clz_x <<= 1; \ - (count) = __clz_c; \ - } while (0) - -#define gmp_ctz(count, x) do { \ - mp_limb_t __ctz_x = (x); \ - unsigned __ctz_c = 0; \ - gmp_clz (__ctz_c, __ctz_x & - __ctz_x); \ - (count) = GMP_LIMB_BITS - 1 - __ctz_c; \ - } while (0) - -#define gmp_add_ssaaaa(sh, sl, ah, al, bh, bl) \ - do { \ - mp_limb_t __x; \ - __x = (al) + (bl); \ - (sh) = (ah) + (bh) + (__x < (al)); \ - (sl) = __x; \ - } while (0) - -#define gmp_sub_ddmmss(sh, sl, ah, al, bh, bl) \ - do { \ - mp_limb_t __x; \ - __x = (al) - (bl); \ - (sh) = (ah) - (bh) - ((al) < (bl)); \ - (sl) = __x; \ - } while (0) - -#define gmp_umul_ppmm(w1, w0, u, v) \ - do { \ - int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; \ - if (sizeof(unsigned int) * CHAR_BIT >= 2 * GMP_LIMB_BITS) \ - { \ - unsigned int __ww = (unsigned int) (u) * (v); \ - w0 = (mp_limb_t) __ww; \ - w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ - } \ - else if (GMP_ULONG_BITS >= 2 * GMP_LIMB_BITS) \ - { \ - unsigned long int __ww = (unsigned long int) (u) * (v); \ - w0 = (mp_limb_t) __ww; \ - w1 = (mp_limb_t) (__ww >> LOCAL_GMP_LIMB_BITS); \ - } \ - else { \ - mp_limb_t __x0, __x1, __x2, __x3; \ - unsigned __ul, __vl, __uh, __vh; \ - mp_limb_t __u = (u), __v = (v); \ - \ - __ul = __u & GMP_LLIMB_MASK; \ - __uh = __u >> (GMP_LIMB_BITS / 2); \ - __vl = __v & GMP_LLIMB_MASK; \ - __vh = __v >> (GMP_LIMB_BITS / 2); \ - \ - __x0 = (mp_limb_t) __ul * __vl; \ - __x1 = (mp_limb_t) __ul * __vh; \ - __x2 = (mp_limb_t) __uh * __vl; \ - __x3 = (mp_limb_t) __uh * __vh; \ - \ - __x1 += __x0 >> (GMP_LIMB_BITS / 2);/* this can't give carry */ \ - __x1 += __x2; /* but this indeed can */ \ - if (__x1 < __x2) /* did we get it? */ \ - __x3 += GMP_HLIMB_BIT; /* yes, add it in the proper pos. */ \ - \ - (w1) = __x3 + (__x1 >> (GMP_LIMB_BITS / 2)); \ - (w0) = (__x1 << (GMP_LIMB_BITS / 2)) + (__x0 & GMP_LLIMB_MASK); \ - } \ - } while (0) - -#define gmp_udiv_qrnnd_preinv(q, r, nh, nl, d, di) \ - do { \ - mp_limb_t _qh, _ql, _r, _mask; \ - gmp_umul_ppmm (_qh, _ql, (nh), (di)); \ - gmp_add_ssaaaa (_qh, _ql, _qh, _ql, (nh) + 1, (nl)); \ - _r = (nl) - _qh * (d); \ - _mask = -(mp_limb_t) (_r > _ql); /* both > and >= are OK */ \ - _qh += _mask; \ - _r += _mask & (d); \ - if (_r >= (d)) \ - { \ - _r -= (d); \ - _qh++; \ - } \ - \ - (r) = _r; \ - (q) = _qh; \ - } while (0) - -#define gmp_udiv_qr_3by2(q, r1, r0, n2, n1, n0, d1, d0, dinv) \ - do { \ - mp_limb_t _q0, _t1, _t0, _mask; \ - gmp_umul_ppmm ((q), _q0, (n2), (dinv)); \ - gmp_add_ssaaaa ((q), _q0, (q), _q0, (n2), (n1)); \ - \ - /* Compute the two most significant limbs of n - q'd */ \ - (r1) = (n1) - (d1) * (q); \ - gmp_sub_ddmmss ((r1), (r0), (r1), (n0), (d1), (d0)); \ - gmp_umul_ppmm (_t1, _t0, (d0), (q)); \ - gmp_sub_ddmmss ((r1), (r0), (r1), (r0), _t1, _t0); \ - (q)++; \ - \ - /* Conditionally adjust q and the remainders */ \ - _mask = - (mp_limb_t) ((r1) >= _q0); \ - (q) += _mask; \ - gmp_add_ssaaaa ((r1), (r0), (r1), (r0), _mask & (d1), _mask & (d0)); \ - if ((r1) >= (d1)) \ - { \ - if ((r1) > (d1) || (r0) >= (d0)) \ - { \ - (q)++; \ - gmp_sub_ddmmss ((r1), (r0), (r1), (r0), (d1), (d0)); \ - } \ - } \ - } while (0) - -/* Swap macros. */ -#define MP_LIMB_T_SWAP(x, y) \ - do { \ - mp_limb_t __mp_limb_t_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_limb_t_swap__tmp; \ - } while (0) -#define MP_SIZE_T_SWAP(x, y) \ - do { \ - mp_size_t __mp_size_t_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_size_t_swap__tmp; \ - } while (0) -#define MP_BITCNT_T_SWAP(x,y) \ - do { \ - mp_bitcnt_t __mp_bitcnt_t_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_bitcnt_t_swap__tmp; \ - } while (0) -#define MP_PTR_SWAP(x, y) \ - do { \ - mp_ptr __mp_ptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_ptr_swap__tmp; \ - } while (0) -#define MP_SRCPTR_SWAP(x, y) \ - do { \ - mp_srcptr __mp_srcptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mp_srcptr_swap__tmp; \ - } while (0) - -#define MPN_PTR_SWAP(xp,xs, yp,ys) \ - do { \ - MP_PTR_SWAP (xp, yp); \ - MP_SIZE_T_SWAP (xs, ys); \ - } while(0) -#define MPN_SRCPTR_SWAP(xp,xs, yp,ys) \ - do { \ - MP_SRCPTR_SWAP (xp, yp); \ - MP_SIZE_T_SWAP (xs, ys); \ - } while(0) - -#define MPZ_PTR_SWAP(x, y) \ - do { \ - mpz_ptr __mpz_ptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mpz_ptr_swap__tmp; \ - } while (0) -#define MPZ_SRCPTR_SWAP(x, y) \ - do { \ - mpz_srcptr __mpz_srcptr_swap__tmp = (x); \ - (x) = (y); \ - (y) = __mpz_srcptr_swap__tmp; \ - } while (0) - -const int mp_bits_per_limb = GMP_LIMB_BITS; - - -/* Memory allocation and other helper functions. */ -static void -gmp_die (const char *msg) -{ - fprintf (stderr, "%s\n", msg); - abort(); -} - -static void * -gmp_default_alloc (size_t size) -{ - void *p; - - assert (size > 0); - - p = malloc (size); - if (!p) - gmp_die("gmp_default_alloc: Virtual memory exhausted."); - - return p; -} - -static void * -gmp_default_realloc (void *old, size_t unused_old_size, size_t new_size) -{ - void * p; - - p = realloc (old, new_size); - - if (!p) - gmp_die("gmp_default_realloc: Virtual memory exhausted."); - - return p; -} - -static void -gmp_default_free (void *p, size_t unused_size) -{ - free (p); -} - -static void * (*gmp_allocate_func) (size_t) = gmp_default_alloc; -static void * (*gmp_reallocate_func) (void *, size_t, size_t) = gmp_default_realloc; -static void (*gmp_free_func) (void *, size_t) = gmp_default_free; - -void -mp_get_memory_functions (void *(**alloc_func) (size_t), - void *(**realloc_func) (void *, size_t, size_t), - void (**free_func) (void *, size_t)) -{ - if (alloc_func) - *alloc_func = gmp_allocate_func; - - if (realloc_func) - *realloc_func = gmp_reallocate_func; - - if (free_func) - *free_func = gmp_free_func; -} - -void -mp_set_memory_functions (void *(*alloc_func) (size_t), - void *(*realloc_func) (void *, size_t, size_t), - void (*free_func) (void *, size_t)) -{ - if (!alloc_func) - alloc_func = gmp_default_alloc; - if (!realloc_func) - realloc_func = gmp_default_realloc; - if (!free_func) - free_func = gmp_default_free; - - gmp_allocate_func = alloc_func; - gmp_reallocate_func = realloc_func; - gmp_free_func = free_func; -} - -#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)); -} - -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 - * by - */ - - 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, signed long int 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 (unsigned long int, x)); - mpz_neg (r, r); - } - else - { - r->_mp_size = -1; - MPZ_REALLOC (r, 1)[0] = GMP_NEG_CAST (unsigned long int, x); - } -} - -void -mpz_set_ui (mpz_t r, unsigned long int 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, signed long int x) -{ - mpz_init (r); - mpz_set_si (r, x); -} - -void -mpz_init_set_ui (mpz_t r, unsigned long int 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 (LONG_MAX + LONG_MIN == 0 || mpz_cmp_ui (u, LONG_MAX) <= 0) && - mpz_cmpabs_ui (u, GMP_NEG_CAST (unsigned long int, LONG_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); -} - -long int -mpz_get_si (const mpz_t u) -{ - unsigned long r = mpz_get_ui (u); - unsigned long c = -LONG_MAX - LONG_MIN; - - if (u->_mp_size < 0) - /* This expression is necessary to properly handle -LONG_MIN */ - return -(long) c - (long) ((r - c) & LONG_MAX); - else - return (long) (r & LONG_MAX); -} - -unsigned long int -mpz_get_ui (const mpz_t u) -{ - if (GMP_LIMB_BITS < GMP_ULONG_BITS) - { - int LOCAL_GMP_LIMB_BITS = GMP_LIMB_BITS; - unsigned long 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, long 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 (unsigned long int, v)); -} - -int -mpz_cmp_ui (const mpz_t u, unsigned long 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, unsigned long v) -{ - mp_size_t un = GMP_ABS (u->_mp_size); - - if (! mpn_absfits_ulong_p (u->_mp_d, un)) - return 1; - else - { - unsigned long 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, unsigned long 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, unsigned long b) -{ - mpz_ui_sub (r, b, a); - mpz_neg (r, r); -} - -void -mpz_ui_sub (mpz_t r, unsigned long 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, long int v) -{ - if (v < 0) - { - mpz_mul_ui (r, u, GMP_NEG_CAST (unsigned long int, v)); - mpz_neg (r, r); - } - else - mpz_mul_ui (r, u, v); -} - -void -mpz_mul_ui (mpz_t r, const mpz_t u, unsigned long int 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, unsigned long int 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, unsigned long int 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 unsigned long -mpz_div_qr_ui (mpz_t q, mpz_t r, - const mpz_t n, unsigned long d, enum mpz_div_round_mode mode) -{ - unsigned long 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; -} - -unsigned long -mpz_cdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, r, n, d, GMP_DIV_CEIL); -} - -unsigned long -mpz_fdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, r, n, d, GMP_DIV_FLOOR); -} - -unsigned long -mpz_tdiv_qr_ui (mpz_t q, mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, r, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_cdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_CEIL); -} - -unsigned long -mpz_fdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_FLOOR); -} - -unsigned long -mpz_tdiv_q_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_cdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_CEIL); -} -unsigned long -mpz_fdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); -} -unsigned long -mpz_tdiv_r_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_cdiv_ui (const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_CEIL); -} - -unsigned long -mpz_fdiv_ui (const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_FLOOR); -} - -unsigned long -mpz_tdiv_ui (const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, NULL, n, d, GMP_DIV_TRUNC); -} - -unsigned long -mpz_mod_ui (mpz_t r, const mpz_t n, unsigned long d) -{ - return mpz_div_qr_ui (NULL, r, n, d, GMP_DIV_FLOOR); -} - -void -mpz_divexact_ui (mpz_t q, const mpz_t n, unsigned long d) -{ - gmp_assert_nocarry (mpz_div_qr_ui (q, NULL, n, d, GMP_DIV_TRUNC)); -} - -int -mpz_divisible_ui_p (const mpz_t n, unsigned long 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; -} - -unsigned long -mpz_gcd_ui (mpz_t g, const mpz_t u, unsigned long 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 */ - signed long 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 */ - signed long 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, unsigned long 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, unsigned long e) -{ - unsigned long 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, unsigned long blimb, unsigned long 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, unsigned long 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, unsigned long 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, unsigned long 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, unsigned long n, unsigned long 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, unsigned long n) -{ - mpz_mfac_uiui (x, n, 2); -} - -void -mpz_fac_ui (mpz_t x, unsigned long n) -{ - mpz_mfac_uiui (x, n, 1); -} - -void -mpz_bin_uiui (mpz_t r, unsigned long n, unsigned long 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 long */ -/* Returns (U_k == 0) and sets V=V_k and Qk=Q^k. */ -static int -gmp_lucas_mod (mpz_t V, mpz_t Qk, long Q, - mp_bitcnt_t b0, const mpz_t n) -{ - mp_bitcnt_t bs; - mpz_t U; - int res; - - assert (b0 > 0); - assert (Q <= - (LONG_MIN / 2)); - assert (Q >= - (LONG_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. */ - long 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) ? (long) (D >> 2) + 1 : -(long) (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, (unsigned long) 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); - 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; -} diff --git a/src/mini-gmp.h b/src/mini-gmp.h deleted file mode 100644 index 7cce3f7a328..00000000000 --- a/src/mini-gmp.h +++ /dev/null @@ -1,304 +0,0 @@ -/* mini-gmp, a minimalistic implementation of a GNU GMP subset. - -Copyright 2011-2015, 2017, 2019 Free Software Foundation, Inc. - -This file is part of the GNU MP Library. - -The GNU MP Library is free software; you can redistribute it and/or modify -it under the terms of either: - - * the GNU Lesser General Public License as published by the Free - Software Foundation; either version 3 of the License, or (at your - option) any later version. - -or - - * the GNU General Public License as published by the Free Software - Foundation; either version 2 of the License, or (at your option) any - later version. - -or both in parallel, as here. - -The GNU MP Library is distributed in the hope that it will be useful, but -WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License -for more details. - -You should have received copies of the GNU General Public License and the -GNU Lesser General Public License along with the GNU MP Library. If not, -see https://www.gnu.org/licenses/. */ - -/* About mini-gmp: This is a minimal implementation of a subset of the - GMP interface. It is intended for inclusion into applications which - have modest bignums needs, as a fallback when the real GMP library - is not installed. - - This file defines the public interface. */ - -#ifndef __MINI_GMP_H__ -#define __MINI_GMP_H__ - -/* For size_t */ -#include - -#if defined (__cplusplus) -extern "C" { -#endif - -void mp_set_memory_functions (void *(*) (size_t), - void *(*) (void *, size_t, size_t), - void (*) (void *, size_t)); - -void mp_get_memory_functions (void *(**) (size_t), - void *(**) (void *, size_t, size_t), - void (**) (void *, size_t)); - -#ifndef MINI_GMP_LIMB_TYPE -#define MINI_GMP_LIMB_TYPE long -#endif - -typedef unsigned MINI_GMP_LIMB_TYPE mp_limb_t; -typedef long mp_size_t; -typedef unsigned long mp_bitcnt_t; - -typedef mp_limb_t *mp_ptr; -typedef const mp_limb_t *mp_srcptr; - -typedef struct -{ - int _mp_alloc; /* Number of *limbs* allocated and pointed - to by the _mp_d field. */ - int _mp_size; /* abs(_mp_size) is the number of limbs the - last field points to. If _mp_size is - negative this is a negative number. */ - mp_limb_t *_mp_d; /* Pointer to the limbs. */ -} __mpz_struct; - -typedef __mpz_struct mpz_t[1]; - -typedef __mpz_struct *mpz_ptr; -typedef const __mpz_struct *mpz_srcptr; - -extern const int mp_bits_per_limb; - -void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t); -void mpn_copyd (mp_ptr, mp_srcptr, mp_size_t); -void mpn_zero (mp_ptr, mp_size_t); - -int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t); -int mpn_zero_p (mp_srcptr, mp_size_t); - -mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); -mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); -mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); - -mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); -mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); -mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); - -mp_limb_t mpn_mul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); -mp_limb_t mpn_addmul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); -mp_limb_t mpn_submul_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t); - -mp_limb_t mpn_mul (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t); -void mpn_mul_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t); -void mpn_sqr (mp_ptr, mp_srcptr, mp_size_t); -int mpn_perfect_square_p (mp_srcptr, mp_size_t); -mp_size_t mpn_sqrtrem (mp_ptr, mp_ptr, mp_srcptr, mp_size_t); - -mp_limb_t mpn_lshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int); -mp_limb_t mpn_rshift (mp_ptr, mp_srcptr, mp_size_t, unsigned int); - -mp_bitcnt_t mpn_scan0 (mp_srcptr, mp_bitcnt_t); -mp_bitcnt_t mpn_scan1 (mp_srcptr, mp_bitcnt_t); - -void mpn_com (mp_ptr, mp_srcptr, mp_size_t); -mp_limb_t mpn_neg (mp_ptr, mp_srcptr, mp_size_t); - -mp_bitcnt_t mpn_popcount (mp_srcptr, mp_size_t); - -mp_limb_t mpn_invert_3by2 (mp_limb_t, mp_limb_t); -#define mpn_invert_limb(x) mpn_invert_3by2 ((x), 0) - -size_t mpn_get_str (unsigned char *, int, mp_ptr, mp_size_t); -mp_size_t mpn_set_str (mp_ptr, const unsigned char *, size_t, int); - -void mpz_init (mpz_t); -void mpz_init2 (mpz_t, mp_bitcnt_t); -void mpz_clear (mpz_t); - -#define mpz_odd_p(z) (((z)->_mp_size != 0) & (int) (z)->_mp_d[0]) -#define mpz_even_p(z) (! mpz_odd_p (z)) - -int mpz_sgn (const mpz_t); -int mpz_cmp_si (const mpz_t, long); -int mpz_cmp_ui (const mpz_t, unsigned long); -int mpz_cmp (const mpz_t, const mpz_t); -int mpz_cmpabs_ui (const mpz_t, unsigned long); -int mpz_cmpabs (const mpz_t, const mpz_t); -int mpz_cmp_d (const mpz_t, double); -int mpz_cmpabs_d (const mpz_t, double); - -void mpz_abs (mpz_t, const mpz_t); -void mpz_neg (mpz_t, const mpz_t); -void mpz_swap (mpz_t, mpz_t); - -void mpz_add_ui (mpz_t, const mpz_t, unsigned long); -void mpz_add (mpz_t, const mpz_t, const mpz_t); -void mpz_sub_ui (mpz_t, const mpz_t, unsigned long); -void mpz_ui_sub (mpz_t, unsigned long, const mpz_t); -void mpz_sub (mpz_t, const mpz_t, const mpz_t); - -void mpz_mul_si (mpz_t, const mpz_t, long int); -void mpz_mul_ui (mpz_t, const mpz_t, unsigned long int); -void mpz_mul (mpz_t, const mpz_t, const mpz_t); -void mpz_mul_2exp (mpz_t, const mpz_t, mp_bitcnt_t); -void mpz_addmul_ui (mpz_t, const mpz_t, unsigned long int); -void mpz_addmul (mpz_t, const mpz_t, const mpz_t); -void mpz_submul_ui (mpz_t, const mpz_t, unsigned long int); -void mpz_submul (mpz_t, const mpz_t, const mpz_t); - -void mpz_cdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); -void mpz_fdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); -void mpz_tdiv_qr (mpz_t, mpz_t, const mpz_t, const mpz_t); -void mpz_cdiv_q (mpz_t, const mpz_t, const mpz_t); -void mpz_fdiv_q (mpz_t, const mpz_t, const mpz_t); -void mpz_tdiv_q (mpz_t, const mpz_t, const mpz_t); -void mpz_cdiv_r (mpz_t, const mpz_t, const mpz_t); -void mpz_fdiv_r (mpz_t, const mpz_t, const mpz_t); -void mpz_tdiv_r (mpz_t, const mpz_t, const mpz_t); - -void mpz_cdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); -void mpz_fdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); -void mpz_tdiv_q_2exp (mpz_t, const mpz_t, mp_bitcnt_t); -void mpz_cdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); -void mpz_fdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); -void mpz_tdiv_r_2exp (mpz_t, const mpz_t, mp_bitcnt_t); - -void mpz_mod (mpz_t, const mpz_t, const mpz_t); - -void mpz_divexact (mpz_t, const mpz_t, const mpz_t); - -int mpz_divisible_p (const mpz_t, const mpz_t); -int mpz_congruent_p (const mpz_t, const mpz_t, const mpz_t); - -unsigned long mpz_cdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); -unsigned long mpz_fdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); -unsigned long mpz_tdiv_qr_ui (mpz_t, mpz_t, const mpz_t, unsigned long); -unsigned long mpz_cdiv_q_ui (mpz_t, const mpz_t, unsigned long); -unsigned long mpz_fdiv_q_ui (mpz_t, const mpz_t, unsigned long); -unsigned long mpz_tdiv_q_ui (mpz_t, const mpz_t, unsigned long); -unsigned long mpz_cdiv_r_ui (mpz_t, const mpz_t, unsigned long); -unsigned long mpz_fdiv_r_ui (mpz_t, const mpz_t, unsigned long); -unsigned long mpz_tdiv_r_ui (mpz_t, const mpz_t, unsigned long); -unsigned long mpz_cdiv_ui (const mpz_t, unsigned long); -unsigned long mpz_fdiv_ui (const mpz_t, unsigned long); -unsigned long mpz_tdiv_ui (const mpz_t, unsigned long); - -unsigned long mpz_mod_ui (mpz_t, const mpz_t, unsigned long); - -void mpz_divexact_ui (mpz_t, const mpz_t, unsigned long); - -int mpz_divisible_ui_p (const mpz_t, unsigned long); - -unsigned long mpz_gcd_ui (mpz_t, const mpz_t, unsigned long); -void mpz_gcd (mpz_t, const mpz_t, const mpz_t); -void mpz_gcdext (mpz_t, mpz_t, mpz_t, const mpz_t, const mpz_t); -void mpz_lcm_ui (mpz_t, const mpz_t, unsigned long); -void mpz_lcm (mpz_t, const mpz_t, const mpz_t); -int mpz_invert (mpz_t, const mpz_t, const mpz_t); - -void mpz_sqrtrem (mpz_t, mpz_t, const mpz_t); -void mpz_sqrt (mpz_t, const mpz_t); -int mpz_perfect_square_p (const mpz_t); - -void mpz_pow_ui (mpz_t, const mpz_t, unsigned long); -void mpz_ui_pow_ui (mpz_t, unsigned long, unsigned long); -void mpz_powm (mpz_t, const mpz_t, const mpz_t, const mpz_t); -void mpz_powm_ui (mpz_t, const mpz_t, unsigned long, const mpz_t); - -void mpz_rootrem (mpz_t, mpz_t, const mpz_t, unsigned long); -int mpz_root (mpz_t, const mpz_t, unsigned long); - -void mpz_fac_ui (mpz_t, unsigned long); -void mpz_2fac_ui (mpz_t, unsigned long); -void mpz_mfac_uiui (mpz_t, unsigned long, unsigned long); -void mpz_bin_uiui (mpz_t, unsigned long, unsigned long); - -int mpz_probab_prime_p (const mpz_t, int); - -int mpz_tstbit (const mpz_t, mp_bitcnt_t); -void mpz_setbit (mpz_t, mp_bitcnt_t); -void mpz_clrbit (mpz_t, mp_bitcnt_t); -void mpz_combit (mpz_t, mp_bitcnt_t); - -void mpz_com (mpz_t, const mpz_t); -void mpz_and (mpz_t, const mpz_t, const mpz_t); -void mpz_ior (mpz_t, const mpz_t, const mpz_t); -void mpz_xor (mpz_t, const mpz_t, const mpz_t); - -mp_bitcnt_t mpz_popcount (const mpz_t); -mp_bitcnt_t mpz_hamdist (const mpz_t, const mpz_t); -mp_bitcnt_t mpz_scan0 (const mpz_t, mp_bitcnt_t); -mp_bitcnt_t mpz_scan1 (const mpz_t, mp_bitcnt_t); - -int mpz_fits_slong_p (const mpz_t); -int mpz_fits_ulong_p (const mpz_t); -long int mpz_get_si (const mpz_t); -unsigned long int mpz_get_ui (const mpz_t); -double mpz_get_d (const mpz_t); -size_t mpz_size (const mpz_t); -mp_limb_t mpz_getlimbn (const mpz_t, mp_size_t); - -void mpz_realloc2 (mpz_t, mp_bitcnt_t); -mp_srcptr mpz_limbs_read (mpz_srcptr); -mp_ptr mpz_limbs_modify (mpz_t, mp_size_t); -mp_ptr mpz_limbs_write (mpz_t, mp_size_t); -void mpz_limbs_finish (mpz_t, mp_size_t); -mpz_srcptr mpz_roinit_n (mpz_t, mp_srcptr, mp_size_t); - -#define MPZ_ROINIT_N(xp, xs) {{0, (xs),(xp) }} - -void mpz_set_si (mpz_t, signed long int); -void mpz_set_ui (mpz_t, unsigned long int); -void mpz_set (mpz_t, const mpz_t); -void mpz_set_d (mpz_t, double); - -void mpz_init_set_si (mpz_t, signed long int); -void mpz_init_set_ui (mpz_t, unsigned long int); -void mpz_init_set (mpz_t, const mpz_t); -void mpz_init_set_d (mpz_t, double); - -size_t mpz_sizeinbase (const mpz_t, int); -char *mpz_get_str (char *, int, const mpz_t); -int mpz_set_str (mpz_t, const char *, int); -int mpz_init_set_str (mpz_t, const char *, int); - -/* This long list taken from gmp.h. */ -/* For reference, "defined(EOF)" cannot be used here. In g++ 2.95.4, - defines EOF but not FILE. */ -#if defined (FILE) \ - || defined (H_STDIO) \ - || defined (_H_STDIO) /* AIX */ \ - || defined (_STDIO_H) /* glibc, Sun, SCO */ \ - || defined (_STDIO_H_) /* BSD, OSF */ \ - || defined (__STDIO_H) /* Borland */ \ - || defined (__STDIO_H__) /* IRIX */ \ - || defined (_STDIO_INCLUDED) /* HPUX */ \ - || defined (__dj_include_stdio_h_) /* DJGPP */ \ - || defined (_FILE_DEFINED) /* Microsoft */ \ - || defined (__STDIO__) /* Apple MPW MrC */ \ - || defined (_MSL_STDIO_H) /* Metrowerks */ \ - || defined (_STDIO_H_INCLUDED) /* QNX4 */ \ - || defined (_ISO_STDIO_ISO_H) /* Sun C++ */ \ - || defined (__STDIO_LOADED) /* VMS */ -size_t mpz_out_str (FILE *, int, const mpz_t); -#endif - -void mpz_import (mpz_t, size_t, int, size_t, int, size_t, const void *); -void *mpz_export (void *, size_t *, int, size_t, int, size_t, const mpz_t); - -#if defined (__cplusplus) -} -#endif -#endif /* __MINI_GMP_H__ */ diff --git a/test/Makefile.in b/test/Makefile.in index f03c194a7cb..10e3d9617d3 100644 --- a/test/Makefile.in +++ b/test/Makefile.in @@ -255,8 +255,8 @@ else FPIC_CFLAGS = -fPIC endif -GMP_LIB = @GMP_LIB@ -GMP_OBJ = $(if @GMP_OBJ@, ../src/@GMP_OBJ@) +GMP_H = @GMP_H@ +LIB_GMP = @LIB_GMP@ # Note: emacs-module.h is generated from emacs-module.h.in, hence we # look in ../src, not $(srcdir)/../src. @@ -273,7 +273,8 @@ src/emacs-module-tests.log src/emacs-module-tests.elc: $(test_module) $(test_module): $(test_module:${SO}=.c) ../src/emacs-module.h $(AM_V_at)${MKDIR_P} $(dir $@) $(AM_V_CCLD)$(CC) -shared $(CPPFLAGS) $(MODULE_CFLAGS) $(LDFLAGS) \ - -o $@ $< $(GMP_LIB) $(GMP_OBJ:.o=.c) \ + -o $@ $< $(LIB_GMP) \ + $(and $(GMP_H),$(srcdir)/../lib/mini-gmp-gnulib.c) \ $(srcdir)/../lib/timespec.c $(srcdir)/../lib/gettime.c endif diff --git a/test/data/emacs-module/mod-test.c b/test/data/emacs-module/mod-test.c index 5e3112f4471..1e64bcd65f1 100644 --- a/test/data/emacs-module/mod-test.c +++ b/test/data/emacs-module/mod-test.c @@ -43,12 +43,7 @@ uintptr_t _beginthread (void (__cdecl *)(void *), unsigned, void *); # include #endif -#ifdef HAVE_GMP #include -#else -#include "mini-gmp.h" -#endif - #include #include "timespec.h"