1 /* Include file for internal GNU MP types and definitions.
2 
3 Copyright (C) 1991-2022 Free Software Foundation, Inc.
4 
5 This file is part of the GNU MP Library.
6 
7 The GNU MP Library is free software; you can redistribute it and/or modify
8 it under the terms of the GNU Lesser General Public License as published by
9 the Free Software Foundation; either version 2.1 of the License, or (at your
10 option) any later version.
11 
12 The GNU MP Library is distributed in the hope that it will be useful, but
13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
15 License for more details.
16 
17 You should have received a copy of the GNU Lesser General Public License
18 along with the GNU MP Library; see the file COPYING.LIB.  If not, see
19 <https://www.gnu.org/licenses/>.  */
20 
21 /* When using gcc, make sure to use its builtin alloca.  */
22 #if ! defined (alloca) && defined (__GNUC__)
23 #define alloca __builtin_alloca
24 #define HAVE_ALLOCA
25 #endif
26 
27 /* When using cc, do whatever necessary to allow use of alloca.  For many
28    machines, this means including alloca.h.  IBM's compilers need a #pragma
29    in "each module that needs to use alloca".  */
30 #if ! defined (alloca)
31 /* We need lots of variants for MIPS, to cover all versions and perversions
32    of OSes for MIPS.  */
33 #if defined (__mips) || defined (MIPSEL) || defined (MIPSEB) \
34  || defined (_MIPSEL) || defined (_MIPSEB) || defined (__sgi) \
35  || defined (__alpha) || defined (__sparc) || defined (sparc) \
36  || defined (__ksr__)
37 #include <alloca.h>
38 #define HAVE_ALLOCA
39 #endif
40 #if defined (_IBMR2)
41 #pragma alloca
42 #define HAVE_ALLOCA
43 #endif
44 #if defined (__DECC)
45 #define alloca(x) __ALLOCA(x)
46 #define HAVE_ALLOCA
47 #endif
48 #endif
49 
50 #if (! defined (alloca) && ! defined (HAVE_ALLOCA)) \
51     || defined (USE_STACK_ALLOC)
52 #include "stack-alloc.h"
53 #else
54 #define TMP_DECL(m)
55 #define TMP_ALLOC(x) alloca(x)
56 #define TMP_MARK(m)
57 #define TMP_FREE(m)
58 #endif
59 
60 #ifndef NULL
61 #define NULL ((void *) 0)
62 #endif
63 
64 #if ! defined (__GNUC__)
65 #define inline			/* Empty */
66 #endif
67 
68 /* Get MAX/MIN macros.  */
69 #include <sys/param.h>
70 
71 /* Field access macros.  */
72 #define SIZ(x) ((x)->_mp_size)
73 #define PTR(x) ((x)->_mp_d)
74 #define EXP(x) ((x)->_mp_exp)
75 #define PREC(x) ((x)->_mp_prec)
76 #define ALLOC(x) ((x)->_mp_alloc)
77 
78 #include "gmp-mparam.h"
79 /* #include "longlong.h" */
80 
81 #if defined (__STDC__)  || defined (__cplusplus)
82 void *malloc (size_t);
83 void *realloc (void *, size_t);
84 void free (void *);
85 
86 extern void *	(*_mp_allocate_func) (size_t);
87 extern void *	(*_mp_reallocate_func) (void *, size_t, size_t);
88 extern void	(*_mp_free_func) (void *, size_t);
89 
90 void *_mp_default_allocate (size_t);
91 void *_mp_default_reallocate (void *, size_t, size_t);
92 void _mp_default_free (void *, size_t);
93 
94 #else
95 
96 #define const			/* Empty */
97 #define signed			/* Empty */
98 
99 void *malloc ();
100 void *realloc ();
101 void free ();
102 
103 extern void *	(*_mp_allocate_func) ();
104 extern void *	(*_mp_reallocate_func) ();
105 extern void	(*_mp_free_func) ();
106 
107 void *_mp_default_allocate ();
108 void *_mp_default_reallocate ();
109 void _mp_default_free ();
110 #endif
111 
112 /* Copy NLIMBS *limbs* from SRC to DST.  */
113 #define MPN_COPY_INCR(DST, SRC, NLIMBS) \
114   do {									\
115     mp_size_t __i;							\
116     for (__i = 0; __i < (NLIMBS); __i++)				\
117       (DST)[__i] = (SRC)[__i];						\
118   } while (0)
119 #define MPN_COPY_DECR(DST, SRC, NLIMBS) \
120   do {									\
121     mp_size_t __i;							\
122     for (__i = (NLIMBS) - 1; __i >= 0; __i--)				\
123       (DST)[__i] = (SRC)[__i];						\
124   } while (0)
125 #define MPN_COPY MPN_COPY_INCR
126 
127 /* Zero NLIMBS *limbs* AT DST.  */
128 #define MPN_ZERO(DST, NLIMBS) \
129   do {									\
130     mp_size_t __i;							\
131     for (__i = 0; __i < (NLIMBS); __i++)				\
132       (DST)[__i] = 0;							\
133   } while (0)
134 
135 #define MPN_NORMALIZE(DST, NLIMBS) \
136   do {									\
137     while (NLIMBS > 0)							\
138       {									\
139 	if ((DST)[(NLIMBS) - 1] != 0)					\
140 	  break;							\
141 	NLIMBS--;							\
142       }									\
143   } while (0)
144 #define MPN_NORMALIZE_NOT_ZERO(DST, NLIMBS) \
145   do {									\
146     while (1)								\
147       {									\
148 	if ((DST)[(NLIMBS) - 1] != 0)					\
149 	  break;							\
150 	NLIMBS--;							\
151       }									\
152   } while (0)
153 
154 /* Initialize the MP_INT X with space for NLIMBS limbs.
155    X should be a temporary variable, and it will be automatically
156    cleared out when the running function returns.
157    We use __x here to make it possible to accept both mpz_ptr and mpz_t
158    arguments.  */
159 #define MPZ_TMP_INIT(X, NLIMBS) \
160   do {									\
161     mpz_ptr __x = (X);							\
162     __x->_mp_alloc = (NLIMBS);						\
163     __x->_mp_d = (mp_ptr) TMP_ALLOC ((NLIMBS) * BYTES_PER_MP_LIMB);	\
164   } while (0)
165 
166 #define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
167   do {									\
168     if ((size) < KARATSUBA_THRESHOLD)					\
169       impn_mul_n_basecase (prodp, up, vp, size);			\
170     else								\
171       impn_mul_n (prodp, up, vp, size, tspace);			\
172   } while (0);
173 #define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
174   do {									\
175     if ((size) < KARATSUBA_THRESHOLD)					\
176       impn_sqr_n_basecase (prodp, up, size);				\
177     else								\
178       impn_sqr_n (prodp, up, size, tspace);				\
179   } while (0);
180 
181 /* Structure for conversion between internal binary format and
182    strings in base 2..36.  */
183 struct bases
184 {
185   /* Number of digits in the conversion base that always fits in an mp_limb_t.
186      For example, for base 10 on a machine where a mp_limb_t has 32 bits this
187      is 9, since 10**9 is the largest number that fits into a mp_limb_t.  */
188   int chars_per_limb;
189 
190   /* log(2)/log(conversion_base) */
191   float chars_per_bit_exactly;
192 
193   /* base**chars_per_limb, i.e. the biggest number that fits a word, built by
194      factors of base.  Exception: For 2, 4, 8, etc, big_base is log2(base),
195      i.e. the number of bits used to represent each digit in the base.  */
196   mp_limb_t big_base;
197 
198   /* A BITS_PER_MP_LIMB bit approximation to 1/big_base, represented as a
199      fixed-point number.  Instead of dividing by big_base an application can
200      choose to multiply by big_base_inverted.  */
201   mp_limb_t big_base_inverted;
202 };
203 
204 extern const struct bases __mp_bases[];
205 extern mp_size_t __gmp_default_fp_limb_precision;
206 
207 /* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
208    limb not larger than (2**(2*BITS_PER_MP_LIMB))/D - (2**BITS_PER_MP_LIMB).
209    If this would yield overflow, DI should be the largest possible number
210    (i.e., only ones).  For correct operation, the most significant bit of D
211    has to be set.  Put the quotient in Q and the remainder in R.  */
212 #define udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
213   do {									\
214     mp_limb_t _ql __attribute__ ((unused));				\
215     mp_limb_t _q, _r;							\
216     mp_limb_t _xh, _xl;							\
217     umul_ppmm (_q, _ql, (nh), (di));					\
218     _q += (nh);			/* DI is 2**BITS_PER_MP_LIMB too small */\
219     umul_ppmm (_xh, _xl, _q, (d));					\
220     sub_ddmmss (_xh, _r, (nh), (nl), _xh, _xl);				\
221     if (_xh != 0)							\
222       {									\
223 	sub_ddmmss (_xh, _r, _xh, _r, 0, (d));				\
224 	_q += 1;							\
225 	if (_xh != 0)							\
226 	  {								\
227 	    sub_ddmmss (_xh, _r, _xh, _r, 0, (d));			\
228 	    _q += 1;							\
229 	  }								\
230       }									\
231     if (_r >= (d))							\
232       {									\
233 	_r -= (d);							\
234 	_q += 1;							\
235       }									\
236     (r) = _r;								\
237     (q) = _q;								\
238   } while (0)
239 /* Like udiv_qrnnd_preinv, but for any value D.  DNORM is D shifted left
240    so that its most significant bit is set.  LGUP is ceil(log2(D)).  */
241 #define udiv_qrnnd_preinv2gen(q, r, nh, nl, d, di, dnorm, lgup) \
242   do {									\
243     mp_limb_t n2, n10, n1, nadj, q1;					\
244     mp_limb_t _xh, _xl;							\
245     n2 = ((nh) << (BITS_PER_MP_LIMB - (lgup))) + ((nl) >> 1 >> (l - 1));\
246     n10 = (nl) << (BITS_PER_MP_LIMB - (lgup));				\
247     n1 = ((mp_limb_signed_t) n10 >> (BITS_PER_MP_LIMB - 1));		\
248     nadj = n10 + (n1 & (dnorm));					\
249     umul_ppmm (_xh, _xl, di, n2 - n1);					\
250     add_ssaaaa (_xh, _xl, _xh, _xl, 0, nadj);				\
251     q1 = ~(n2 + _xh);							\
252     umul_ppmm (_xh, _xl, q1, d);					\
253     add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl);				\
254     _xh -= (d);								\
255     (r) = _xl + ((d) & _xh);						\
256     (q) = _xh - q1;							\
257   } while (0)
258 /* Exactly like udiv_qrnnd_preinv, but branch-free.  It is not clear which
259    version to use.  */
260 #define udiv_qrnnd_preinv2norm(q, r, nh, nl, d, di) \
261   do {									\
262     mp_limb_t n2, n10, n1, nadj, q1;					\
263     mp_limb_t _xh, _xl;							\
264     n2 = (nh);								\
265     n10 = (nl);								\
266     n1 = ((mp_limb_signed_t) n10 >> (BITS_PER_MP_LIMB - 1));		\
267     nadj = n10 + (n1 & (d));						\
268     umul_ppmm (_xh, _xl, di, n2 - n1);					\
269     add_ssaaaa (_xh, _xl, _xh, _xl, 0, nadj);				\
270     q1 = ~(n2 + _xh);							\
271     umul_ppmm (_xh, _xl, q1, d);					\
272     add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl);				\
273     _xh -= (d);								\
274     (r) = _xl + ((d) & _xh);						\
275     (q) = _xh - q1;							\
276   } while (0)
277 
278 #if defined (__GNUC__)
279 /* Define stuff for longlong.h.  */
280 typedef unsigned int UQItype	__attribute__ ((mode (QI)));
281 typedef 	 int SItype	__attribute__ ((mode (SI)));
282 typedef unsigned int USItype	__attribute__ ((mode (SI)));
283 typedef		 int DItype	__attribute__ ((mode (DI)));
284 typedef unsigned int UDItype	__attribute__ ((mode (DI)));
285 #else
286 typedef unsigned char UQItype;
287 typedef 	 long SItype;
288 typedef unsigned long USItype;
289 #endif
290 
291 typedef mp_limb_t UWtype;
292 typedef unsigned int UHWtype;
293 #define W_TYPE_SIZE BITS_PER_MP_LIMB
294 
295 /* Internal mpn calls */
296 #define impn_mul_n_basecase	__MPN(impn_mul_n_basecase)
297 #define impn_mul_n		__MPN(impn_mul_n)
298 #define impn_sqr_n_basecase	__MPN(impn_sqr_n_basecase)
299 #define impn_sqr_n		__MPN(impn_sqr_n)
300 
301 #ifndef _PROTO
302 #if defined (__STDC__) || defined (__cplusplus)
303 #define _PROTO(x) x
304 #else
305 #define _PROTO(x) ()
306 #endif
307 #endif
308 
309 /* Prototypes for internal mpn calls.  */
310 extern void impn_mul_n_basecase _PROTO ((mp_ptr prodp, mp_srcptr up,
311 					 mp_srcptr vp, mp_size_t size))
312      attribute_hidden;
313 extern void impn_mul_n _PROTO ((mp_ptr prodp, mp_srcptr up, mp_srcptr vp,
314 				mp_size_t size, mp_ptr tspace))
315      attribute_hidden;
316 extern void impn_sqr_n_basecase _PROTO ((mp_ptr prodp, mp_srcptr up,
317 					 mp_size_t size))
318      attribute_hidden;
319 extern void impn_sqr_n _PROTO ((mp_ptr prodp, mp_srcptr up, mp_size_t size,
320 				mp_ptr tspace))
321      attribute_hidden;
322