stdlib/gmp-impl.h

   1 /* Include file for internal GNU MP types and definitions.
   2
   3 Copyright (C) 1991-2016 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 <http://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 (HAVE_ALLOCA) || defined (USE_STACK_ALLOC)
  51 #include "stack-alloc.h"
  52 #else
  53 #define TMP_DECL(m)
  54 #define TMP_ALLOC(x) alloca(x)
  55 #define TMP_MARK(m)
  56 #define TMP_FREE(m)
  57 #endif
  58
  59 #ifndef NULL
  60 #define NULL ((void *) 0)
  61 #endif
  62
  63 #if ! defined (__GNUC__)
  64 #define inline                  /* Empty */
  65 #endif
  66
  67 #ifndef MIN
  68 #define MIN(l,o) ((l) < (o) ? (l) : (o))
  69 #endif
  70 #ifndef MAX
  71 #define MAX(h,i) ((h) > (i) ? (h) : (i))
  72 #endif
  73
  74 /* Field access macros.  */
  75 #define SIZ(x) ((x)->_mp_size)
  76 #define PTR(x) ((x)->_mp_d)
  77 #define EXP(x) ((x)->_mp_exp)
  78 #define PREC(x) ((x)->_mp_prec)
  79 #define ALLOC(x) ((x)->_mp_alloc)
  80
  81 #include "gmp-mparam.h"
  82 /* #include "longlong.h" */
  83
  84 #if defined (__STDC__)  || defined (__cplusplus)
  85 void *malloc (size_t);
  86 void *realloc (void *, size_t);
  87 void free (void *);
  88
  89 extern void *   (*_mp_allocate_func) (size_t);
  90 extern void *   (*_mp_reallocate_func) (void *, size_t, size_t);
  91 extern void     (*_mp_free_func) (void *, size_t);
  92
  93 void *_mp_default_allocate (size_t);
  94 void *_mp_default_reallocate (void *, size_t, size_t);
  95 void _mp_default_free (void *, size_t);
  96
  97 #else
  98
  99 #define const                   /* Empty */
 100 #define signed                  /* Empty */
 101
 102 void *malloc ();
 103 void *realloc ();
 104 void free ();
 105
 106 extern void *   (*_mp_allocate_func) ();
 107 extern void *   (*_mp_reallocate_func) ();
 108 extern void     (*_mp_free_func) ();
 109
 110 void *_mp_default_allocate ();
 111 void *_mp_default_reallocate ();
 112 void _mp_default_free ();
 113 #endif
 114
 115 /* Copy NLIMBS *limbs* from SRC to DST.  */
 116 #define MPN_COPY_INCR(DST, SRC, NLIMBS) \
 117   do {                                                                  \
 118     mp_size_t __i;                                                      \
 119     for (__i = 0; __i < (NLIMBS); __i++)                                \
 120       (DST)[__i] = (SRC)[__i];                                          \
 121   } while (0)
 122 #define MPN_COPY_DECR(DST, SRC, NLIMBS) \
 123   do {                                                                  \
 124     mp_size_t __i;                                                      \
 125     for (__i = (NLIMBS) - 1; __i >= 0; __i--)                           \
 126       (DST)[__i] = (SRC)[__i];                                          \
 127   } while (0)
 128 #define MPN_COPY MPN_COPY_INCR
 129
 130 /* Zero NLIMBS *limbs* AT DST.  */
 131 #define MPN_ZERO(DST, NLIMBS) \
 132   do {                                                                  \
 133     mp_size_t __i;                                                      \
 134     for (__i = 0; __i < (NLIMBS); __i++)                                \
 135       (DST)[__i] = 0;                                                   \
 136   } while (0)
 137
 138 #define MPN_NORMALIZE(DST, NLIMBS) \
 139   do {                                                                  \
 140     while (NLIMBS > 0)                                                  \
 141       {                                                                 \
 142         if ((DST)[(NLIMBS) - 1] != 0)                                   \
 143           break;                                                        \
 144         NLIMBS--;                                                       \
 145       }                                                                 \
 146   } while (0)
 147 #define MPN_NORMALIZE_NOT_ZERO(DST, NLIMBS) \
 148   do {                                                                  \
 149     while (1)                                                           \
 150       {                                                                 \
 151         if ((DST)[(NLIMBS) - 1] != 0)                                   \
 152           break;                                                        \
 153         NLIMBS--;                                                       \
 154       }                                                                 \
 155   } while (0)
 156
 157 /* Initialize the MP_INT X with space for NLIMBS limbs.
 158    X should be a temporary variable, and it will be automatically
 159    cleared out when the running function returns.
 160    We use __x here to make it possible to accept both mpz_ptr and mpz_t
 161    arguments.  */
 162 #define MPZ_TMP_INIT(X, NLIMBS) \
 163   do {                                                                  \
 164     mpz_ptr __x = (X);                                                  \
 165     __x->_mp_alloc = (NLIMBS);                                          \
 166     __x->_mp_d = (mp_ptr) TMP_ALLOC ((NLIMBS) * BYTES_PER_MP_LIMB);     \
 167   } while (0)
 168
 169 #define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
 170   do {                                                                  \
 171     if ((size) < KARATSUBA_THRESHOLD)                                   \
 172       impn_mul_n_basecase (prodp, up, vp, size);                        \
 173     else                                                                \
 174       impn_mul_n (prodp, up, vp, size, tspace);                 \
 175   } while (0);
 176 #define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
 177   do {                                                                  \
 178     if ((size) < KARATSUBA_THRESHOLD)                                   \
 179       impn_sqr_n_basecase (prodp, up, size);                            \
 180     else                                                                \
 181       impn_sqr_n (prodp, up, size, tspace);                             \
 182   } while (0);
 183
 184 /* Structure for conversion between internal binary format and
 185    strings in base 2..36.  */
 186 struct bases
 187 {
 188   /* Number of digits in the conversion base that always fits in an mp_limb_t.
 189      For example, for base 10 on a machine where a mp_limb_t has 32 bits this
 190      is 9, since 10**9 is the largest number that fits into a mp_limb_t.  */
 191   int chars_per_limb;
 192
 193   /* log(2)/log(conversion_base) */
 194   float chars_per_bit_exactly;
 195
 196   /* base**chars_per_limb, i.e. the biggest number that fits a word, built by
 197      factors of base.  Exception: For 2, 4, 8, etc, big_base is log2(base),
 198      i.e. the number of bits used to represent each digit in the base.  */
 199   mp_limb_t big_base;
 200
 201   /* A BITS_PER_MP_LIMB bit approximation to 1/big_base, represented as a
 202      fixed-point number.  Instead of dividing by big_base an application can
 203      choose to multiply by big_base_inverted.  */
 204   mp_limb_t big_base_inverted;
 205 };
 206
 207 extern const struct bases __mp_bases[];
 208 extern mp_size_t __gmp_default_fp_limb_precision;
 209
 210 /* Divide the two-limb number in (NH,,NL) by D, with DI being the largest
 211    limb not larger than (2**(2*BITS_PER_MP_LIMB))/D - (2**BITS_PER_MP_LIMB).
 212    If this would yield overflow, DI should be the largest possible number
 213    (i.e., only ones).  For correct operation, the most significant bit of D
 214    has to be set.  Put the quotient in Q and the remainder in R.  */
 215 #define udiv_qrnnd_preinv(q, r, nh, nl, d, di) \
 216   do {                                                                  \
 217     mp_limb_t _ql __attribute__ ((unused));                             \
 218     mp_limb_t _q, _r;                                                   \
 219     mp_limb_t _xh, _xl;                                                 \
 220     umul_ppmm (_q, _ql, (nh), (di));                                    \
 221     _q += (nh);                 /* DI is 2**BITS_PER_MP_LIMB too small */\
 222     umul_ppmm (_xh, _xl, _q, (d));                                      \
 223     sub_ddmmss (_xh, _r, (nh), (nl), _xh, _xl);                         \
 224     if (_xh != 0)                                                       \
 225       {                                                                 \
 226         sub_ddmmss (_xh, _r, _xh, _r, 0, (d));                          \
 227         _q += 1;                                                        \
 228         if (_xh != 0)                                                   \
 229           {                                                             \
 230             sub_ddmmss (_xh, _r, _xh, _r, 0, (d));                      \
 231             _q += 1;                                                    \
 232           }                                                             \
 233       }                                                                 \
 234     if (_r >= (d))                                                      \
 235       {                                                                 \
 236         _r -= (d);                                                      \
 237         _q += 1;                                                        \
 238       }                                                                 \
 239     (r) = _r;                                                           \
 240     (q) = _q;                                                           \
 241   } while (0)
 242 /* Like udiv_qrnnd_preinv, but for any value D.  DNORM is D shifted left
 243    so that its most significant bit is set.  LGUP is ceil(log2(D)).  */
 244 #define udiv_qrnnd_preinv2gen(q, r, nh, nl, d, di, dnorm, lgup) \
 245   do {                                                                  \
 246     mp_limb_t n2, n10, n1, nadj, q1;                                    \
 247     mp_limb_t _xh, _xl;                                                 \
 248     n2 = ((nh) << (BITS_PER_MP_LIMB - (lgup))) + ((nl) >> 1 >> (l - 1));\
 249     n10 = (nl) << (BITS_PER_MP_LIMB - (lgup));                          \
 250     n1 = ((mp_limb_signed_t) n10 >> (BITS_PER_MP_LIMB - 1));            \
 251     nadj = n10 + (n1 & (dnorm));                                        \
 252     umul_ppmm (_xh, _xl, di, n2 - n1);                                  \
 253     add_ssaaaa (_xh, _xl, _xh, _xl, 0, nadj);                           \
 254     q1 = ~(n2 + _xh);                                                   \
 255     umul_ppmm (_xh, _xl, q1, d);                                        \
 256     add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl);                            \
 257     _xh -= (d);                                                         \
 258     (r) = _xl + ((d) & _xh);                                            \
 259     (q) = _xh - q1;                                                     \
 260   } while (0)
 261 /* Exactly like udiv_qrnnd_preinv, but branch-free.  It is not clear which
 262    version to use.  */
 263 #define udiv_qrnnd_preinv2norm(q, r, nh, nl, d, di) \
 264   do {                                                                  \
 265     mp_limb_t n2, n10, n1, nadj, q1;                                    \
 266     mp_limb_t _xh, _xl;                                                 \
 267     n2 = (nh);                                                          \
 268     n10 = (nl);                                                         \
 269     n1 = ((mp_limb_signed_t) n10 >> (BITS_PER_MP_LIMB - 1));            \
 270     nadj = n10 + (n1 & (d));                                            \
 271     umul_ppmm (_xh, _xl, di, n2 - n1);                                  \
 272     add_ssaaaa (_xh, _xl, _xh, _xl, 0, nadj);                           \
 273     q1 = ~(n2 + _xh);                                                   \
 274     umul_ppmm (_xh, _xl, q1, d);                                        \
 275     add_ssaaaa (_xh, _xl, _xh, _xl, nh, nl);                            \
 276     _xh -= (d);                                                         \
 277     (r) = _xl + ((d) & _xh);                                            \
 278     (q) = _xh - q1;                                                     \
 279   } while (0)
 280
 281 #if defined (__GNUC__)
 282 /* Define stuff for longlong.h.  */
 283 typedef unsigned int UQItype    __attribute__ ((mode (QI)));
 284 typedef          int SItype     __attribute__ ((mode (SI)));
 285 typedef unsigned int USItype    __attribute__ ((mode (SI)));
 286 typedef          int DItype     __attribute__ ((mode (DI)));
 287 typedef unsigned int UDItype    __attribute__ ((mode (DI)));
 288 #else
 289 typedef unsigned char UQItype;
 290 typedef          long SItype;
 291 typedef unsigned long USItype;
 292 #endif
 293
 294 typedef mp_limb_t UWtype;
 295 typedef unsigned int UHWtype;
 296 #define W_TYPE_SIZE BITS_PER_MP_LIMB
 297
 298 /* Internal mpn calls */
 299 #define impn_mul_n_basecase     __MPN(impn_mul_n_basecase)
 300 #define impn_mul_n              __MPN(impn_mul_n)
 301 #define impn_sqr_n_basecase     __MPN(impn_sqr_n_basecase)
 302 #define impn_sqr_n              __MPN(impn_sqr_n)
 303
 304 #ifndef _PROTO
 305 #if defined (__STDC__) || defined (__cplusplus)
 306 #define _PROTO(x) x
 307 #else
 308 #define _PROTO(x) ()
 309 #endif
 310 #endif
 311
 312 /* Prototypes for internal mpn calls.  */
 313 extern void impn_mul_n_basecase _PROTO ((mp_ptr prodp, mp_srcptr up,
 314                                          mp_srcptr vp, mp_size_t size));
 315 extern void impn_mul_n _PROTO ((mp_ptr prodp, mp_srcptr up, mp_srcptr vp,
 316                                 mp_size_t size, mp_ptr tspace));
 317 extern void impn_sqr_n_basecase _PROTO ((mp_ptr prodp, mp_srcptr up,
 318                                          mp_size_t size));
 319 extern void impn_sqr_n _PROTO ((mp_ptr prodp, mp_srcptr up, mp_size_t size,
 320                                 mp_ptr tspace));
 321
 322
 323
 324 #ifndef IEEE_DOUBLE_BIG_ENDIAN
 325 #define IEEE_DOUBLE_BIG_ENDIAN 1
 326 #endif
 327
 328 #ifndef IEEE_DOUBLE_MIXED_ENDIAN
 329 #define IEEE_DOUBLE_MIXED_ENDIAN 0
 330 #endif
 331
 332 #if IEEE_DOUBLE_MIXED_ENDIAN
 333 union ieee_double_extract
 334 {
 335   struct
 336     {
 337       unsigned int manh:20;
 338       unsigned int exp:11;
 339       unsigned int sig:1;
 340       unsigned int manl:32;
 341     } s;
 342   double d;
 343 };
 344 #else
 345 #if IEEE_DOUBLE_BIG_ENDIAN
 346 union ieee_double_extract
 347 {
 348   struct
 349     {
 350       unsigned int sig:1;
 351       unsigned int exp:11;
 352       unsigned int manh:20;
 353       unsigned int manl:32;
 354     } s;
 355   double d;
 356 };
 357 #else
 358 union ieee_double_extract
 359 {
 360   struct
 361     {
 362       unsigned int manl:32;
 363       unsigned int manh:20;
 364       unsigned int exp:11;
 365       unsigned int sig:1;
 366     } s;
 367   double d;
 368 };
 369 #endif
 370 #endif