github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpz/fib_ui.c (about)

     1  /* mpz_fib_ui -- calculate Fibonacci numbers.
     2  
     3  Copyright 2000-2002, 2005, 2012, 2014 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 either:
     9  
    10    * the GNU Lesser General Public License as published by the Free
    11      Software Foundation; either version 3 of the License, or (at your
    12      option) any later version.
    13  
    14  or
    15  
    16    * the GNU General Public License as published by the Free Software
    17      Foundation; either version 2 of the License, or (at your option) any
    18      later version.
    19  
    20  or both in parallel, as here.
    21  
    22  The GNU MP Library is distributed in the hope that it will be useful, but
    23  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
    24  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    25  for more details.
    26  
    27  You should have received copies of the GNU General Public License and the
    28  GNU Lesser General Public License along with the GNU MP Library.  If not,
    29  see https://www.gnu.org/licenses/.  */
    30  
    31  #include <stdio.h>
    32  #include "gmp.h"
    33  #include "gmp-impl.h"
    34  #include "longlong.h"
    35  
    36  
    37  /* change to "#define TRACE(x) x" to get some traces */
    38  #define TRACE(x)
    39  
    40  
    41  /* In the F[2k+1] below for k odd, the -2 won't give a borrow from the low
    42     limb because the result F[2k+1] is an F[4m+3] and such numbers are always
    43     == 1, 2 or 5 mod 8, whereas an underflow would leave 6 or 7.  (This is
    44     the same as in mpn_fib2_ui.)
    45  
    46     In the F[2k+1] for k even, the +2 won't give a carry out of the low limb
    47     in normal circumstances.  This is an F[4m+1] and we claim that F[3*2^b+1]
    48     == 1 mod 2^b is the first F[4m+1] congruent to 0 or 1 mod 2^b, and hence
    49     if n < 2^GMP_NUMB_BITS then F[n] cannot have a low limb of 0 or 1.  No
    50     proof for this claim, but it's been verified up to b==32 and has such a
    51     nice pattern it must be true :-).  Of interest is that F[3*2^b] == 0 mod
    52     2^(b+1) seems to hold too.
    53  
    54     When n >= 2^GMP_NUMB_BITS, which can arise in a nails build, then the low
    55     limb of F[4m+1] can certainly be 1, and an mpn_add_1 must be used.  */
    56  
    57  void
    58  mpz_fib_ui (mpz_ptr fn, unsigned long n)
    59  {
    60    mp_ptr         fp, xp, yp;
    61    mp_size_t      size, xalloc;
    62    unsigned long  n2;
    63    mp_limb_t      c;
    64    TMP_DECL;
    65  
    66    if (n <= FIB_TABLE_LIMIT)
    67      {
    68        PTR(fn)[0] = FIB_TABLE (n);
    69        SIZ(fn) = (n != 0);      /* F[0]==0, others are !=0 */
    70        return;
    71      }
    72  
    73    n2 = n/2;
    74    xalloc = MPN_FIB2_SIZE (n2) + 1;
    75    fp = MPZ_NEWALLOC (fn, 2 * xalloc);
    76  
    77    TMP_MARK;
    78    TMP_ALLOC_LIMBS_2 (xp,xalloc, yp,xalloc);
    79    size = mpn_fib2_ui (xp, yp, n2);
    80  
    81    TRACE (printf ("mpz_fib_ui last step n=%lu size=%ld bit=%lu\n",
    82  		 n >> 1, size, n&1);
    83  	 mpn_trace ("xp", xp, size);
    84  	 mpn_trace ("yp", yp, size));
    85  
    86    if (n & 1)
    87      {
    88        /* F[2k+1] = (2F[k]+F[k-1])*(2F[k]-F[k-1]) + 2*(-1)^k  */
    89        mp_size_t  xsize, ysize;
    90  
    91  #if HAVE_NATIVE_mpn_add_n_sub_n
    92        xp[size] = mpn_lshift (xp, xp, size, 1);
    93        yp[size] = 0;
    94        ASSERT_NOCARRY (mpn_add_n_sub_n (xp, yp, xp, yp, size+1));
    95        xsize = size + (xp[size] != 0);
    96        ASSERT (yp[size] <= 1);
    97        ysize = size + yp[size];
    98  #else
    99        mp_limb_t  c2;
   100  
   101        c2 = mpn_lshift (fp, xp, size, 1);
   102        c = c2 + mpn_add_n (xp, fp, yp, size);
   103        xp[size] = c;
   104        xsize = size + (c != 0);
   105        c2 -= mpn_sub_n (yp, fp, yp, size);
   106        yp[size] = c2;
   107        ASSERT (c2 <= 1);
   108        ysize = size + c2;
   109  #endif
   110  
   111        size = xsize + ysize;
   112        c = mpn_mul (fp, xp, xsize, yp, ysize);
   113  
   114  #if GMP_NUMB_BITS >= BITS_PER_ULONG
   115        /* no overflow, see comments above */
   116        ASSERT (n & 2 ? fp[0] >= 2 : fp[0] <= GMP_NUMB_MAX-2);
   117        fp[0] += (n & 2 ? -CNST_LIMB(2) : CNST_LIMB(2));
   118  #else
   119        if (n & 2)
   120  	{
   121  	  ASSERT (fp[0] >= 2);
   122  	  fp[0] -= 2;
   123  	}
   124        else
   125  	{
   126  	  ASSERT (c != GMP_NUMB_MAX); /* because it's the high of a mul */
   127  	  c += mpn_add_1 (fp, fp, size-1, CNST_LIMB(2));
   128  	  fp[size-1] = c;
   129  	}
   130  #endif
   131      }
   132    else
   133      {
   134        /* F[2k] = F[k]*(F[k]+2F[k-1]) */
   135  
   136        mp_size_t  xsize, ysize;
   137  #if HAVE_NATIVE_mpn_addlsh1_n
   138        c = mpn_addlsh1_n (yp, xp, yp, size);
   139  #else
   140        c = mpn_lshift (yp, yp, size, 1);
   141        c += mpn_add_n (yp, yp, xp, size);
   142  #endif
   143        yp[size] = c;
   144        xsize = size;
   145        ysize = size + (c != 0);
   146        size += ysize;
   147        c = mpn_mul (fp, yp, ysize, xp, xsize);
   148      }
   149  
   150    /* one or two high zeros */
   151    size -= (c == 0);
   152    size -= (fp[size-1] == 0);
   153    SIZ(fn) = size;
   154  
   155    TRACE (printf ("done special, size=%ld\n", size);
   156  	 mpn_trace ("fp ", fp, size));
   157  
   158    TMP_FREE;
   159  }