contrib/mpfr/mulders.c

   1 /* Mulder's MulHigh function (short product)
   2
   3 Copyright 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
   4 Contributed by the Arenaire and Cacao projects, INRIA.
   5
   6 This file is part of the GNU MPFR Library.
   7
   8 The GNU MPFR Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 2.1 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MPFR Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MPFR Library; see the file COPYING.LIB.  If not, write to
  20 the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
  21 MA 02110-1301, USA. */
  22
  23 #define MPFR_NEED_LONGLONG_H
  24 #include "mpfr-impl.h"
  25
  26 #ifndef MUL_FFT_THRESHOLD
  27 #define MUL_FFT_THRESHOLD 8448
  28 #endif
  29
  30 /* Don't use MPFR_MULHIGH_SIZE since it is handled by tuneup */
  31 #ifdef MPFR_MULHIGH_TAB_SIZE
  32 static short mulhigh_ktab[MPFR_MULHIGH_TAB_SIZE];
  33 #else
  34 static short mulhigh_ktab[] = {MPFR_MULHIGH_TAB};
  35 #define MPFR_MULHIGH_TAB_SIZE \
  36   ((mp_size_t) (sizeof(mulhigh_ktab) / sizeof(mulhigh_ktab[0])))
  37 #endif
  38
  39 /* Put in  rp[n..2n-1] an approximation of the n high limbs
  40    of {mp, n} * {np, n}.
  41    The error is at worst of ln(n) for rp[n] and rp[n-1] is totally wrong */
  42 static void
  43 mpfr_mulhigh_n_basecase (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n)
  44 {
  45   mp_size_t i;
  46
  47   rp += n-1;
  48   umul_ppmm (rp[1], rp[0], up[n-1], vp[0]);
  49   for (i = 1 ; i < n ; i++)
  50     rp[i+1] = mpn_addmul_1 (rp, up + (n - i - 1), i+1, vp[i]);
  51 }
  52
  53 void
  54 mpfr_mulhigh_n (mp_ptr rp, mp_srcptr np, mp_srcptr mp, mp_size_t n)
  55 {
  56   mp_size_t k;
  57
  58   MPFR_ASSERTD (MPFR_MULHIGH_TAB_SIZE > 4);
  59   k = MPFR_LIKELY (n < MPFR_MULHIGH_TAB_SIZE) ? mulhigh_ktab[n] : 2*n/3;
  60   MPFR_ASSERTD (k == -1 || k == 0 || (k > n/2 && k < n));
  61   if (k < 0)
  62     mpn_mul_basecase (rp, np, n, mp, n);
  63   else if (k == 0)
  64     mpfr_mulhigh_n_basecase (rp, np, mp, n);
  65   else if (n > MUL_FFT_THRESHOLD)
  66     mpn_mul_n (rp, np, mp, n);
  67   else
  68     {
  69       mp_size_t l = n - k;
  70       mp_limb_t cy;
  71
  72       mpn_mul_n (rp + 2 * l, np + l, mp + l, k); /* fills rp[2l..2n-1] */
  73       mpfr_mulhigh_n (rp, np + k, mp, l);          /* fills rp[l-1..2l-1] */
  74       cy = mpn_add_n (rp + n - 1, rp + n - 1, rp + l - 1, l + 1);
  75       mpfr_mulhigh_n (rp, np, mp + k, l);          /* fills rp[l-1..2l-1] */
  76       cy += mpn_add_n (rp + n - 1, rp + n - 1, rp + l - 1, l + 1);
  77       mpn_add_1 (rp + n + l, rp + n + l, k, cy); /* propagate carry */
  78     }
  79 }
  80
  81 #ifdef MPFR_SQRHIGH_TAB_SIZE
  82 static short sqrhigh_ktab[MPFR_SQRHIGH_TAB_SIZE];
  83 #else
  84 static short sqrhigh_ktab[] = {MPFR_SQRHIGH_TAB};
  85 #define MPFR_SQRHIGH_TAB_SIZE (sizeof(sqrhigh_ktab) / sizeof(sqrhigh_ktab[0]))
  86 #endif
  87
  88 void
  89 mpfr_sqrhigh_n (mp_ptr rp, mp_srcptr np, mp_size_t n)
  90 {
  91   mp_size_t k;
  92
  93   MPFR_ASSERTD (MPFR_SQRHIGH_TAB_SIZE > 4);
  94   k = MPFR_LIKELY (n < MPFR_SQRHIGH_TAB_SIZE) ? sqrhigh_ktab[n] : 2*n/3;
  95   MPFR_ASSERTD (k == -1 || k == 0 || (k > n/2 && k < n));
  96   if (k < 0)
  97     /* we can't use mpn_sqr_basecase here, since it requires
  98        n <= SQR_KARATSUBA_THRESHOLD, where SQR_KARATSUBA_THRESHOLD
  99        is not exported by GMP */
 100     mpn_sqr_n (rp, np, n);
 101   else if (k == 0)
 102     mpfr_mulhigh_n_basecase (rp, np, np, n);
 103   else
 104     {
 105       mp_size_t l = n - k;
 106       mp_limb_t cy;
 107
 108       mpn_sqr_n (rp + 2 * l, np + l, k);          /* fills rp[2l..2n-1] */
 109       mpfr_mulhigh_n (rp, np, np + k, l);         /* fills rp[l-1..2l-1] */
 110       /* FIXME: maybe shift by 2 is a better idea but it has to handle carry*/
 111       cy = mpn_add_n (rp + n - 1, rp + n - 1, rp + l - 1, l + 1);
 112       cy += mpn_add_n (rp + n - 1, rp + n - 1, rp + l - 1, l + 1);
 113       mpn_add_1 (rp + n + l, rp + n + l, k, cy); /* propagate carry */
 114     }
 115 }