mul_ui.c

/* mpf_mul_ui -- Multiply a float and an unsigned integer.

Copyright 1993, 1994, 1996, 2001, 2003, 2004 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/.  */

#include "gmp-impl.h"
#include "longlong.h"


/* The core operation is a multiply of PREC(r) limbs from u by v, producing
   either PREC(r) or PREC(r)+1 result limbs.  If u is shorter than PREC(r),
   then we take only as much as it has.  If u is longer we incorporate a
   carry from the lower limbs.

   If u has just 1 extra limb, then the carry to add is high(up[0]*v).  That
   is of course what mpn_mul_1 would do if it was called with PREC(r)+1
   limbs of input.

   If u has more than 1 extra limb, then there can be a further carry bit
   out of lower uncalculated limbs (the way the low of one product adds to
   the high of the product below it).  This is of course what an mpn_mul_1
   would do if it was called with the full u operand.  But we instead work
   downwards explicitly, until a carry occurs or until a value other than
   GMP_NUMB_MAX occurs (that being the only value a carry bit can propagate
   across).

   The carry determination normally requires two umul_ppmm's, only rarely
   will GMP_NUMB_MAX occur and require further products.

   The carry limb is conveniently added into the mul_1 using mpn_mul_1c when
   that function exists, otherwise a subsequent mpn_add_1 is needed.

   Clearly when mpn_mul_1c is used the carry must be calculated first.  But
   this is also the case when add_1 is used, since if r==u and ABSIZ(r) >
   PREC(r) then the mpn_mul_1 overwrites the low part of the input.

   A reuse r==u with size > prec can occur from a size PREC(r)+1 in the
   usual way, or it can occur from an mpf_set_prec_raw leaving a bigger
   sized value.  In both cases we can end up calling mpn_mul_1 with
   overlapping src and dst regions, but this will be with dst < src and such
   an overlap is permitted.

   Not done:

   No attempt is made to determine in advance whether the result will be
   PREC(r) or PREC(r)+1 limbs.  If it's going to be PREC(r)+1 then we could
   take one less limb from u and generate just PREC(r), that of course
   satisfying application requested precision.  But any test counting bits
   or forming the high product would almost certainly take longer than the
   incremental cost of an extra limb in mpn_mul_1.

   Enhancements:

   Repeated mpf_mul_ui's with an even v will accumulate low zero bits on the
   result, leaving low zero limbs after a while, which it might be nice to
   strip to save work in subsequent operations.  Calculating the low limb
   explicitly would let us direct mpn_mul_1 to put the balance at rp when
   the low is zero (instead of normally rp+1).  But it's not clear whether
   this would be worthwhile.  Explicit code for the low limb will probably
   be slower than having it done in mpn_mul_1, so we need to consider how
   often a zero will be stripped and how much that's likely to save
   later.  */

void
mpf_mul_ui (mpf_ptr r, mpf_srcptr u, unsigned long int v)
{
  mp_srcptr up;
  mp_size_t usize;
  mp_size_t size;
  mp_size_t prec, excess;
  mp_limb_t cy_limb, vl, cbit, cin;
  mp_ptr rp;

  usize = u->_mp_size;
  if (UNLIKELY (v == 0) || UNLIKELY (usize == 0))
    {
      r->_mp_size = 0;
      r->_mp_exp = 0;
      return;
    }

#if BITS_PER_ULONG > GMP_NUMB_BITS  /* avoid warnings about shift amount */
  if (v > GMP_NUMB_MAX)
    {
      mpf_t     vf;
      mp_limb_t vp[2];
      vp[0] = v & GMP_NUMB_MASK;
      vp[1] = v >> GMP_NUMB_BITS;
      PTR(vf) = vp;
      SIZ(vf) = 2;
      ASSERT_CODE (PREC(vf) = 2);
      EXP(vf) = 2;
      mpf_mul (r, u, vf);
      return;
    }
#endif

  size = ABS (usize);
  prec = r->_mp_prec;
  up = u->_mp_d;
  vl = v;
  excess = size - prec;
  cin = 0;

  if (excess > 0)
    {
      /* up is bigger than desired rp, shorten it to prec limbs and
         determine a carry-in */

      mp_limb_t  vl_shifted = vl << GMP_NAIL_BITS;
      mp_limb_t  hi, lo, next_lo, sum;
      mp_size_t  i;

      /* high limb of top product */
      i = excess - 1;
      umul_ppmm (cin, lo, up[i], vl_shifted);

      /* and carry bit out of products below that, if any */
      for (;;)
        {
          i--;
          if (i < 0)
            break;

          umul_ppmm (hi, next_lo, up[i], vl_shifted);
          lo >>= GMP_NAIL_BITS;
          ADDC_LIMB (cbit, sum, hi, lo);
          cin += cbit;
          lo = next_lo;

          /* Continue only if the sum is GMP_NUMB_MAX.  GMP_NUMB_MAX is the
             only value a carry from below can propagate across.  If we've
             just seen the carry out (ie. cbit!=0) then sum!=GMP_NUMB_MAX,
             so this test stops us for that case too.  */
          if (LIKELY (sum != GMP_NUMB_MAX))
            break;
        }

      up += excess;
      size = prec;
    }

  rp = r->_mp_d;
#if HAVE_NATIVE_mpn_mul_1c
  cy_limb = mpn_mul_1c (rp, up, size, vl, cin);
#else
  cy_limb = mpn_mul_1 (rp, up, size, vl);
  __GMPN_ADD_1 (cbit, rp, rp, size, cin);
  cy_limb += cbit;
#endif
  rp[size] = cy_limb;
  cy_limb = cy_limb != 0;
  r->_mp_exp = u->_mp_exp + cy_limb;
  size += cy_limb;
  r->_mp_size = usize >= 0 ? size : -size;
}