path: root/mul.c

/* mpfr_mul -- multiply two floating-point numbers

Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005
  Free Software Foundation, Inc.

This file is part of the MPFR Library.

The MPFR Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The MPFR 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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the MPFR Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
MA 02111-1307, USA. */

#include <stdio.h>
#define MPFR_NEED_LONGLONG_H
#include "mpfr-impl.h"


/********* BEGINNING CHECK *************/

/* Check if we have to check the result of mpfr_mul.
   TODO: Find a better (and faster?) check than using old implementation */
#ifdef WANT_ASSERT
# if WANT_ASSERT >= 2

int mpfr_mul2 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode);
static int
mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode) 
{
  /* Old implementation */
  int sign_product, cc, inexact;
  mp_exp_t  ax;
  mp_limb_t *tmp;
  mp_limb_t b1;
  mp_prec_t bq, cq;
  mp_size_t bn, cn, tn, k;
  TMP_DECL(marker);

  /* deal with special cases */
  if (MPFR_ARE_SINGULAR(b,c))
    {
      if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
	{
	  MPFR_SET_NAN(a);
	  MPFR_RET_NAN;
	}
      sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
      if (MPFR_IS_INF(b))
	{
	  if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
	    {
	      MPFR_SET_SIGN(a,sign_product);
	      MPFR_SET_INF(a);
	      MPFR_RET(0); /* exact */
	    }
	  else
	    {
	      MPFR_SET_NAN(a);
	      MPFR_RET_NAN;
	    }
	}
      else if (MPFR_IS_INF(c))
	{
	  if (MPFR_NOTZERO(b))
	    {
	      MPFR_SET_SIGN(a, sign_product);
	      MPFR_SET_INF(a);
	      MPFR_RET(0); /* exact */
	    }
	  else
	    {
	      MPFR_SET_NAN(a);
	      MPFR_RET_NAN;
	    }
	}
      else
	{
	  MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
	  MPFR_SET_SIGN(a, sign_product);
	  MPFR_SET_ZERO(a);
	  MPFR_RET(0); /* 0 * 0 is exact */
	}
    }
  MPFR_CLEAR_FLAGS(a);
  sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
 
  ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);

  bq = MPFR_PREC(b);
  cq = MPFR_PREC(c);
  
  MPFR_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
 
  bn = (bq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of b */
  cn = (cq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of c */
  k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
  tn = (bq + cq + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB; 
  /* <= k, thus no int overflow */
  MPFR_ASSERTD(tn <= k);

  /* Check for no size_t overflow*/
  MPFR_ASSERTD((size_t) k <= ((size_t) ~0) / BYTES_PER_MP_LIMB);
  TMP_MARK(marker); 
  tmp = (mp_limb_t *) TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);

  /* multiplies two mantissa in temporary allocated space */
  b1 = (MPFR_LIKELY(bn >= cn)) ? 
    mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn)
    : mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn);

  /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
     with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
  b1 >>= BITS_PER_MP_LIMB - 1; /* msb from the product */

  /* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
     then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
     and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
  tmp += k - tn;
  if (MPFR_UNLIKELY(b1 == 0))
    mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
  cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq, 
		       MPFR_IS_NEG_SIGN(sign_product), 
		       MPFR_PREC (a), rnd_mode, &inexact);

  /* cc = 1 ==> result is a power of two */
  if (MPFR_UNLIKELY(cc))
    MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;

  TMP_FREE(marker);

  {
    mp_exp_t ax2 = ax + (mp_exp_t) (b1 - 1 + cc);
    if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
      return mpfr_overflow (a, rnd_mode, sign_product);
    if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
      {
	/* In the rounding to the nearest mode, if the exponent of the exact
	   result (i.e. before rounding, i.e. without taking cc into account)
	   is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
	   both arguments are powers of 2), then round to zero. */
	if (rnd_mode == GMP_RNDN &&
	    (ax + (mp_exp_t) b1 < __gmpfr_emin ||
	     (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
	  rnd_mode = GMP_RNDZ;
	return mpfr_underflow (a, rnd_mode, sign_product);
      }
    MPFR_SET_EXP (a, ax2);
    MPFR_SET_SIGN(a, sign_product);
  }
  return inexact;
}

int
mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
{
  mpfr_t ta, tb, tc;
  int inexact1, inexact2;

  mpfr_init2 (ta, MPFR_PREC (a));
  mpfr_init2 (tb, MPFR_PREC (b));
  mpfr_init2 (tc, MPFR_PREC (c));
  MPFR_ASSERTN (mpfr_set (tb, b, GMP_RNDN) == 0);
  MPFR_ASSERTN (mpfr_set (tc, c, GMP_RNDN) == 0);

  inexact2 = mpfr_mul3 (ta, tb, tc, rnd_mode);
  inexact1  = mpfr_mul2 (a, b, c, rnd_mode);
  if (mpfr_cmp (ta, a) || inexact1*inexact2 < 0 
      || (inexact1*inexact2 == 0 && (inexact1|inexact2) != 0))
    {
      printf("mpfr_mul return different values for %s\n"
             "Prec_a= %lu Prec_b= %lu Prec_c= %lu\nB=",
             mpfr_print_rnd_mode (rnd_mode),
             MPFR_PREC (a), MPFR_PREC (b), MPFR_PREC (c));
      mpfr_out_str (stdout, 16, 0, tb, GMP_RNDN);
      printf("\nC="); mpfr_out_str (stdout, 16, 0, tc, GMP_RNDN);
      printf("\nOldMul: "); mpfr_out_str (stdout, 16, 0, ta, GMP_RNDN);
      printf("\nNewMul: "); mpfr_out_str (stdout, 16, 0, a, GMP_RNDN);
      printf("\nNewInexact = %d | OldInexact = %d\n", inexact1, inexact2);
      MPFR_ASSERTN(0);
    }

  mpfr_clears (ta, tb, tc, NULL);
  return inexact1;
}

# define mpfr_mul mpfr_mul2
# endif
#endif

/****** END OF CHECK *******/

/* Multiply 2 mpfr_t */

int
mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
{
  int sign, inexact;
  mp_exp_t  ax, ax2;
  mp_limb_t *tmp;
  mp_limb_t b1;
  mp_prec_t bq, cq;
  mp_size_t bn, cn, tn, k;
  TMP_DECL (marker);

  MPFR_LOG_FUNC (("b[%#R]=%R c[%#R]=%R rnd=%d", b, b, c, c, rnd_mode),
		 ("a[%#R]=%R inexact=%d", a, a, inexact));

  /* deal with special cases */
  if (MPFR_ARE_SINGULAR (b, c))
    {
      if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
	{
	  MPFR_SET_NAN (a);
	  MPFR_RET_NAN;
	}
      sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
      if (MPFR_IS_INF (b))
	{
	  if (!MPFR_IS_ZERO (c))
	    {
	      MPFR_SET_SIGN (a, sign);
	      MPFR_SET_INF (a);
	      MPFR_RET (0);
	    }
	  else
	    {
	      MPFR_SET_NAN (a);
	      MPFR_RET_NAN;
	    }
	}
      else if (MPFR_IS_INF (c))
	{
	  if (!MPFR_IS_ZERO (b))
	    {
	      MPFR_SET_SIGN (a, sign);
	      MPFR_SET_INF (a);
	      MPFR_RET(0);
	    }
	  else
	    {
	      MPFR_SET_NAN (a);
	      MPFR_RET_NAN;
	    }
	}
      else
	{
	  MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
	  MPFR_SET_SIGN (a, sign);
	  MPFR_SET_ZERO (a);
	  MPFR_RET (0);
	}
    }
  MPFR_CLEAR_FLAGS (a);
  sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));

  ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
  /* Note: the exponent of the exact result will be e = bx + cx + ec with
     ec in {-1,0,1} and the following assumes that e is representable. */

  /* FIXME: Useful since we do an exponent check after ?
   * It is useful iff the precision is big, there is an overflow
   * and we are doing further mults...*/
#ifdef HUGE
  if (MPFR_UNLIKELY (ax > __gmpfr_emax + 1))
    return mpfr_overflow (a, rnd_mode, sign);
  if (MPFR_UNLIKELY (ax < __gmpfr_emin - 2))
  return mpfr_underflow (a, rnd_mode == GMP_RNDN ? GMP_RNDZ : rnd_mode,
			     sign);
#endif

  bq = MPFR_PREC (b);
  cq = MPFR_PREC (c);

  MPFR_ASSERTD (bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */

  bn = (bq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of b */
  cn = (cq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of c */
  k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
  tn = (bq + cq + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
  MPFR_ASSERTD (tn <= k); /* tn <= k, thus no int overflow */

  /* Check for no size_t overflow*/
  MPFR_ASSERTD ((size_t) k <= ((size_t) ~0) / BYTES_PER_MP_LIMB);
  TMP_MARK (marker);
  tmp = (mp_limb_t *) TMP_ALLOC ((size_t) k * BYTES_PER_MP_LIMB);

  /* multiplies two mantissa in temporary allocated space */
#if 0
  b1 = MPFR_LIKELY (bn >= cn)
    ? mpn_mul (tmp, MPFR_MANT (b), bn, MPFR_MANT (c), cn)
    : mpn_mul (tmp, MPFR_MANT (c), cn, MPFR_MANT (b), bn);

  /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
     with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
  b1 >>= BITS_PER_MP_LIMB - 1; /* msb from the product */

  /* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
     then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
     and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
  tmp += k - tn;
  if (MPFR_UNLIKELY (b1 == 0))
    mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */

#else

  if (MPFR_UNLIKELY (bn < cn)) 
    {
      mpfr_srcptr tmp = b;
      mp_size_t tn  = bn;
      b = c;
      bn = cn;
      c = tmp;
      cn = tn;
    }
  MPFR_ASSERTD (bn >= cn);
  if (MPFR_UNLIKELY (bn > MPFR_MUL_THRESHOLD))
    {
      mp_limb_t *bp, *cp;
      mp_size_t n;
      mp_prec_t p;

      /* Compute estimated precision of mulhigh.
	 We could use `+ (n < cn) + (n < bn)' instead of `+ 2',
	 but does it worth it? */
      n = MPFR_LIMB_SIZE (a) + 1;
      n = MIN (n, cn);
      MPFR_ASSERTD (n >= 1 && 2*n <= k && n <= cn && n <= bn);
      p = n*BITS_PER_MP_LIMB - MPFR_INT_CEIL_LOG2 (n + 2);
      bp = MPFR_MANT (b) + bn - n;
      cp = MPFR_MANT (c) + cn - n;
      /* Check if MulHigh can produce a roundable result.
	 We may lost 1 bit due to RNDN, 1 due to final shift. */
      if (MPFR_UNLIKELY (MPFR_PREC (a) > p - 5))
	{
	  if (MPFR_UNLIKELY (MPFR_PREC (a) > p - 5 + BITS_PER_MP_LIMB))
	    {
	      /* MulHigh can't produce a roundable result. */
	      MPFR_LOG_MSG (("mpfr_mulhigh can't be used (%lu VS %lu)\n",
			     MPFR_PREC (a), p));
	      goto full_multiply;
	    }
	  /* Add one extra limb to mantissa of b and c. */
	  if (bn > n)
	    bp --;
	  else
	    {
	      bp = TMP_ALLOC ((n+1)*sizeof (mp_limb_t));
	      bp[0] = 0;
	      MPN_COPY (bp+1, MPFR_MANT (b)+bn-n, n);	
	    }
	  if (cn > n)
	    cp --; /* FIXME: Could this happen? */
	  else
	    {
	      cp = TMP_ALLOC ((n+1)*sizeof (mp_limb_t));	      
	      cp[0] = 0;
	      MPN_COPY (cp+1, MPFR_MANT (c)+cn-n, n);
	    }
	  /* We will compute with one extra limb */
	  n++;
	  p = n*BITS_PER_MP_LIMB - MPFR_INT_CEIL_LOG2 (n + 2);
	  p += BITS_PER_MP_LIMB;
	  MPFR_ASSERTD (MPFR_PREC (a) <= p - 5);
	  if (MPFR_LIKELY (k < 2*n))
	    {
	      tmp = TMP_ALLOC (2*n*sizeof (mp_limb_t));
	      tmp += 2*n-k; /* `tmp' still points to an area of `k' limbs */
	    }
	}
      MPFR_LOG_MSG (("Use mpfr_mulhigh (%lu VS %lu)\n", MPFR_PREC (a), p));
      /* Compute an approximation of the product of b and c */
      mpfr_mulhigh_n (tmp+k-2*n, bp, cp, n);

      /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
	 with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
      b1 = tmp[k-1] >> (BITS_PER_MP_LIMB - 1); /* msb from the product */
      
      /* If the mantissas of b and c are uniformly distributed in ]1/2, 1],
	 then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
	 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
      tmp += k - tn;
      if (MPFR_UNLIKELY (b1 == 0))
	mpn_lshift (tmp, tmp, tn, 1);
      MPFR_ASSERTD (MPFR_LIMB_MSB (tmp[tn-1]) != 0);

      if (MPFR_UNLIKELY (!mpfr_round_p (tmp, tn, p+b1-1,
					MPFR_PREC(a)+(rnd_mode==GMP_RNDN))))
	{
	  tmp -= k-tn; /* tmp may have changed, FIX IT!!!!! */
	  goto full_multiply; 
	}
      }
  else
    {
    full_multiply:
      MPFR_LOG_MSG (("Use mpn_mul\n", 0));
      b1 = mpn_mul (tmp, MPFR_MANT (b), bn, MPFR_MANT (c), cn);      

      /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
	 with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
      b1 >>= BITS_PER_MP_LIMB - 1; /* msb from the product */
      
      /* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
	 then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
	 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
      tmp += k - tn;
      if (MPFR_UNLIKELY (b1 == 0))
	mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
    }
#endif

  ax2 = ax + (mp_exp_t) (b1 - 1);
  MPFR_RNDRAW (inexact, a, tmp, bq+cq, rnd_mode, sign, ax2++);
  TMP_FREE (marker);
  MPFR_EXP  (a) = ax2; /* Can't use MPFR_SET_EXP: Expo may be out of range */
  MPFR_SET_SIGN (a, sign);
  if (MPFR_UNLIKELY (ax2 > __gmpfr_emax))
    return mpfr_overflow (a, rnd_mode, sign);
  if (MPFR_UNLIKELY (ax2 < __gmpfr_emin))
    {
      /* In the rounding to the nearest mode, if the exponent of the exact
	 result (i.e. before rounding, i.e. without taking cc into account)
	 is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
	 both arguments are powers of 2), then round to zero. */
      if (rnd_mode == GMP_RNDN
	  && (ax + (mp_exp_t) b1 < __gmpfr_emin
	      || (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
	rnd_mode = GMP_RNDZ;
      return mpfr_underflow (a, rnd_mode, sign);
    }
  return inexact;
}