src/gmp-6.1.0/mpn/generic/get_d.c

/* mpn_get_d -- limbs to double conversion.

   THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
   CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
   FUTURE GNU MP RELEASES.

Copyright 2003, 2004, 2007, 2009, 2010, 2012 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.h"
#include "gmp-impl.h"
#include "longlong.h"

#ifndef _GMP_IEEE_FLOATS
#define _GMP_IEEE_FLOATS 0
#endif

/* To force use of the generic C code for testing, put
   "#define _GMP_IEEE_FLOATS 0" at this point.  */


/* In alpha gcc prior to 3.4, signed DI comparisons involving constants are
   rearranged from "x < n" to "x+(-n) < 0", which is of course hopelessly
   wrong if that addition overflows.

   The workaround here avoids this bug by ensuring n is not a literal constant.
   Note that this is alpha specific.  The offending transformation is/was in
   alpha.c alpha_emit_conditional_branch() under "We want to use cmpcc/bcc".

   Bizarrely, this happens also with Cray cc on alphaev5-cray-unicosmk2.0.6.X,
   and has the same solution.  Don't know why or how.  */

#if HAVE_HOST_CPU_FAMILY_alpha				\
  && ((defined (__GNUC__) && ! __GMP_GNUC_PREREQ(3,4))	\
      || defined (_CRAY))
static volatile const long CONST_1024 = 1024;
static volatile const long CONST_NEG_1023 = -1023;
static volatile const long CONST_NEG_1022_SUB_53 = -1022 - 53;
#else
#define CONST_1024	      (1024)
#define CONST_NEG_1023	      (-1023)
#define CONST_NEG_1022_SUB_53 (-1022 - 53)
#endif


/* Return the value {ptr,size}*2^exp, and negative if sign<0.  Must have
   size>=1, and a non-zero high limb ptr[size-1].

   When we know the fp format, the result is truncated towards zero.  This is
   consistent with other gmp conversions, like mpz_set_f or mpz_set_q, and is
   easy to implement and test.

   When we do not know the format, such truncation seems much harder.  One
   would need to defeat any rounding mode, including round-up.

   It's felt that GMP is not primarily concerned with hardware floats, and
   really isn't enhanced by getting involved with hardware rounding modes
   (which could even be some weird unknown style), so something unambiguous and
   straightforward is best.


   The IEEE code below is the usual case, it knows either a 32-bit or 64-bit
   limb and is done with shifts and masks.  The 64-bit case in particular
   should come out nice and compact.

   The generic code used to work one bit at a time, which was not only slow,
   but implicitly relied upon denorms for intermediates, since the lowest bits'
   weight of a perfectly valid fp number underflows in non-denorm.  Therefore,
   the generic code now works limb-per-limb, initially creating a number x such
   that 1 <= x <= BASE.  (BASE is reached only as result of rounding.)  Then
   x's exponent is scaled with explicit code (not ldexp to avoid libm
   dependency).  It is a tap-dance to avoid underflow or overflow, beware!


   Traps:

   Hardware traps for overflow to infinity, underflow to zero, or unsupported
   denorms may or may not be taken.  The IEEE code works bitwise and so
   probably won't trigger them, the generic code works by float operations and
   so probably will.  This difference might be thought less than ideal, but
   again its felt straightforward code is better than trying to get intimate
   with hardware exceptions (of perhaps unknown nature).


   Not done:

   mpz_get_d in the past handled size==1 with a cast limb->double.  This might
   still be worthwhile there (for up to the mantissa many bits), but for
   mpn_get_d here, the cost of applying "exp" to the resulting exponent would
   probably use up any benefit a cast may have over bit twiddling.  Also, if
   the exponent is pushed into denorm range then bit twiddling is the only
   option, to ensure the desired truncation is obtained.


   Other:

   For reference, note that HPPA 8000, 8200, 8500 and 8600 trap FCNV,UDW,DBL
   to the kernel for values >= 2^63.  This makes it slow, and worse the kernel
   Linux (what versions?) apparently uses untested code in its trap handling
   routines, and gets the sign wrong.  We don't use such a limb-to-double
   cast, neither in the IEEE or generic code.  */



#undef FORMAT_RECOGNIZED

double
mpn_get_d (mp_srcptr up, mp_size_t size, mp_size_t sign, long exp)
{
  int lshift, nbits;
  mp_limb_t x, mhi, mlo;

  ASSERT (size >= 0);
  ASSERT_MPN (up, size);
  ASSERT (size == 0 || up[size-1] != 0);

  if (size == 0)
    return 0.0;

  /* Adjust exp to a radix point just above {up,size}, guarding against
     overflow.  After this exp can of course be reduced to anywhere within
     the {up,size} region without underflow.  */
  if (UNLIKELY ((unsigned long) (GMP_NUMB_BITS * size)
		> ((unsigned long) LONG_MAX - exp)))
    {
#if _GMP_IEEE_FLOATS
      goto ieee_infinity;
#endif

      /* generic */
      exp = LONG_MAX;
    }
  else
    {
      exp += GMP_NUMB_BITS * size;
    }

#if _GMP_IEEE_FLOATS
    {
      union ieee_double_extract u;

      up += size;

#if GMP_LIMB_BITS == 64
      mlo = up[-1];
      count_leading_zeros (lshift, mlo);

      exp -= (lshift - GMP_NAIL_BITS) + 1;
      mlo <<= lshift;

      nbits = GMP_LIMB_BITS - lshift;

      if (nbits < 53 && size > 1)
	{
	  x = up[-2];
	  x <<= GMP_NAIL_BITS;
	  x >>= nbits;
	  mlo |= x;
	  nbits += GMP_NUMB_BITS;

	  if (LIMBS_PER_DOUBLE >= 3 && nbits < 53 && size > 2)
	    {
	      x = up[-3];
	      x <<= GMP_NAIL_BITS;
	      x >>= nbits;
	      mlo |= x;
	      nbits += GMP_NUMB_BITS;
	    }
	}
      mhi = mlo >> (32 + 11);
      mlo = mlo >> 11;		/* later implicitly truncated to 32 bits */
#endif
#if GMP_LIMB_BITS == 32
      x = *--up;
      count_leading_zeros (lshift, x);

      exp -= (lshift - GMP_NAIL_BITS) + 1;
      x <<= lshift;
      mhi = x >> 11;

      if (lshift < 11)		/* FIXME: never true if NUMB < 20 bits */
	{
	  /* All 20 bits in mhi */
	  mlo = x << 21;
	  /* >= 1 bit in mlo */
	  nbits = GMP_LIMB_BITS - lshift - 21;
	}
      else
	{
	  if (size > 1)
	    {
	      nbits = GMP_LIMB_BITS - lshift;

	      x = *--up, size--;
	      x <<= GMP_NAIL_BITS;
	      mhi |= x >> nbits >> 11;

	      mlo = x << GMP_LIMB_BITS - nbits - 11;
	      nbits = nbits + 11 - GMP_NAIL_BITS;
	    }
	  else
	    {
	      mlo = 0;
	      goto done;
	    }
	}

      /* Now all needed bits in mhi have been accumulated.  Add bits to mlo.  */

      if (LIMBS_PER_DOUBLE >= 2 && nbits < 32 && size > 1)
	{
	  x = up[-1];
	  x <<= GMP_NAIL_BITS;
	  x >>= nbits;
	  mlo |= x;
	  nbits += GMP_NUMB_BITS;

	  if (LIMBS_PER_DOUBLE >= 3 && nbits < 32 && size > 2)
	    {
	      x = up[-2];
	      x <<= GMP_NAIL_BITS;
	      x >>= nbits;
	      mlo |= x;
	      nbits += GMP_NUMB_BITS;

	      if (LIMBS_PER_DOUBLE >= 4 && nbits < 32 && size > 3)
		{
		  x = up[-3];
		  x <<= GMP_NAIL_BITS;
		  x >>= nbits;
		  mlo |= x;
		  nbits += GMP_NUMB_BITS;
		}
	    }
	}

    done:;

#endif
      if (UNLIKELY (exp >= CONST_1024))
	{
	  /* overflow, return infinity */
	ieee_infinity:
	  mhi = 0;
	  mlo = 0;
	  exp = 1024;
	}
      else if (UNLIKELY (exp <= CONST_NEG_1023))
	{
	  int rshift;

	  if (LIKELY (exp <= CONST_NEG_1022_SUB_53))
	    return 0.0;	 /* denorm underflows to zero */

	  rshift = -1022 - exp;
	  ASSERT (rshift > 0 && rshift < 53);
#if GMP_LIMB_BITS > 53
	  mlo >>= rshift;
	  mhi = mlo >> 32;
#else
	  if (rshift >= 32)
	    {
	      mlo = mhi;
	      mhi = 0;
	      rshift -= 32;
	    }
	  lshift = GMP_LIMB_BITS - rshift;
	  mlo = (mlo >> rshift) | (rshift == 0 ? 0 : mhi << lshift);
	  mhi >>= rshift;
#endif
	  exp = -1023;
	}
      u.s.manh = mhi;
      u.s.manl = mlo;
      u.s.exp = exp + 1023;
      u.s.sig = (sign < 0);
      return u.d;
    }
#define FORMAT_RECOGNIZED 1
#endif

#if HAVE_DOUBLE_VAX_D
    {
      union double_extract u;

      up += size;

      mhi = up[-1];

      count_leading_zeros (lshift, mhi);
      exp -= lshift;
      mhi <<= lshift;

      mlo = 0;
      if (size > 1)
	{
	  mlo = up[-2];
	  if (lshift != 0)
	    mhi += mlo >> (GMP_LIMB_BITS - lshift);
	  mlo <<= lshift;

	  if (size > 2 && lshift > 8)
	    {
	      x = up[-3];
	      mlo += x >> (GMP_LIMB_BITS - lshift);
	    }
	}

      if (UNLIKELY (exp >= 128))
	{
	  /* overflow, return maximum number */
	  mhi = 0xffffffff;
	  mlo = 0xffffffff;
	  exp = 127;
	}
      else if (UNLIKELY (exp < -128))
	{
	  return 0.0;	 /* underflows to zero */
	}

      u.s.man3 = mhi >> 24;	/* drop msb, since implicit */
      u.s.man2 = mhi >> 8;
      u.s.man1 = (mhi << 8) + (mlo >> 24);
      u.s.man0 = mlo >> 8;
      u.s.exp = exp + 128;
      u.s.sig = sign < 0;
      return u.d;
    }
#define FORMAT_RECOGNIZED 1
#endif

#if ! FORMAT_RECOGNIZED
    {      /* Non-IEEE or strange limb size, do something generic. */
      mp_size_t i;
      double d, weight;
      unsigned long uexp;

      /* First generate an fp number disregarding exp, instead keeping things
	 within the numb base factor from 1, which should prevent overflow and
	 underflow even for the most exponent limited fp formats.  The
	 termination criteria should be refined, since we now include too many
	 limbs.  */
      weight = 1/MP_BASE_AS_DOUBLE;
      d = up[size - 1];
      for (i = size - 2; i >= 0; i--)
	{
	  d += up[i] * weight;
	  weight /= MP_BASE_AS_DOUBLE;
	  if (weight == 0)
	    break;
	}

      /* Now apply exp.  */
      exp -= GMP_NUMB_BITS;
      if (exp > 0)
	{
	  weight = 2.0;
	  uexp = exp;
	}
      else
	{
	  weight = 0.5;
	  uexp = 1 - (unsigned long) (exp + 1);
	}
#if 1
      /* Square-and-multiply exponentiation.  */
      if (uexp & 1)
	d *= weight;
      while (uexp >>= 1)
	{
	  weight *= weight;
	  if (uexp & 1)
	    d *= weight;
	}
#else
      /* Plain exponentiation.  */
      while (uexp > 0)
	{
	  d *= weight;
	  uexp--;
	}
#endif

      return sign >= 0 ? d : -d;
    }
#endif
}