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poly_2xm1.c

/*---------------------------------------------------------------------------+
 |  poly_2xm1.c                                                              |
 |                                                                           |
 | Function to compute 2^x-1 by a polynomial approximation.                  |
 |                                                                           |
 | Copyright (C) 1992,1993,1994,1997                                         |
 |                  W. Metzenthen, 22 Parker St, Ormond, Vic 3163, Australia |
 |                  E-mail   billm@suburbia.net                              |
 |                                                                           |
 |                                                                           |
 +---------------------------------------------------------------------------*/

#include "exception.h"
#include "reg_constant.h"
#include "fpu_emu.h"
#include "fpu_system.h"
#include "control_w.h"
#include "poly.h"


#define     HIPOWER     11
static const unsigned long long lterms[HIPOWER] =
{
  0x0000000000000000LL,  /* This term done separately as 12 bytes */
  0xf5fdeffc162c7543LL,
  0x1c6b08d704a0bfa6LL,
  0x0276556df749cc21LL,
  0x002bb0ffcf14f6b8LL,
  0x0002861225ef751cLL,
  0x00001ffcbfcd5422LL,
  0x00000162c005d5f1LL,
  0x0000000da96ccb1bLL,
  0x0000000078d1b897LL,
  0x000000000422b029LL
};

static const Xsig hiterm = MK_XSIG(0xb17217f7, 0xd1cf79ab, 0xc8a39194);

/* Four slices: 0.0 : 0.25 : 0.50 : 0.75 : 1.0,
   These numbers are 2^(1/4), 2^(1/2), and 2^(3/4)
 */
static const Xsig shiftterm0 = MK_XSIG(0, 0, 0);
static const Xsig shiftterm1 = MK_XSIG(0x9837f051, 0x8db8a96f, 0x46ad2318);
static const Xsig shiftterm2 = MK_XSIG(0xb504f333, 0xf9de6484, 0x597d89b3);
static const Xsig shiftterm3 = MK_XSIG(0xd744fcca, 0xd69d6af4, 0x39a68bb9);

static const Xsig *shiftterm[] = { &shiftterm0, &shiftterm1,
                             &shiftterm2, &shiftterm3 };


/*--- poly_2xm1() -----------------------------------------------------------+
 | Requires st(0) which is TAG_Valid and < 1.                                |
 +---------------------------------------------------------------------------*/
int   poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
{
  long int              exponent, shift;
  unsigned long long    Xll;
  Xsig                  accumulator, Denom, argSignif;
  u_char                tag;

  exponent = exponent16(arg);

#ifdef PARANOID
  if ( exponent >= 0 )        /* Don't want a |number| >= 1.0 */
    {
      /* Number negative, too large, or not Valid. */
      EXCEPTION(EX_INTERNAL|0x127);
      return 1;
    }
#endif /* PARANOID */

  argSignif.lsw = 0;
  XSIG_LL(argSignif) = Xll = significand(arg);

  if ( exponent == -1 )
    {
      shift = (argSignif.msw & 0x40000000) ? 3 : 2;
      /* subtract 0.5 or 0.75 */
      exponent -= 2;
      XSIG_LL(argSignif) <<= 2;
      Xll <<= 2;
    }
  else if ( exponent == -2 )
    {
      shift = 1;
      /* subtract 0.25 */
      exponent--;
      XSIG_LL(argSignif) <<= 1;
      Xll <<= 1;
    }
  else
    shift = 0;

  if ( exponent < -2 )
    {
      /* Shift the argument right by the required places. */
      if ( FPU_shrx(&Xll, -2-exponent) >= 0x80000000U )
      Xll++;      /* round up */
    }

  accumulator.lsw = accumulator.midw = accumulator.msw = 0;
  polynomial_Xsig(&accumulator, &Xll, lterms, HIPOWER-1);
  mul_Xsig_Xsig(&accumulator, &argSignif);
  shr_Xsig(&accumulator, 3);

  mul_Xsig_Xsig(&argSignif, &hiterm);   /* The leading term */
  add_two_Xsig(&accumulator, &argSignif, &exponent);

  if ( shift )
    {
      /* The argument is large, use the identity:
       f(x+a) = f(a) * (f(x) + 1) - 1;
       */
      shr_Xsig(&accumulator, - exponent);
      accumulator.msw |= 0x80000000;      /* add 1.0 */
      mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
      accumulator.msw &= 0x3fffffff;      /* subtract 1.0 */
      exponent = 1;
    }

  if ( sign != SIGN_POS )
    {
      /* The argument is negative, use the identity:
           f(-x) = -f(x) / (1 + f(x))
       */
      Denom.lsw = accumulator.lsw;
      XSIG_LL(Denom) = XSIG_LL(accumulator);
      if ( exponent < 0 )
      shr_Xsig(&Denom, - exponent);
      else if ( exponent > 0 )
      {
        /* exponent must be 1 here */
        XSIG_LL(Denom) <<= 1;
        if ( Denom.lsw & 0x80000000 )
          XSIG_LL(Denom) |= 1;
        (Denom.lsw) <<= 1;
      }
      Denom.msw |= 0x80000000;      /* add 1.0 */
      div_Xsig(&accumulator, &Denom, &accumulator);
    }

  /* Convert to 64 bit signed-compatible */
  exponent += round_Xsig(&accumulator);

  result = &st(0);
  significand(result) = XSIG_LL(accumulator);
  setexponent16(result, exponent);

  tag = FPU_round(result, 1, 0, FULL_PRECISION, sign);

  setsign(result, sign);
  FPU_settag0(tag);

  return 0;

}

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