Esempio n. 1
0
/*--- poly_l2p1() -----------------------------------------------------------+
 |   Base 2 logarithm by a polynomial approximation.                         |
 |   log2(x+1)                                                               |
 +---------------------------------------------------------------------------*/
int	poly_l2p1(u_char sign0, u_char sign1,
		  FPU_REG *st0_ptr, FPU_REG *st1_ptr, FPU_REG *dest)
{
  u_char       	tag;
  s32        	exponent;
  Xsig         	accumulator, yaccum;

  if ( exponent16(st0_ptr) < 0 )
    {
      log2_kernel(st0_ptr, sign0, &accumulator, &exponent);

      yaccum.lsw = 0;
      XSIG_LL(yaccum) = significand(st1_ptr);
      mul_Xsig_Xsig(&accumulator, &yaccum);

      exponent += round_Xsig(&accumulator);

      exponent += exponent16(st1_ptr) + 1;
      if ( exponent < EXP_WAY_UNDER ) exponent = EXP_WAY_UNDER;

      significand(dest) = XSIG_LL(accumulator);
      setexponent16(dest, exponent);

      tag = FPU_round(dest, 1, 0, FULL_PRECISION, sign0 ^ sign1);
      FPU_settagi(1, tag);

      if ( tag == TAG_Valid )
	set_precision_flag_up();   /* 80486 appears to always do this */
    }
  else
    {
      /* The magnitude of st0_ptr is far too large. */

      if ( sign0 != SIGN_POS )
	{
	  /* Trying to get the log of a negative number. */
#ifdef PECULIAR_486   /* Stupid 80486 doesn't worry about log(negative). */
	  changesign(st1_ptr);
#else
	  if ( arith_invalid(1) < 0 )
	    return 1;
#endif /* PECULIAR_486 */
	}

      /* 80486 appears to do this */
      if ( sign0 == SIGN_NEG )
	set_precision_flag_down();
      else
	set_precision_flag_up();
    }

  if ( exponent(dest) <= EXP_UNDER )
    EXCEPTION(EX_Underflow);

  return 0;

}
Esempio n. 2
0
/*--- poly_tan() ------------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void	poly_tan(FPU_REG *st0_ptr)
{
  long int    		exponent;
  int                   invert;
  Xsig                  argSq, argSqSq, accumulatoro, accumulatore, accum,
                        argSignif, fix_up;
  unsigned long         adj;

  exponent = exponent(st0_ptr);

#ifdef PARANOID
  if ( signnegative(st0_ptr) )	/* Can't hack a number < 0.0 */
    { arith_invalid(0); return; }  /* Need a positive number */
#endif PARANOID

  /* Split the problem into two domains, smaller and larger than pi/4 */
  if ( (exponent == 0) || ((exponent == -1) && (st0_ptr->sigh > 0xc90fdaa2)) )
    {
      /* The argument is greater than (approx) pi/4 */
      invert = 1;
      accum.lsw = 0;
      XSIG_LL(accum) = significand(st0_ptr);
 
      if ( exponent == 0 )
	{
	  /* The argument is >= 1.0 */
	  /* Put the binary point at the left. */
	  XSIG_LL(accum) <<= 1;
	}
      /* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
      XSIG_LL(accum) = 0x921fb54442d18469LL - XSIG_LL(accum);
      /* This is a special case which arises due to rounding. */
      if ( XSIG_LL(accum) == 0xffffffffffffffffLL )
	{
	  FPU_settag0(TAG_Valid);
	  significand(st0_ptr) = 0x8a51e04daabda360LL;
	  setexponent16(st0_ptr, (0x41 + EXTENDED_Ebias) | SIGN_Negative);
	  return;
	}

      argSignif.lsw = accum.lsw;
      XSIG_LL(argSignif) = XSIG_LL(accum);
      exponent = -1 + norm_Xsig(&argSignif);
    }
  else
    {
      invert = 0;
      argSignif.lsw = 0;
      XSIG_LL(accum) = XSIG_LL(argSignif) = significand(st0_ptr);
 
      if ( exponent < -1 )
	{
	  /* shift the argument right by the required places */
	  if ( FPU_shrx(&XSIG_LL(accum), -1-exponent) >= 0x80000000U )
	    XSIG_LL(accum) ++;	/* round up */
	}
    }

  XSIG_LL(argSq) = XSIG_LL(accum); argSq.lsw = accum.lsw;
  mul_Xsig_Xsig(&argSq, &argSq);
  XSIG_LL(argSqSq) = XSIG_LL(argSq); argSqSq.lsw = argSq.lsw;
  mul_Xsig_Xsig(&argSqSq, &argSqSq);

  /* Compute the negative terms for the numerator polynomial */
  accumulatoro.msw = accumulatoro.midw = accumulatoro.lsw = 0;
  polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddnegterm, HiPOWERon-1);
  mul_Xsig_Xsig(&accumulatoro, &argSq);
  negate_Xsig(&accumulatoro);
  /* Add the positive terms */
  polynomial_Xsig(&accumulatoro, &XSIG_LL(argSqSq), oddplterm, HiPOWERop-1);

  
  /* Compute the positive terms for the denominator polynomial */
  accumulatore.msw = accumulatore.midw = accumulatore.lsw = 0;
  polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evenplterm, HiPOWERep-1);
  mul_Xsig_Xsig(&accumulatore, &argSq);
  negate_Xsig(&accumulatore);
  /* Add the negative terms */
  polynomial_Xsig(&accumulatore, &XSIG_LL(argSqSq), evennegterm, HiPOWERen-1);
  /* Multiply by arg^2 */
  mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
  mul64_Xsig(&accumulatore, &XSIG_LL(argSignif));
  /* de-normalize and divide by 2 */
  shr_Xsig(&accumulatore, -2*(1+exponent) + 1);
  negate_Xsig(&accumulatore);      /* This does 1 - accumulator */

  /* Now find the ratio. */
  if ( accumulatore.msw == 0 )
    {
      /* accumulatoro must contain 1.0 here, (actually, 0) but it
	 really doesn't matter what value we use because it will
	 have negligible effect in later calculations
	 */
      XSIG_LL(accum) = 0x8000000000000000LL;
      accum.lsw = 0;
    }
  else
    {
      div_Xsig(&accumulatoro, &accumulatore, &accum);
    }

  /* Multiply by 1/3 * arg^3 */
  mul64_Xsig(&accum, &XSIG_LL(argSignif));
  mul64_Xsig(&accum, &XSIG_LL(argSignif));
  mul64_Xsig(&accum, &XSIG_LL(argSignif));
  mul64_Xsig(&accum, &twothirds);
  shr_Xsig(&accum, -2*(exponent+1));

  /* tan(arg) = arg + accum */
  add_two_Xsig(&accum, &argSignif, &exponent);

  if ( invert )
    {
      /* We now have the value of tan(pi_2 - arg) where pi_2 is an
	 approximation for pi/2
	 */
      /* The next step is to fix the answer to compensate for the
	 error due to the approximation used for pi/2
	 */

      /* This is (approx) delta, the error in our approx for pi/2
	 (see above). It has an exponent of -65
	 */
      XSIG_LL(fix_up) = 0x898cc51701b839a2LL;
      fix_up.lsw = 0;

      if ( exponent == 0 )
	adj = 0xffffffff;   /* We want approx 1.0 here, but
			       this is close enough. */
      else if ( exponent > -30 )
	{
	  adj = accum.msw >> -(exponent+1);      /* tan */
	  adj = mul_32_32(adj, adj);             /* tan^2 */
	}
      else
Esempio n. 3
0
/*--- poly_atan() -----------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void	poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
		  FPU_REG *st1_ptr, u_char st1_tag)
{
  u_char	transformed, inverted,
                sign1, sign2;
  int           exponent;
  long int   	dummy_exp;
  Xsig          accumulator, Numer, Denom, accumulatore, argSignif,
                argSq, argSqSq;
  u_char        tag;
  
  sign1 = getsign(st0_ptr);
  sign2 = getsign(st1_ptr);
  if ( st0_tag == TAG_Valid )
    {
      exponent = exponent(st0_ptr);
    }
  else
    {
      /* This gives non-compatible stack contents... */
      FPU_to_exp16(st0_ptr, st0_ptr);
      exponent = exponent16(st0_ptr);
    }
  if ( st1_tag == TAG_Valid )
    {
      exponent -= exponent(st1_ptr);
    }
  else
    {
      /* This gives non-compatible stack contents... */
      FPU_to_exp16(st1_ptr, st1_ptr);
      exponent -= exponent16(st1_ptr);
    }

  if ( (exponent < 0) || ((exponent == 0) &&
			  ((st0_ptr->sigh < st1_ptr->sigh) ||
			   ((st0_ptr->sigh == st1_ptr->sigh) &&
			    (st0_ptr->sigl < st1_ptr->sigl))) ) )
    {
      inverted = 1;
      Numer.lsw = Denom.lsw = 0;
      XSIG_LL(Numer) = significand(st0_ptr);
      XSIG_LL(Denom) = significand(st1_ptr);
    }
  else
    {
      inverted = 0;
      exponent = -exponent;
      Numer.lsw = Denom.lsw = 0;
      XSIG_LL(Numer) = significand(st1_ptr);
      XSIG_LL(Denom) = significand(st0_ptr);
     }
  div_Xsig(&Numer, &Denom, &argSignif);
  exponent += norm_Xsig(&argSignif);

  if ( (exponent >= -1)
      || ((exponent == -2) && (argSignif.msw > 0xd413ccd0)) )
    {
      /* The argument is greater than sqrt(2)-1 (=0.414213562...) */
      /* Convert the argument by an identity for atan */
      transformed = 1;

      if ( exponent >= 0 )
	{
#ifdef PARANOID
	  if ( !( (exponent == 0) && 
		 (argSignif.lsw == 0) && (argSignif.midw == 0) &&
		 (argSignif.msw == 0x80000000) ) )
	    {
	      EXCEPTION(EX_INTERNAL|0x104);  /* There must be a logic error */
	      return;
	    }
#endif /* PARANOID */
	  argSignif.msw = 0;   /* Make the transformed arg -> 0.0 */
	}
      else
	{
	  Numer.lsw = Denom.lsw = argSignif.lsw;
	  XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);

	  if ( exponent < -1 )
	    shr_Xsig(&Numer, -1-exponent);
	  negate_Xsig(&Numer);
      
	  shr_Xsig(&Denom, -exponent);
	  Denom.msw |= 0x80000000;
      
	  div_Xsig(&Numer, &Denom, &argSignif);

	  exponent = -1 + norm_Xsig(&argSignif);
	}
    }
  else
    {
      transformed = 0;
    }

  argSq.lsw = argSignif.lsw; argSq.midw = argSignif.midw;
  argSq.msw = argSignif.msw;
  mul_Xsig_Xsig(&argSq, &argSq);
  
  argSqSq.lsw = argSq.lsw; argSqSq.midw = argSq.midw; argSqSq.msw = argSq.msw;
  mul_Xsig_Xsig(&argSqSq, &argSqSq);

  accumulatore.lsw = argSq.lsw;
  XSIG_LL(accumulatore) = XSIG_LL(argSq);

  shr_Xsig(&argSq, 2*(-1-exponent-1));
  shr_Xsig(&argSqSq, 4*(-1-exponent-1));

  /* Now have argSq etc with binary point at the left
     .1xxxxxxxx */

  /* Do the basic fixed point polynomial evaluation */
  accumulator.msw = accumulator.midw = accumulator.lsw = 0;
  polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
		   oddplterms, HIPOWERop-1);
  mul64_Xsig(&accumulator, &XSIG_LL(argSq));
  negate_Xsig(&accumulator);
  polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms, HIPOWERon-1);
  negate_Xsig(&accumulator);
  add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);

  mul64_Xsig(&accumulatore, &denomterm);
  shr_Xsig(&accumulatore, 1 + 2*(-1-exponent));
  accumulatore.msw |= 0x80000000;

  div_Xsig(&accumulator, &accumulatore, &accumulator);

  mul_Xsig_Xsig(&accumulator, &argSignif);
  mul_Xsig_Xsig(&accumulator, &argSq);

  shr_Xsig(&accumulator, 3);
  negate_Xsig(&accumulator);
  add_Xsig_Xsig(&accumulator, &argSignif);

  if ( transformed )
    {
      /* compute pi/4 - accumulator */
      shr_Xsig(&accumulator, -1-exponent);
      negate_Xsig(&accumulator);
      add_Xsig_Xsig(&accumulator, &pi_signif);
      exponent = -1;
    }

  if ( inverted )
    {
      /* compute pi/2 - accumulator */
      shr_Xsig(&accumulator, -exponent);
      negate_Xsig(&accumulator);
      add_Xsig_Xsig(&accumulator, &pi_signif);
      exponent = 0;
    }

  if ( sign1 )
    {
      /* compute pi - accumulator */
      shr_Xsig(&accumulator, 1 - exponent);
      negate_Xsig(&accumulator);
      add_Xsig_Xsig(&accumulator, &pi_signif);
      exponent = 1;
    }

  exponent += round_Xsig(&accumulator);

  significand(st1_ptr) = XSIG_LL(accumulator);
  setexponent16(st1_ptr, exponent);

  tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
  FPU_settagi(1, tag);

  set_precision_flag_up();  /* We do not really know if up or down,
			       use this as the default. */

}
Esempio n. 4
0
/*--- poly_2xm1() -----------------------------------------------------------+
 | Requires st(0) which is TAG_Valid and < 1.                                |
 +---------------------------------------------------------------------------*/
int	poly_2xm1(u_char sign, FPU_REG *arg, FPU_REG *result)
{
  s32       exponent, shift;
  u64       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;

}
void poly_atan(FPU_REG *st0_ptr, u_char st0_tag,
	       FPU_REG *st1_ptr, u_char st1_tag)
{
	u_char transformed, inverted, sign1, sign2;
	int exponent;
	long int dummy_exp;
	Xsig accumulator, Numer, Denom, accumulatore, argSignif, argSq, argSqSq;
	u_char tag;

	sign1 = getsign(st0_ptr);
	sign2 = getsign(st1_ptr);
	if (st0_tag == TAG_Valid) {
		exponent = exponent(st0_ptr);
	} else {
		
		FPU_to_exp16(st0_ptr, st0_ptr);
		exponent = exponent16(st0_ptr);
	}
	if (st1_tag == TAG_Valid) {
		exponent -= exponent(st1_ptr);
	} else {
		
		FPU_to_exp16(st1_ptr, st1_ptr);
		exponent -= exponent16(st1_ptr);
	}

	if ((exponent < 0) || ((exponent == 0) &&
			       ((st0_ptr->sigh < st1_ptr->sigh) ||
				((st0_ptr->sigh == st1_ptr->sigh) &&
				 (st0_ptr->sigl < st1_ptr->sigl))))) {
		inverted = 1;
		Numer.lsw = Denom.lsw = 0;
		XSIG_LL(Numer) = significand(st0_ptr);
		XSIG_LL(Denom) = significand(st1_ptr);
	} else {
		inverted = 0;
		exponent = -exponent;
		Numer.lsw = Denom.lsw = 0;
		XSIG_LL(Numer) = significand(st1_ptr);
		XSIG_LL(Denom) = significand(st0_ptr);
	}
	div_Xsig(&Numer, &Denom, &argSignif);
	exponent += norm_Xsig(&argSignif);

	if ((exponent >= -1)
	    || ((exponent == -2) && (argSignif.msw > 0xd413ccd0))) {
		
		
		transformed = 1;

		if (exponent >= 0) {
#ifdef PARANOID
			if (!((exponent == 0) &&
			      (argSignif.lsw == 0) && (argSignif.midw == 0) &&
			      (argSignif.msw == 0x80000000))) {
				EXCEPTION(EX_INTERNAL | 0x104);	
				return;
			}
#endif 
			argSignif.msw = 0;	
		} else {
			Numer.lsw = Denom.lsw = argSignif.lsw;
			XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);

			if (exponent < -1)
				shr_Xsig(&Numer, -1 - exponent);
			negate_Xsig(&Numer);

			shr_Xsig(&Denom, -exponent);
			Denom.msw |= 0x80000000;

			div_Xsig(&Numer, &Denom, &argSignif);

			exponent = -1 + norm_Xsig(&argSignif);
		}
	} else {
		transformed = 0;
	}

	argSq.lsw = argSignif.lsw;
	argSq.midw = argSignif.midw;
	argSq.msw = argSignif.msw;
	mul_Xsig_Xsig(&argSq, &argSq);

	argSqSq.lsw = argSq.lsw;
	argSqSq.midw = argSq.midw;
	argSqSq.msw = argSq.msw;
	mul_Xsig_Xsig(&argSqSq, &argSqSq);

	accumulatore.lsw = argSq.lsw;
	XSIG_LL(accumulatore) = XSIG_LL(argSq);

	shr_Xsig(&argSq, 2 * (-1 - exponent - 1));
	shr_Xsig(&argSqSq, 4 * (-1 - exponent - 1));


	
	accumulator.msw = accumulator.midw = accumulator.lsw = 0;
	polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
			oddplterms, HIPOWERop - 1);
	mul64_Xsig(&accumulator, &XSIG_LL(argSq));
	negate_Xsig(&accumulator);
	polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms,
			HIPOWERon - 1);
	negate_Xsig(&accumulator);
	add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);

	mul64_Xsig(&accumulatore, &denomterm);
	shr_Xsig(&accumulatore, 1 + 2 * (-1 - exponent));
	accumulatore.msw |= 0x80000000;

	div_Xsig(&accumulator, &accumulatore, &accumulator);

	mul_Xsig_Xsig(&accumulator, &argSignif);
	mul_Xsig_Xsig(&accumulator, &argSq);

	shr_Xsig(&accumulator, 3);
	negate_Xsig(&accumulator);
	add_Xsig_Xsig(&accumulator, &argSignif);

	if (transformed) {
		
		shr_Xsig(&accumulator, -1 - exponent);
		negate_Xsig(&accumulator);
		add_Xsig_Xsig(&accumulator, &pi_signif);
		exponent = -1;
	}

	if (inverted) {
		
		shr_Xsig(&accumulator, -exponent);
		negate_Xsig(&accumulator);
		add_Xsig_Xsig(&accumulator, &pi_signif);
		exponent = 0;
	}

	if (sign1) {
		
		shr_Xsig(&accumulator, 1 - exponent);
		negate_Xsig(&accumulator);
		add_Xsig_Xsig(&accumulator, &pi_signif);
		exponent = 1;
	}

	exponent += round_Xsig(&accumulator);

	significand(st1_ptr) = XSIG_LL(accumulator);
	setexponent16(st1_ptr, exponent);

	tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign2);
	FPU_settagi(1, tag);

	set_precision_flag_up();	

}
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) {	/*                              */
		/*                                           */
		EXCEPTION(EX_INTERNAL | 0x127);
		return 1;
	}
#endif /*          */

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

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

	if (exponent < -2) {
		/*                                                  */
		if (FPU_shrx(&Xll, -2 - exponent) >= 0x80000000U)
			Xll++;	/*          */
	}

	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);	/*                  */
	add_two_Xsig(&accumulator, &argSignif, &exponent);

	if (shift) {
		/*                                         
                                    
   */
		shr_Xsig(&accumulator, -exponent);
		accumulator.msw |= 0x80000000;	/*         */
		mul_Xsig_Xsig(&accumulator, shiftterm[shift]);
		accumulator.msw &= 0x3fffffff;	/*              */
		exponent = 1;
	}

	if (sign != SIGN_POS) {
		/*                                            
                               
   */
		Denom.lsw = accumulator.lsw;
		XSIG_LL(Denom) = XSIG_LL(accumulator);
		if (exponent < 0)
			shr_Xsig(&Denom, -exponent);
		else if (exponent > 0) {
			/*                         */
			XSIG_LL(Denom) <<= 1;
			if (Denom.lsw & 0x80000000)
				XSIG_LL(Denom) |= 1;
			(Denom.lsw) <<= 1;
		}
		Denom.msw |= 0x80000000;	/*         */
		div_Xsig(&accumulator, &Denom, &accumulator);
	}

	/*                                     */
	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;

}
Esempio n. 7
0
/*--- poly_l2() -------------------------------------------------------------+
 |   Base 2 logarithm by a polynomial approximation.                         |
 +---------------------------------------------------------------------------*/
void poly_l2(FPU_REG *st0_ptr, FPU_REG *st1_ptr, u_char st1_sign)
{
	long int exponent, expon, expon_expon;
	Xsig accumulator, expon_accum, yaccum;
	u_char sign, argsign;
	FPU_REG x;
	int tag;

	exponent = exponent16(st0_ptr);

	/* From st0_ptr, make a number > sqrt(2)/2 and < sqrt(2) */
	if (st0_ptr->sigh > (unsigned)0xb504f334) {
		/* Treat as  sqrt(2)/2 < st0_ptr < 1 */
		significand(&x) = -significand(st0_ptr);
		setexponent16(&x, -1);
		exponent++;
		argsign = SIGN_NEG;
	} else {
		/* Treat as  1 <= st0_ptr < sqrt(2) */
		x.sigh = st0_ptr->sigh - 0x80000000;
		x.sigl = st0_ptr->sigl;
		setexponent16(&x, 0);
		argsign = SIGN_POS;
	}
	tag = FPU_normalize_nuo(&x);

	if (tag == TAG_Zero) {
		expon = 0;
		accumulator.msw = accumulator.midw = accumulator.lsw = 0;
	} else {
		log2_kernel(&x, argsign, &accumulator, &expon);
	}

	if (exponent < 0) {
		sign = SIGN_NEG;
		exponent = -exponent;
	} else
		sign = SIGN_POS;
	expon_accum.msw = exponent;
	expon_accum.midw = expon_accum.lsw = 0;
	if (exponent) {
		expon_expon = 31 + norm_Xsig(&expon_accum);
		shr_Xsig(&accumulator, expon_expon - expon);

		if (sign ^ argsign)
			negate_Xsig(&accumulator);
		add_Xsig_Xsig(&accumulator, &expon_accum);
	} else {
		expon_expon = expon;
		sign = argsign;
	}

	yaccum.lsw = 0;
	XSIG_LL(yaccum) = significand(st1_ptr);
	mul_Xsig_Xsig(&accumulator, &yaccum);

	expon_expon += round_Xsig(&accumulator);

	if (accumulator.msw == 0) {
		FPU_copy_to_reg1(&CONST_Z, TAG_Zero);
		return;
	}

	significand(st1_ptr) = XSIG_LL(accumulator);
	setexponent16(st1_ptr, expon_expon + exponent16(st1_ptr) + 1);

	tag = FPU_round(st1_ptr, 1, 0, FULL_PRECISION, sign ^ st1_sign);
	FPU_settagi(1, tag);

	set_precision_flag_up();	/* 80486 appears to always do this */

	return;

}
Esempio n. 8
0
/*--- log2_kernel() ---------------------------------------------------------+
 |   Base 2 logarithm by a polynomial approximation.                         |
 |   log2(x+1)                                                               |
 +---------------------------------------------------------------------------*/
static void log2_kernel(FPU_REG const *arg, u_char argsign, Xsig *accum_result,
			long int *expon)
{
	long int exponent, adj;
	unsigned long long Xsq;
	Xsig accumulator, Numer, Denom, argSignif, arg_signif;

	exponent = exponent16(arg);
	Numer.lsw = Denom.lsw = 0;
	XSIG_LL(Numer) = XSIG_LL(Denom) = significand(arg);
	if (argsign == SIGN_POS) {
		shr_Xsig(&Denom, 2 - (1 + exponent));
		Denom.msw |= 0x80000000;
		div_Xsig(&Numer, &Denom, &argSignif);
	} else {
		shr_Xsig(&Denom, 1 - (1 + exponent));
		negate_Xsig(&Denom);
		if (Denom.msw & 0x80000000) {
			div_Xsig(&Numer, &Denom, &argSignif);
			exponent++;
		} else {
			/* Denom must be 1.0 */
			argSignif.lsw = Numer.lsw;
			argSignif.midw = Numer.midw;
			argSignif.msw = Numer.msw;
		}
	}

#ifndef PECULIAR_486
	/* Should check here that  |local_arg|  is within the valid range */
	if (exponent >= -2) {
		if ((exponent > -2) || (argSignif.msw > (unsigned)0xafb0ccc0)) {
			/* The argument is too large */
		}
	}
#endif /* PECULIAR_486 */

	arg_signif.lsw = argSignif.lsw;
	XSIG_LL(arg_signif) = XSIG_LL(argSignif);
	adj = norm_Xsig(&argSignif);
	accumulator.lsw = argSignif.lsw;
	XSIG_LL(accumulator) = XSIG_LL(argSignif);
	mul_Xsig_Xsig(&accumulator, &accumulator);
	shr_Xsig(&accumulator, 2 * (-1 - (1 + exponent + adj)));
	Xsq = XSIG_LL(accumulator);
	if (accumulator.lsw & 0x80000000)
		Xsq++;

	accumulator.msw = accumulator.midw = accumulator.lsw = 0;
	/* Do the basic fixed point polynomial evaluation */
	polynomial_Xsig(&accumulator, &Xsq, logterms, HIPOWER - 1);

	mul_Xsig_Xsig(&accumulator, &argSignif);
	shr_Xsig(&accumulator, 6 - adj);

	mul32_Xsig(&arg_signif, leadterm);
	add_two_Xsig(&accumulator, &arg_signif, &exponent);

	*expon = exponent + 1;
	accum_result->lsw = accumulator.lsw;
	accum_result->midw = accumulator.midw;
	accum_result->msw = accumulator.msw;

}
void poly_sine(FPU_REG *st0_ptr)
{
	int exponent, echange;
	Xsig accumulator, argSqrd, argTo4;
	unsigned long fix_up, adj;
	unsigned long long fixed_arg;
	FPU_REG result;

	exponent = exponent(st0_ptr);

	accumulator.lsw = accumulator.midw = accumulator.msw = 0;

	
	
	if ((exponent < -1)
	    || ((exponent == -1) && (st0_ptr->sigh <= 0xe21240aa))) {
		

		argSqrd.msw = st0_ptr->sigh;
		argSqrd.midw = st0_ptr->sigl;
		argSqrd.lsw = 0;
		mul64_Xsig(&argSqrd, &significand(st0_ptr));
		shr_Xsig(&argSqrd, 2 * (-1 - exponent));
		argTo4.msw = argSqrd.msw;
		argTo4.midw = argSqrd.midw;
		argTo4.lsw = argSqrd.lsw;
		mul_Xsig_Xsig(&argTo4, &argTo4);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
				N_COEFF_N - 1);
		mul_Xsig_Xsig(&accumulator, &argSqrd);
		negate_Xsig(&accumulator);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
				N_COEFF_P - 1);

		shr_Xsig(&accumulator, 2);	
		accumulator.msw |= 0x80000000;	

		mul64_Xsig(&accumulator, &significand(st0_ptr));
		mul64_Xsig(&accumulator, &significand(st0_ptr));
		mul64_Xsig(&accumulator, &significand(st0_ptr));

		
		exponent = 3 * exponent;

		
		shr_Xsig(&accumulator, exponent(st0_ptr) - exponent);

		negate_Xsig(&accumulator);
		XSIG_LL(accumulator) += significand(st0_ptr);

		echange = round_Xsig(&accumulator);

		setexponentpos(&result, exponent(st0_ptr) + echange);
	} else {
		
		

		fixed_arg = significand(st0_ptr);

		if (exponent == 0) {
			

			
			fixed_arg <<= 1;
		}
		
		fixed_arg = 0x921fb54442d18469LL - fixed_arg;
		
		if (fixed_arg == 0xffffffffffffffffLL)
			fixed_arg = 0;

		XSIG_LL(argSqrd) = fixed_arg;
		argSqrd.lsw = 0;
		mul64_Xsig(&argSqrd, &fixed_arg);

		XSIG_LL(argTo4) = XSIG_LL(argSqrd);
		argTo4.lsw = argSqrd.lsw;
		mul_Xsig_Xsig(&argTo4, &argTo4);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
				N_COEFF_NH - 1);
		mul_Xsig_Xsig(&accumulator, &argSqrd);
		negate_Xsig(&accumulator);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
				N_COEFF_PH - 1);
		negate_Xsig(&accumulator);

		mul64_Xsig(&accumulator, &fixed_arg);
		mul64_Xsig(&accumulator, &fixed_arg);

		shr_Xsig(&accumulator, 3);
		negate_Xsig(&accumulator);

		add_Xsig_Xsig(&accumulator, &argSqrd);

		shr_Xsig(&accumulator, 1);

		accumulator.lsw |= 1;	
		negate_Xsig(&accumulator);


		
		fix_up = 0x898cc517;
		
		if (argSqrd.msw & 0xffc00000) {
			
			fix_up -= mul_32_32(0x898cc517, argSqrd.msw) / 6;
		}
		fix_up = mul_32_32(fix_up, LL_MSW(fixed_arg));

		adj = accumulator.lsw;	
		accumulator.lsw -= fix_up;
		if (accumulator.lsw > adj)
			XSIG_LL(accumulator)--;

		echange = round_Xsig(&accumulator);

		setexponentpos(&result, echange - 1);
	}

	significand(&result) = XSIG_LL(accumulator);
	setsign(&result, getsign(st0_ptr));
	FPU_copy_to_reg0(&result, TAG_Valid);

#ifdef PARANOID
	if ((exponent(&result) >= 0)
	    && (significand(&result) > 0x8000000000000000LL)) {
		EXCEPTION(EX_INTERNAL | 0x150);
	}
#endif 

}
void poly_cos(FPU_REG *st0_ptr)
{
	FPU_REG result;
	long int exponent, exp2, echange;
	Xsig accumulator, argSqrd, fix_up, argTo4;
	unsigned long long fixed_arg;

#ifdef PARANOID
	if ((exponent(st0_ptr) > 0)
	    || ((exponent(st0_ptr) == 0)
		&& (significand(st0_ptr) > 0xc90fdaa22168c234LL))) {
		EXCEPTION(EX_Invalid);
		FPU_copy_to_reg0(&CONST_QNaN, TAG_Special);
		return;
	}
#endif 

	exponent = exponent(st0_ptr);

	accumulator.lsw = accumulator.midw = accumulator.msw = 0;

	if ((exponent < -1)
	    || ((exponent == -1) && (st0_ptr->sigh <= 0xb00d6f54))) {
		

		argSqrd.msw = st0_ptr->sigh;
		argSqrd.midw = st0_ptr->sigl;
		argSqrd.lsw = 0;
		mul64_Xsig(&argSqrd, &significand(st0_ptr));

		if (exponent < -1) {
			
			shr_Xsig(&argSqrd, 2 * (-1 - exponent));
		}

		argTo4.msw = argSqrd.msw;
		argTo4.midw = argSqrd.midw;
		argTo4.lsw = argSqrd.lsw;
		mul_Xsig_Xsig(&argTo4, &argTo4);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
				N_COEFF_NH - 1);
		mul_Xsig_Xsig(&accumulator, &argSqrd);
		negate_Xsig(&accumulator);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
				N_COEFF_PH - 1);
		negate_Xsig(&accumulator);

		mul64_Xsig(&accumulator, &significand(st0_ptr));
		mul64_Xsig(&accumulator, &significand(st0_ptr));
		shr_Xsig(&accumulator, -2 * (1 + exponent));

		shr_Xsig(&accumulator, 3);
		negate_Xsig(&accumulator);

		add_Xsig_Xsig(&accumulator, &argSqrd);

		shr_Xsig(&accumulator, 1);

		negate_Xsig(&accumulator);

		if (accumulator.lsw & 0x80000000)
			XSIG_LL(accumulator)++;
		if (accumulator.msw == 0) {
			
			FPU_copy_to_reg0(&CONST_1, TAG_Valid);
			return;
		} else {
			significand(&result) = XSIG_LL(accumulator);

			
			setexponentpos(&result, -1);
		}
	} else {
		fixed_arg = significand(st0_ptr);

		if (exponent == 0) {
			

			
			fixed_arg <<= 1;
		}
		
		fixed_arg = 0x921fb54442d18469LL - fixed_arg;
		
		if (fixed_arg == 0xffffffffffffffffLL)
			fixed_arg = 0;

		exponent = -1;
		exp2 = -1;

		if (!(LL_MSW(fixed_arg) & 0xffff0000)) {
			fixed_arg <<= 16;
			exponent -= 16;
			exp2 -= 16;
		}

		XSIG_LL(argSqrd) = fixed_arg;
		argSqrd.lsw = 0;
		mul64_Xsig(&argSqrd, &fixed_arg);

		if (exponent < -1) {
			
			shr_Xsig(&argSqrd, 2 * (-1 - exponent));
		}

		argTo4.msw = argSqrd.msw;
		argTo4.midw = argSqrd.midw;
		argTo4.lsw = argSqrd.lsw;
		mul_Xsig_Xsig(&argTo4, &argTo4);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
				N_COEFF_N - 1);
		mul_Xsig_Xsig(&accumulator, &argSqrd);
		negate_Xsig(&accumulator);

		polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
				N_COEFF_P - 1);

		shr_Xsig(&accumulator, 2);	
		accumulator.msw |= 0x80000000;	

		mul64_Xsig(&accumulator, &fixed_arg);
		mul64_Xsig(&accumulator, &fixed_arg);
		mul64_Xsig(&accumulator, &fixed_arg);

		
		exponent = 3 * exponent;

		
		shr_Xsig(&accumulator, exp2 - exponent);

		negate_Xsig(&accumulator);
		XSIG_LL(accumulator) += fixed_arg;


		
		XSIG_LL(fix_up) = 0x898cc51701b839a2ll;
		fix_up.lsw = 0;

		
		if (argSqrd.msw & 0xffc00000) {
			
			fix_up.msw -= mul_32_32(0x898cc517, argSqrd.msw) / 2;
			fix_up.msw += mul_32_32(0x898cc517, argTo4.msw) / 24;
		}

		exp2 += norm_Xsig(&accumulator);
		shr_Xsig(&accumulator, 1);	
		exp2++;
		shr_Xsig(&fix_up, 65 + exp2);

		add_Xsig_Xsig(&accumulator, &fix_up);

		echange = round_Xsig(&accumulator);

		setexponentpos(&result, exp2 + echange);
		significand(&result) = XSIG_LL(accumulator);
	}

	FPU_copy_to_reg0(&result, TAG_Valid);

#ifdef PARANOID
	if ((exponent(&result) >= 0)
	    && (significand(&result) > 0x8000000000000000LL)) {
		EXCEPTION(EX_INTERNAL | 0x151);
	}
#endif 

}
Esempio n. 11
0
/*--- poly_atan() -----------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void	poly_atan(FPU_REG *arg1, FPU_REG *arg2, FPU_REG *result)
{
  char		        transformed, inverted,
                        sign1 = arg1->sign, sign2 = arg2->sign;
  long int   		exponent, dummy_exp;
  Xsig                  accumulator, Numer, Denom, accumulatore, argSignif,
                        argSq, argSqSq;
  

  arg1->sign = arg2->sign = SIGN_POS;
  if ( (compare(arg2) & ~COMP_Denormal) == COMP_A_lt_B )
    {
      inverted = 1;
      exponent = arg1->exp - arg2->exp;
      Numer.lsw = Denom.lsw = 0;
      XSIG_LL(Numer) = significand(arg1);
      XSIG_LL(Denom) = significand(arg2);
    }
  else
    {
      inverted = 0;
      exponent = arg2->exp - arg1->exp;
      Numer.lsw = Denom.lsw = 0;
      XSIG_LL(Numer) = significand(arg2);
      XSIG_LL(Denom) = significand(arg1);
     }
  div_Xsig(&Numer, &Denom, &argSignif);
  exponent += norm_Xsig(&argSignif);

  if ( (exponent >= -1)
      || ((exponent == -2) && (argSignif.msw > 0xd413ccd0)) )
    {
      /* The argument is greater than sqrt(2)-1 (=0.414213562...) */
      /* Convert the argument by an identity for atan */
      transformed = 1;

      if ( exponent >= 0 )
	{
#ifdef PARANOID
	  if ( !( (exponent == 0) && 
		 (argSignif.lsw == 0) && (argSignif.midw == 0) &&
		 (argSignif.msw == 0x80000000) ) )
	    {
	      EXCEPTION(EX_INTERNAL|0x104);  /* There must be a logic error */
	      return;
	    }
#endif PARANOID
	  argSignif.msw = 0;   /* Make the transformed arg -> 0.0 */
	}
      else
	{
	  Numer.lsw = Denom.lsw = argSignif.lsw;
	  XSIG_LL(Numer) = XSIG_LL(Denom) = XSIG_LL(argSignif);

	  if ( exponent < -1 )
	    shr_Xsig(&Numer, -1-exponent);
	  negate_Xsig(&Numer);
      
	  shr_Xsig(&Denom, -exponent);
	  Denom.msw |= 0x80000000;
      
	  div_Xsig(&Numer, &Denom, &argSignif);

	  exponent = -1 + norm_Xsig(&argSignif);
	}
    }
  else
    {
      transformed = 0;
    }

  argSq.lsw = argSignif.lsw; argSq.midw = argSignif.midw;
  argSq.msw = argSignif.msw;
  mul_Xsig_Xsig(&argSq, &argSq);
  
  argSqSq.lsw = argSq.lsw; argSqSq.midw = argSq.midw; argSqSq.msw = argSq.msw;
  mul_Xsig_Xsig(&argSqSq, &argSqSq);

  accumulatore.lsw = argSq.lsw;
  XSIG_LL(accumulatore) = XSIG_LL(argSq);

  shr_Xsig(&argSq, 2*(-1-exponent-1));
  shr_Xsig(&argSqSq, 4*(-1-exponent-1));

  /* Now have argSq etc with binary point at the left
     .1xxxxxxxx */

  /* Do the basic fixed point polynomial evaluation */
  accumulator.msw = accumulator.midw = accumulator.lsw = 0;
  polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq),
		   oddplterms, HIPOWERop-1);
  mul64_Xsig(&accumulator, &XSIG_LL(argSq));
  negate_Xsig(&accumulator);
  polynomial_Xsig(&accumulator, &XSIG_LL(argSqSq), oddnegterms, HIPOWERon-1);
  negate_Xsig(&accumulator);
  add_two_Xsig(&accumulator, &fixedpterm, &dummy_exp);

  mul64_Xsig(&accumulatore, &denomterm);
  shr_Xsig(&accumulatore, 1 + 2*(-1-exponent));
  accumulatore.msw |= 0x80000000;

  div_Xsig(&accumulator, &accumulatore, &accumulator);

  mul_Xsig_Xsig(&accumulator, &argSignif);
  mul_Xsig_Xsig(&accumulator, &argSq);

  shr_Xsig(&accumulator, 3);
  negate_Xsig(&accumulator);
  add_Xsig_Xsig(&accumulator, &argSignif);

  if ( transformed )
    {
      /* compute pi/4 - accumulator */
      shr_Xsig(&accumulator, -1-exponent);
      negate_Xsig(&accumulator);
      add_Xsig_Xsig(&accumulator, &pi_signif);
      exponent = -1;
    }

  if ( inverted )
    {
      /* compute pi/2 - accumulator */
      shr_Xsig(&accumulator, -exponent);
      negate_Xsig(&accumulator);
      add_Xsig_Xsig(&accumulator, &pi_signif);
      exponent = 0;
    }

  if ( sign1 )
    {
      /* compute pi - accumulator */
      shr_Xsig(&accumulator, 1 - exponent);
      negate_Xsig(&accumulator);
      add_Xsig_Xsig(&accumulator, &pi_signif);
      exponent = 1;
    }

  exponent += round_Xsig(&accumulator);
  significand(result) = XSIG_LL(accumulator);
  result->exp = exponent + EXP_BIAS;
  result->tag = TW_Valid;
  result->sign = sign2;

}
Esempio n. 12
0
/*--- poly_sine() -----------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void	poly_sine(FPU_REG const *arg, FPU_REG *result)
{
  int                 exponent, echange;
  Xsig                accumulator, argSqrd, argTo4;
  unsigned long       fix_up, adj;
  unsigned long long  fixed_arg;


#ifdef PARANOID
  if ( arg->tag == TW_Zero )
    {
      /* Return 0.0 */
      reg_move(&CONST_Z, result);
      return;
    }
#endif PARANOID

  exponent = arg->exp - EXP_BIAS;

  accumulator.lsw = accumulator.midw = accumulator.msw = 0;

  /* Split into two ranges, for arguments below and above 1.0 */
  /* The boundary between upper and lower is approx 0.88309101259 */
  if ( (exponent < -1) || ((exponent == -1) && (arg->sigh <= 0xe21240aa)) )
    {
      /* The argument is <= 0.88309101259 */

      argSqrd.msw = arg->sigh; argSqrd.midw = arg->sigl; argSqrd.lsw = 0;
      mul64_Xsig(&argSqrd, &significand(arg));
      shr_Xsig(&argSqrd, 2*(-1-exponent));
      argTo4.msw = argSqrd.msw; argTo4.midw = argSqrd.midw;
      argTo4.lsw = argSqrd.lsw;
      mul_Xsig_Xsig(&argTo4, &argTo4);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
		      N_COEFF_N-1);
      mul_Xsig_Xsig(&accumulator, &argSqrd);
      negate_Xsig(&accumulator);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
		      N_COEFF_P-1);

      shr_Xsig(&accumulator, 2);    /* Divide by four */
      accumulator.msw |= 0x80000000;  /* Add 1.0 */

      mul64_Xsig(&accumulator, &significand(arg));
      mul64_Xsig(&accumulator, &significand(arg));
      mul64_Xsig(&accumulator, &significand(arg));

      /* Divide by four, FPU_REG compatible, etc */
      exponent = 3*exponent + EXP_BIAS;

      /* The minimum exponent difference is 3 */
      shr_Xsig(&accumulator, arg->exp - exponent);

      negate_Xsig(&accumulator);
      XSIG_LL(accumulator) += significand(arg);

      echange = round_Xsig(&accumulator);

      result->exp = arg->exp + echange;
    }
  else
    {
      /* The argument is > 0.88309101259 */
      /* We use sin(arg) = cos(pi/2-arg) */

      fixed_arg = significand(arg);

      if ( exponent == 0 )
	{
	  /* The argument is >= 1.0 */

	  /* Put the binary point at the left. */
	  fixed_arg <<= 1;
	}
      /* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
      fixed_arg = 0x921fb54442d18469LL - fixed_arg;

      XSIG_LL(argSqrd) = fixed_arg; argSqrd.lsw = 0;
      mul64_Xsig(&argSqrd, &fixed_arg);

      XSIG_LL(argTo4) = XSIG_LL(argSqrd); argTo4.lsw = argSqrd.lsw;
      mul_Xsig_Xsig(&argTo4, &argTo4);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
		      N_COEFF_NH-1);
      mul_Xsig_Xsig(&accumulator, &argSqrd);
      negate_Xsig(&accumulator);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
		      N_COEFF_PH-1);
      negate_Xsig(&accumulator);

      mul64_Xsig(&accumulator, &fixed_arg);
      mul64_Xsig(&accumulator, &fixed_arg);

      shr_Xsig(&accumulator, 3);
      negate_Xsig(&accumulator);

      add_Xsig_Xsig(&accumulator, &argSqrd);

      shr_Xsig(&accumulator, 1);

      accumulator.lsw |= 1;  /* A zero accumulator here would cause problems */
      negate_Xsig(&accumulator);

      /* The basic computation is complete. Now fix the answer to
	 compensate for the error due to the approximation used for
	 pi/2
	 */

      /* This has an exponent of -65 */
      fix_up = 0x898cc517;
      /* The fix-up needs to be improved for larger args */
      if ( argSqrd.msw & 0xffc00000 )
	{
	  /* Get about 32 bit precision in these: */
	  mul_32_32(0x898cc517, argSqrd.msw, &adj);
	  fix_up -= adj/6;
	}
      mul_32_32(fix_up, LL_MSW(fixed_arg), &fix_up);

      adj = accumulator.lsw;    /* temp save */
      accumulator.lsw -= fix_up;
      if ( accumulator.lsw > adj )
	XSIG_LL(accumulator) --;

      echange = round_Xsig(&accumulator);

      result->exp = EXP_BIAS - 1 + echange;
    }

  significand(result) = XSIG_LL(accumulator);
  result->tag = TW_Valid;
  result->sign = arg->sign;

#ifdef PARANOID
  if ( (result->exp >= EXP_BIAS)
      && (significand(result) > 0x8000000000000000LL) )
    {
      EXCEPTION(EX_INTERNAL|0x150);
    }
#endif PARANOID

}
Esempio n. 13
0
/*--- poly_cos() ------------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void	poly_cos(FPU_REG const *arg, FPU_REG *result)
{
  long int            exponent, exp2, echange;
  Xsig                accumulator, argSqrd, fix_up, argTo4;
  unsigned long       adj;
  unsigned long long  fixed_arg;


#ifdef PARANOID
  if ( arg->tag == TW_Zero )
    {
      /* Return 1.0 */
      reg_move(&CONST_1, result);
      return;
    }

  if ( (arg->exp > EXP_BIAS)
      || ((arg->exp == EXP_BIAS)
	  && (significand(arg) > 0xc90fdaa22168c234LL)) )
    {
      EXCEPTION(EX_Invalid);
      reg_move(&CONST_QNaN, result);
      return;
    }
#endif PARANOID

  exponent = arg->exp - EXP_BIAS;

  accumulator.lsw = accumulator.midw = accumulator.msw = 0;

  if ( (exponent < -1) || ((exponent == -1) && (arg->sigh <= 0xb00d6f54)) )
    {
      /* arg is < 0.687705 */

      argSqrd.msw = arg->sigh; argSqrd.midw = arg->sigl; argSqrd.lsw = 0;
      mul64_Xsig(&argSqrd, &significand(arg));

      if ( exponent < -1 )
	{
	  /* shift the argument right by the required places */
	  shr_Xsig(&argSqrd, 2*(-1-exponent));
	}

      argTo4.msw = argSqrd.msw; argTo4.midw = argSqrd.midw;
      argTo4.lsw = argSqrd.lsw;
      mul_Xsig_Xsig(&argTo4, &argTo4);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_h,
		      N_COEFF_NH-1);
      mul_Xsig_Xsig(&accumulator, &argSqrd);
      negate_Xsig(&accumulator);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_h,
		      N_COEFF_PH-1);
      negate_Xsig(&accumulator);

      mul64_Xsig(&accumulator, &significand(arg));
      mul64_Xsig(&accumulator, &significand(arg));
      shr_Xsig(&accumulator, -2*(1+exponent));

      shr_Xsig(&accumulator, 3);
      negate_Xsig(&accumulator);

      add_Xsig_Xsig(&accumulator, &argSqrd);

      shr_Xsig(&accumulator, 1);

      /* It doesn't matter if accumulator is all zero here, the
	 following code will work ok */
      negate_Xsig(&accumulator);

      if ( accumulator.lsw & 0x80000000 )
	XSIG_LL(accumulator) ++;
      if ( accumulator.msw == 0 )
	{
	  /* The result is 1.0 */
	  reg_move(&CONST_1, result);
	}
      else
	{
	  significand(result) = XSIG_LL(accumulator);
      
	  /* will be a valid positive nr with expon = -1 */
	  *(short *)&(result->sign) = 0;
	  result->exp = EXP_BIAS - 1;
	}
    }
  else
    {
      fixed_arg = significand(arg);

      if ( exponent == 0 )
	{
	  /* The argument is >= 1.0 */

	  /* Put the binary point at the left. */
	  fixed_arg <<= 1;
	}
      /* pi/2 in hex is: 1.921fb54442d18469 898CC51701B839A2 52049C1 */
      fixed_arg = 0x921fb54442d18469LL - fixed_arg;

      exponent = -1;
      exp2 = -1;

      /* A shift is needed here only for a narrow range of arguments,
	 i.e. for fixed_arg approx 2^-32, but we pick up more... */
      if ( !(LL_MSW(fixed_arg) & 0xffff0000) )
	{
	  fixed_arg <<= 16;
	  exponent -= 16;
	  exp2 -= 16;
	}

      XSIG_LL(argSqrd) = fixed_arg; argSqrd.lsw = 0;
      mul64_Xsig(&argSqrd, &fixed_arg);

      if ( exponent < -1 )
	{
	  /* shift the argument right by the required places */
	  shr_Xsig(&argSqrd, 2*(-1-exponent));
	}

      argTo4.msw = argSqrd.msw; argTo4.midw = argSqrd.midw;
      argTo4.lsw = argSqrd.lsw;
      mul_Xsig_Xsig(&argTo4, &argTo4);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), neg_terms_l,
		      N_COEFF_N-1);
      mul_Xsig_Xsig(&accumulator, &argSqrd);
      negate_Xsig(&accumulator);

      polynomial_Xsig(&accumulator, &XSIG_LL(argTo4), pos_terms_l,
		      N_COEFF_P-1);

      shr_Xsig(&accumulator, 2);    /* Divide by four */
      accumulator.msw |= 0x80000000;  /* Add 1.0 */

      mul64_Xsig(&accumulator, &fixed_arg);
      mul64_Xsig(&accumulator, &fixed_arg);
      mul64_Xsig(&accumulator, &fixed_arg);

      /* Divide by four, FPU_REG compatible, etc */
      exponent = 3*exponent;

      /* The minimum exponent difference is 3 */
      shr_Xsig(&accumulator, exp2 - exponent);

      negate_Xsig(&accumulator);
      XSIG_LL(accumulator) += fixed_arg;

      /* The basic computation is complete. Now fix the answer to
	 compensate for the error due to the approximation used for
	 pi/2
	 */

      /* This has an exponent of -65 */
      XSIG_LL(fix_up) = 0x898cc51701b839a2ll;
      fix_up.lsw = 0;

      /* The fix-up needs to be improved for larger args */
      if ( argSqrd.msw & 0xffc00000 )
	{
	  /* Get about 32 bit precision in these: */
	  mul_32_32(0x898cc517, argSqrd.msw, &adj);
	  fix_up.msw -= adj/2;
	  mul_32_32(0x898cc517, argTo4.msw, &adj);
	  fix_up.msw += adj/24;
	}

      exp2 += norm_Xsig(&accumulator);
      shr_Xsig(&accumulator, 1); /* Prevent overflow */
      exp2++;
      shr_Xsig(&fix_up, 65 + exp2);

      add_Xsig_Xsig(&accumulator, &fix_up);

      echange = round_Xsig(&accumulator);

      result->exp = exp2 + EXP_BIAS + echange;
      *(short *)&(result->sign) = 0;      /* Is a valid positive nr */
      significand(result) = XSIG_LL(accumulator);
    }

#ifdef PARANOID
  if ( (result->exp >= EXP_BIAS)
      && (significand(result) > 0x8000000000000000LL) )
    {
      EXCEPTION(EX_INTERNAL|0x151);
    }
#endif PARANOID

}