poly_ata.c

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/*---------------------------------------------------------------------------+
 |  p_atan.c                                                                 |
 |                                                                           |
 | Compute the tan of a FPU_REG, using a polynomial approximation.           |
 |                                                                           |
 | Copyright (C) 1992,1993                                                   |
 |                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,      |
 |                       Australia.  E-mail   [e-mail]    |
 |                                                                           |
 |                                                                           |
 +---------------------------------------------------------------------------*/

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


#define	HIPOWERon	6	/* odd poly, negative terms */
static unsigned const oddnegterms[HIPOWERon][2] =
{
  { 0x00000000, 0x00000000 }, /* for + 1.0 */
  { 0x763b6f3d, 0x1adc4428 },
  { 0x20f0630b, 0x0502909d },
  { 0x4e825578, 0x0198ce38 },
  { 0x22b7cb87, 0x008da6e3 },
  { 0x9b30ca03, 0x00239c79 }
} ;

#define	HIPOWERop	6	/* odd poly, positive terms */
static unsigned const	oddplterms[HIPOWERop][2] =
{
  { 0xa6f67cb8, 0x94d910bd },
  { 0xa02ffab4, 0x0a43cb45 },
  { 0x04265e6b, 0x02bf5655 },
  { 0x0a728914, 0x00f280f7 },
  { 0x6d640e01, 0x004d6556 },
  { 0xf1dd2dbf, 0x000a530a }
};

static unsigned long long const denomterm = 0xea2e6612fc4bd208LL;


/*--- poly_atan() -----------------------------------------------------------+
 |                                                                           |
 +---------------------------------------------------------------------------*/
void	poly_atan(FPU_REG *arg)
{
  char		recursions = 0;
  short		exponent;
  FPU_REG       odd_poly, even_poly, pos_poly, neg_poly, ratio;
  FPU_REG       argSq;
  unsigned long long     arg_signif, argSqSq;
  

#ifdef PARANOID
  if ( arg->sign != 0 )	/* Can't hack a number < 0.0 */
    { arith_invalid(arg); return; }  /* Need a positive number */
#endif PARANOID

  exponent = arg->exp - EXP_BIAS;
  
  if ( arg->tag == TW_Zero )
    {
      /* Return 0.0 */
      reg_move(&CONST_Z, arg);
      return;
    }
  
  if ( exponent >= -2 )
    {
      /* argument is in the range  [0.25 .. 1.0] */
      if ( exponent >= 0 )
	{
#ifdef PARANOID
	  if ( (exponent == 0) && 
	      (arg->sigl == 0) && (arg->sigh == 0x80000000) )
#endif PARANOID
	    {
	      reg_move(&CONST_PI4, arg);
	      return;
	    }
#ifdef PARANOID
	  EXCEPTION(EX_INTERNAL|0x104);	/* There must be a logic error */
	  return;
#endif PARANOID
	}

      /* If the argument is greater than sqrt(2)-1 (=0.414213562...) */
      /* convert the argument by an identity for atan */
      if ( (exponent >= -1) || (arg->sigh > 0xd413ccd0) )
	{
	  FPU_REG numerator, denom;

	  recursions++;

	  arg_signif = significand(arg);
	  if ( exponent < -1 )
	    {
	      if ( shrx(&arg_signif, -1-exponent) >= 0x80000000U )
		arg_signif++;	/* round up */
	    }
	  significand(&numerator) = -arg_signif;
	  numerator.exp = EXP_BIAS - 1;
	  normalize(&numerator);                       /* 1 - arg */

	  arg_signif = significand(arg);
	  if ( shrx(&arg_signif, -exponent) >= 0x80000000U )
	    arg_signif++;	/* round up */
	  significand(&denom) = arg_signif;
	  denom.sigh |= 0x80000000;                    /* 1 + arg */

	  arg->exp = numerator.exp;
	  reg_u_div(&numerator, &denom, arg, FULL_PRECISION);

	  exponent = arg->exp - EXP_BIAS;
	}
    }

  arg_signif = significand(arg);

#ifdef PARANOID
  /* This must always be true */
  if ( exponent >= -1 )
    {
      EXCEPTION(EX_INTERNAL|0x120);	/* There must be a logic error */
    }
#endif PARANOID

  /* shift the argument right by the required places */
  if ( shrx(&arg_signif, -1-exponent) >= 0x80000000U )
    arg_signif++;	/* round up */
  
  /* Now have arg_signif with binary point at the left
     .1xxxxxxxx */
  mul64(&arg_signif, &arg_signif, &significand(&argSq));
  mul64(&significand(&argSq), &significand(&argSq), &argSqSq);

  /* will be a valid positive nr with expon = 0 */
  *(short *)&(pos_poly.sign) = 0;
  pos_poly.exp = EXP_BIAS;

  /* Do the basic fixed point polynomial evaluation */
  polynomial(&pos_poly.sigl, (unsigned *)&argSqSq,
	     (unsigned short (*)[4])oddplterms, HIPOWERop-1);
  mul64(&significand(&argSq), &significand(&pos_poly),
	&significand(&pos_poly));

  /* will be a valid positive nr with expon = 0 */
  *(short *)&(neg_poly.sign) = 0;
  neg_poly.exp = EXP_BIAS;

  /* Do the basic fixed point polynomial evaluation */
  polynomial(&neg_poly.sigl, (unsigned *)&argSqSq,
	     (unsigned short (*)[4])oddnegterms, HIPOWERon-1);

  /* Subtract the mantissas */
  significand(&pos_poly) -= significand(&neg_poly);

  reg_move(&pos_poly, &odd_poly);
  poly_add_1(&odd_poly);

  /* will be a valid positive nr with expon = 0 */
  *(short *)&(even_poly.sign) = 0;

  mul64(&significand(&argSq), &denomterm, &significand(&even_poly));

  poly_add_1(&even_poly);

  reg_div(&odd_poly, &even_poly, &ratio, FULL_PRECISION);

  reg_u_mul(&ratio, arg, arg, FULL_PRECISION);

  if ( recursions )
    reg_sub(&CONST_PI4, arg, arg, FULL_PRECISION);

}


/* The argument to this function must be polynomial() compatible,
   i.e. have an exponent (not checked) of EXP_BIAS-1 but need not
   be normalized.
   This function adds 1.0 to the (assumed positive) argument. */
void poly_add_1(FPU_REG *src)
{
/* Rounding in a consistent direction produces better results
   for the use of this function in poly_atan. Simple truncation
   is used here instead of round-to-nearest. */

#ifdef OBSOLETE
char round = (src->sigl & 3) == 3;
#endif OBSOLETE

shrx(&src->sigl, 1);

#ifdef OBSOLETE
if ( round ) significand(src)++;   /* Round to even */
#endif OBSOLETE

src->sigh |= 0x80000000;

src->exp = EXP_BIAS;

}