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poly_atan.c

/*---------------------------------------------------------------------------+
 |  poly_atan.c                                                              |
 |                                                                           |
 | Compute the arctan of a FPU_REG, using 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 "status_w.h"
#include "control_w.h"
#include "poly.h"


#define     HIPOWERon   6     /* odd poly, negative terms */
static const unsigned long long oddnegterms[HIPOWERon] =
{
  0x0000000000000000LL, /* Dummy (not for - 1.0) */
  0x015328437f756467LL,
  0x0005dda27b73dec6LL,
  0x0000226bf2bfb91aLL,
  0x000000ccc439c5f7LL,
  0x0000000355438407LL
} ;

#define     HIPOWERop   6     /* odd poly, positive terms */
static const unsigned long long oddplterms[HIPOWERop] =
{
/*  0xaaaaaaaaaaaaaaabLL,  transferred to fixedpterm[] */
  0x0db55a71875c9ac2LL,
  0x0029fce2d67880b0LL,
  0x0000dfd3908b4596LL,
  0x00000550fd61dab4LL,
  0x0000001c9422b3f9LL,
  0x000000003e3301e1LL
};

static const unsigned long long denomterm = 0xebd9b842c5c53a0eLL;

static const Xsig fixedpterm = MK_XSIG(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa);

static const Xsig pi_signif = MK_XSIG(0xc90fdaa2, 0x2168c234, 0xc4c6628b);


/*--- 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. */

}

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