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/*---------------------------------------------------------------------------+

 |  poly_atan.c                                                              |

 |                                                                           |

 | Compute the arctan of a FPU_REG, using a polynomial approximation.        |

 |                                                                           |

 | Copyright (C) 1992,1993,1994                                              |

 |                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,      |

 |                       Australia.  E-mail   billm@vaxc.cc.monash.edu.au    |

 |                                                                           |

 |                                                                           |

 +---------------------------------------------------------------------------*/

#include "exception.h"

#include "reg_constant.h"

#include "fpu_emu.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 *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;

}