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poly_tan.c

/*---------------------------------------------------------------------------+
 |  poly_tan.c                                                               |
 |                                                                           |
 | Compute the tan of a FPU_REG, using a polynomial approximation.           |
 |                                                                           |
 | Copyright (C) 1992,1993,1994,1997,1999                                    |
 |                       W. Metzenthen, 22 Parker St, Ormond, Vic 3163,      |
 |                       Australia.  E-mail   billm@melbpc.org.au            |
 |                                                                           |
 |                                                                           |
 +---------------------------------------------------------------------------*/

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


#define     HiPOWERop   3     /* odd poly, positive terms */
static const unsigned long long oddplterm[HiPOWERop] =
{
  0x0000000000000000LL,
  0x0051a1cf08fca228LL,
  0x0000000071284ff7LL
};

#define     HiPOWERon   2     /* odd poly, negative terms */
static const unsigned long long oddnegterm[HiPOWERon] =
{
   0x1291a9a184244e80LL,
   0x0000583245819c21LL
};

#define     HiPOWERep   2     /* even poly, positive terms */
static const unsigned long long evenplterm[HiPOWERep] =
{
  0x0e848884b539e888LL,
  0x00003c7f18b887daLL
};

#define     HiPOWERen   2     /* even poly, negative terms */
static const unsigned long long evennegterm[HiPOWERen] =
{
  0xf1f0200fd51569ccLL,
  0x003afb46105c4432LL
};

static const unsigned long long twothirds = 0xaaaaaaaaaaaaaaabLL;


/*--- 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
      adj = 0;
      adj = mul_32_32(0x898cc517, adj);          /* delta * tan^2 */

      fix_up.msw += adj;
      if ( !(fix_up.msw & 0x80000000) )   /* did fix_up overflow ? */
      {
        /* Yes, we need to add an msb */
        shr_Xsig(&fix_up, 1);
        fix_up.msw |= 0x80000000;
        shr_Xsig(&fix_up, 64 + exponent);
      }
      else
      shr_Xsig(&fix_up, 65 + exponent);

      add_two_Xsig(&accum, &fix_up, &exponent);

      /* accum now contains tan(pi/2 - arg).
       Use tan(arg) = 1.0 / tan(pi/2 - arg)
       */
      accumulatoro.lsw = accumulatoro.midw = 0;
      accumulatoro.msw = 0x80000000;
      div_Xsig(&accumulatoro, &accum, &accum);
      exponent = - exponent - 1;
    }

  /* Transfer the result */
  round_Xsig(&accum);
  FPU_settag0(TAG_Valid);
  significand(st0_ptr) = XSIG_LL(accum);
  setexponent16(st0_ptr, exponent + EXTENDED_Ebias);  /* Result is positive. */

}

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