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

 |  poly_sin.c                                                               |

 |                                                                           |

 |  Computation of an approximation of the sin function and the cosine       |

 |  function by a polynomial.                                                |

 |                                                                           |

 | 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 "control_w.h"

#include "poly.h"

#define N_COEFF_P       4

#define N_COEFF_N       4

static const unsigned long long pos_terms_l[N_COEFF_P] =

{

  0xaaaaaaaaaaaaaaabLL,

  0x00d00d00d00cf906LL,

  0x000006b99159a8bbLL,

  0x000000000d7392e6LL

};

static const unsigned long long neg_terms_l[N_COEFF_N] =

{

  0x2222222222222167LL,

  0x0002e3bc74aab624LL,

  0x0000000b09229062LL,

  0x00000000000c7973LL

};

#define N_COEFF_PH      4

#define N_COEFF_NH      4

static const unsigned long long pos_terms_h[N_COEFF_PH] =

{

  0x0000000000000000LL,

  0x05b05b05b05b0406LL,

  0x000049f93edd91a9LL,

  0x00000000c9c9ed62LL

};

static const unsigned long long neg_terms_h[N_COEFF_NH] =

{

  0xaaaaaaaaaaaaaa98LL,

  0x001a01a01a019064LL,

  0x0000008f76c68a77LL,

  0x0000000000d58f5eLL

};

/*--- 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

}

/*--- 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

}