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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
 
}