/* k_rem_pio2f.c -- float version of e_rem_pio2.c

   Copyright (C) 2011-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011

   The GNU C Library is free software; you can redistribute it and/or

   modify it under the terms of the GNU Library General Public License as

   published by the Free Software Foundation; either version 2 of the

   License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,

   but WITHOUT ANY WARRANTY; without even the implied warranty of

   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

   Library General Public License for more details.

   You should have received a copy of the GNU Library General Public

   License along with the GNU C Library; see the file COPYING.LIB.  If

   not, see <http://www.gnu.org/licenses/>.  */

#include <math.h>

#include <math_private.h>

#include "s_float_bitwise.h"

static const float two_over_pi[] = {

  1.62000000e+02, 2.49000000e+02, 1.31000000e+02, 1.10000000e+02,

  7.80000000e+01, 6.80000000e+01, 2.10000000e+01, 4.10000000e+01,

  2.52000000e+02, 3.90000000e+01, 8.70000000e+01, 2.09000000e+02,

  2.45000000e+02, 5.20000000e+01, 2.21000000e+02, 1.92000000e+02,

  2.19000000e+02, 9.80000000e+01, 1.49000000e+02, 1.53000000e+02,

  6.00000000e+01, 6.70000000e+01, 1.44000000e+02, 6.50000000e+01,

  2.54000000e+02, 8.10000000e+01, 9.90000000e+01, 1.71000000e+02,

  2.22000000e+02, 1.87000000e+02, 1.97000000e+02, 9.70000000e+01,

  1.83000000e+02, 3.60000000e+01, 1.10000000e+02, 5.80000000e+01,

  6.60000000e+01, 7.70000000e+01, 2.10000000e+02, 2.24000000e+02,

  6.00000000e+00, 7.30000000e+01, 4.60000000e+01, 2.34000000e+02,

  9.00000000e+00, 2.09000000e+02, 1.46000000e+02, 2.80000000e+01,

  2.54000000e+02, 2.90000000e+01, 2.35000000e+02, 2.80000000e+01,

  1.77000000e+02, 4.10000000e+01, 1.67000000e+02, 6.20000000e+01,

  2.32000000e+02, 1.30000000e+02, 5.30000000e+01, 2.45000000e+02,

  4.60000000e+01, 1.87000000e+02, 6.80000000e+01, 1.32000000e+02,

  2.33000000e+02, 1.56000000e+02, 1.12000000e+02, 3.80000000e+01,

  1.80000000e+02, 9.50000000e+01, 1.26000000e+02, 6.50000000e+01,

  5.70000000e+01, 1.45000000e+02, 2.14000000e+02, 5.70000000e+01,

  1.31000000e+02, 8.30000000e+01, 5.70000000e+01, 2.44000000e+02,

  1.56000000e+02, 1.32000000e+02, 9.50000000e+01, 1.39000000e+02,

  1.89000000e+02, 2.49000000e+02, 4.00000000e+01, 5.90000000e+01,

  3.10000000e+01, 2.48000000e+02, 1.51000000e+02, 2.55000000e+02,

  2.22000000e+02, 5.00000000e+00, 1.52000000e+02, 1.50000000e+01,

  2.39000000e+02, 4.70000000e+01, 1.70000000e+01, 1.39000000e+02,

  9.00000000e+01, 1.00000000e+01, 1.09000000e+02, 3.10000000e+01,

  1.09000000e+02, 5.40000000e+01, 1.26000000e+02, 2.07000000e+02,

  3.90000000e+01, 2.03000000e+02, 9.00000000e+00, 1.83000000e+02,

  7.90000000e+01, 7.00000000e+01, 6.30000000e+01, 1.02000000e+02,

  1.58000000e+02, 9.50000000e+01, 2.34000000e+02, 4.50000000e+01,

  1.17000000e+02, 3.90000000e+01, 1.86000000e+02, 1.99000000e+02,

  2.35000000e+02, 2.29000000e+02, 2.41000000e+02, 1.23000000e+02,

  6.10000000e+01, 7.00000000e+00, 5.70000000e+01, 2.47000000e+02,

  1.38000000e+02, 8.20000000e+01, 1.46000000e+02, 2.34000000e+02,

  1.07000000e+02, 2.51000000e+02, 9.50000000e+01, 1.77000000e+02,

  3.10000000e+01, 1.41000000e+02, 9.30000000e+01, 8.00000000e+00,

  8.60000000e+01, 3.00000000e+00, 4.80000000e+01, 7.00000000e+01,

  2.52000000e+02, 1.23000000e+02, 1.07000000e+02, 1.71000000e+02,

  2.40000000e+02, 2.07000000e+02, 1.88000000e+02, 3.20000000e+01,

  1.54000000e+02, 2.44000000e+02, 5.40000000e+01, 2.90000000e+01,

  1.69000000e+02, 2.27000000e+02, 1.45000000e+02, 9.70000000e+01,

  9.40000000e+01, 2.30000000e+02, 2.70000000e+01, 8.00000000e+00,

  1.01000000e+02, 1.53000000e+02, 1.33000000e+02, 9.50000000e+01,

  2.00000000e+01, 1.60000000e+02, 1.04000000e+02, 6.40000000e+01,

  1.41000000e+02, 2.55000000e+02, 2.16000000e+02, 1.28000000e+02,

  7.70000000e+01, 1.15000000e+02, 3.90000000e+01, 4.90000000e+01,

  6.00000000e+00, 6.00000000e+00, 2.10000000e+01, 8.60000000e+01,

  2.02000000e+02, 1.15000000e+02, 1.68000000e+02, 2.01000000e+02,

  9.60000000e+01, 2.26000000e+02, 1.23000000e+02, 1.92000000e+02,

  1.40000000e+02, 1.07000000e+02

};

static const float PIo2[] = {

  1.5703125000e+00,		/* 0x3fc90000 */

  4.5776367188e-04,		/* 0x39f00000 */

  2.5987625122e-05,		/* 0x37da0000 */

  7.5437128544e-08,		/* 0x33a20000 */

  6.0026650317e-11,		/* 0x2e840000 */

  7.3896444519e-13,		/* 0x2b500000 */

  5.3845816694e-15,		/* 0x27c20000 */

  5.6378512969e-18,		/* 0x22d00000 */

  8.3009228831e-20,		/* 0x1fc40000 */

  3.2756352257e-22,		/* 0x1bc60000 */

  6.3331015649e-25,		/* 0x17440000 */

};

static const float zero  = 0.0000000000e+00;

static const float one   = 1.0000000000;

static const float twon8 = 3.9062500000e-03;

static const float two8  = 2.5600000000e+02;

int32_t

__fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx)

{

  int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih, exp;

  float z, fw, f[20], fq[20], q[20];

  /* initialize jk */

  jp = jk = 9;

  /* determine jx,jv,q0, note that 3>q0 */

  jx = nx - 1;

  exp = __float_get_exp (e0) - 127;

  jv = (exp - 3) / 8;

  if (jv < 0)

    jv = 0;

  q0 = exp - 8 * (jv + 1);

  /* set up f[0] to f[jx+jk] where f[jx+jk] = two_over_pi[jv+jk] */

  j = jv - jx;

  m = jx + jk;

  for (i = 0; i <= m; i++, j++)

    f[i] = (j < 0) ? zero : two_over_pi[j];

  /* compute q[0],q[1],...q[jk] */

  for (i = 0; i <= jk; i++)

    {

      for (j = 0, fw = 0.0; j <= jx; j++)

	fw += x[j] * f[jx + i - j];

      q[i] = fw;

    }

  jz = jk;

recompute:

  /* distill q[] into iq[] reversingly */

  for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)

    {

      fw = __truncf (twon8 * z);

      iq[i] = (int32_t) (z - two8 * fw);

      z = q[j - 1] + fw;

    }

  /* compute n */

  z = __scalbnf (z, q0);	/* actual value of z */

  z -= 8.0 * __floorf (z * 0.125);	/* trim off integer >= 8 */

  n = (int32_t) z;

  z -= __truncf (z);

  ih = 0;

  if (q0 > 0)

    {				/* need iq[jz-1] to determine n */

      i = (iq[jz - 1] >> (8 - q0));

      n += i;

      iq[jz - 1] -= i << (8 - q0);

      ih = iq[jz - 1] >> (7 - q0);

    }

  else if (q0 == 0)

    ih = iq[jz - 1] >> 7;

  else if (z >= 0.5)

    ih = 2;

  if (ih > 0)

    {				/* q > 0.5 */

      n += 1;

      carry = 0;

      for (i = 0; i < jz; i++)

	{			/* compute 1-q */

	  j = iq[i];

	  if (carry == 0)

	    {

	      if (j != 0)

		{

		  carry = 1;

		  iq[i] = 0x100 - j;

		}

	    }

	  else

	    iq[i] = 0xff - j;

	}

      if (q0 > 0)

	{			/* rare case: chance is 1 in 12 */

	  switch (q0)

	    {

	    case 1:

	      iq[jz - 1] &= 0x7f;

	      break;

	    case 2:

	      iq[jz - 1] &= 0x3f;

	      break;

	    }

	}

      if (ih == 2)

	{

	  z = one - z;

	  if (carry != 0)

	    z -= __scalbnf (one, q0);

	}

    }

  /* check if recomputation is needed */

  if (z == zero)

    {

      j = 0;

      for (i = jz - 1; i >= jk; i--)

	j |= iq[i];

      if (j == 0)

	{			/* need recomputation */

	  for (k = 1; iq[jk - k] == 0; k++);	/* k = no. of terms needed */

	  for (i = jz + 1; i <= jz + k; i++)

	    {			/* add q[jz+1] to q[jz+k] */

	      f[jx + i] = two_over_pi[jv + i];

	      for (j = 0, fw = 0.0; j <= jx; j++)

		fw += x[j] * f[jx + i - j];

	      q[i] = fw;

	    }

	  jz += k;

	  goto recompute;

	}

    }

  /* chop off zero terms */

  if (z == 0.0)

    {

      jz -= 1;

      q0 -= 8;

      while (iq[jz] == 0)

	{

	  jz--;

	  q0 -= 8;

	}

    }

  else

    {				/* break z into 8-bit if necessary */

      z = __scalbnf (z, -q0);

      if (z >= two8)

	{

	  fw = __truncf (twon8 * z);

	  iq[jz] = (int32_t) (z - two8 * fw);

	  jz += 1;

	  q0 += 8;

	  iq[jz] = (int32_t) fw;

	}

      else

	iq[jz] = (int32_t) z;

    }

  /* convert integer "bit" chunk to floating-point value */

  fw = __scalbnf (one, q0);

  for (i = jz; i >= 0; i--)

    {

      q[i] = fw * (float) iq[i];

      fw *= twon8;

    }

  /* compute PIo2[0,...,jp]*q[jz,...,0] */

  for (i = jz; i >= 0; i--)

    {

      for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)

	fw += PIo2[k] * q[i + k];

      fq[jz - i] = fw;

    }

  /* compress fq[] into y[] */

  fw = 0.0;

  for (i = jz; i >= 0; i--)

    fw += fq[i];

  y[0] = (ih == 0) ? fw : -fw;

  fw = fq[0] - fw;

  for (i = 1; i <= jz; i++)

    fw += fq[i];

  y[1] = (ih == 0) ? fw : -fw;

  return n & 7;

}