/* Compute sine and cosine of argument optimized with vector.

   Copyright (C) 2017 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

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

   modify it under the terms of the GNU Lesser General Public

   License as published by the Free Software Foundation; either

   version 2.1 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

   Lesser General Public License for more details.

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

   License along with the GNU C Library; if not, see

   <http://www.gnu.org/licenses/>.  */

#include <errno.h>

#include <math.h>

#include <math_private.h>

#include <x86intrin.h>

#include <libm-alias-float.h>

#include "s_sincosf.h"

#define SINCOSF __sincosf_fma

#ifndef SINCOSF

# define SINCOSF_FUNC __sincosf

#else

# define SINCOSF_FUNC SINCOSF

#endif

/* Chebyshev constants for sin and cos, range -PI/4 - PI/4.  */

static const __v2df V0 = { -0x1.5555555551cd9p-3, -0x1.ffffffffe98aep-2};

static const __v2df V1 = { 0x1.1111110c2688bp-7, 0x1.55555545c50c7p-5 };

static const __v2df V2 = { -0x1.a019f8b4bd1f9p-13, -0x1.6c16b348b6874p-10 };

static const __v2df V3 = { 0x1.71d7264e6b5b4p-19, 0x1.a00eb9ac43ccp-16 };

static const __v2df V4 = { -0x1.a947e1674b58ap-26, -0x1.23c97dd8844d7p-22 };

/* Chebyshev constants for sin and cos, range 2^-27 - 2^-5.  */

static const __v2df VC0 = { -0x1.555555543d49dp-3, -0x1.fffffff5cc6fdp-2 };

static const __v2df VC1 = { 0x1.110f475cec8c5p-7, 0x1.55514b178dac5p-5 };

static const __v2df v2ones = { 1.0, 1.0 };

/* Compute the sine and cosine values using Chebyshev polynomials where

   THETA is the range reduced absolute value of the input

   and it is less than Pi/4,

   N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide

   whether a sine or cosine approximation is more accurate and

   SIGNBIT is used to add the correct sign after the Chebyshev

   polynomial is computed.  */

static void

reduced_sincos (const double theta, const unsigned int n,

		const unsigned int signbit, float *sinx, float *cosx)

{

  __v2df v2x, v2sx, v2cx;

  const __v2df v2theta = { theta, theta };

  const __v2df v2theta2 = v2theta * v2theta;

  /* Here sinf() and cosf() are calculated using sin Chebyshev polynomial:

     x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))).  */

  v2x = V3 + v2theta2 * V4;    /* S3+x^2*S4.  */

  v2x = V2 + v2theta2 * v2x;   /* S2+x^2*(S3+x^2*S4).  */

  v2x = V1 + v2theta2 * v2x;   /* S1+x^2*(S2+x^2*(S3+x^2*S4)).  */

  v2x = V0 + v2theta2 * v2x;   /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))).  */

  v2x = v2theta2 * v2x;

  v2cx = v2ones + v2x;

  v2sx = v2theta + v2theta * v2x;

  /* We are operating on |x|, so we need to add back the original

     signbit for sinf.  */

  /* Determine positive or negative primary interval.  */

  /* Are we in the primary interval of sin or cos?  */

  if ((n & 2) == 0)

    {

      const __v2df v2sign =

	{

	  ones[((n >> 2) & 1) ^ signbit],

	  ones[((n + 2) >> 2) & 1]

	};

      v2cx[0] = v2sx[0];

      v2cx *= v2sign;

      __v4sf v4sx = _mm_cvtpd_ps (v2cx);

      *sinx = v4sx[0];

      *cosx = v4sx[1];

    }

  else

    {

      const __v2df v2sign =

	{

	  ones[((n + 2) >> 2) & 1],

	  ones[((n >> 2) & 1) ^ signbit]

	};

      v2cx[0] = v2sx[0];

      v2cx *= v2sign;

      __v4sf v4sx = _mm_cvtpd_ps (v2cx);

      *sinx = v4sx[1];

      *cosx = v4sx[0];

    }

}

void

SINCOSF_FUNC (float x, float *sinx, float *cosx)

{

  double theta = x;

  double abstheta = fabs (theta);

  uint32_t ix, xi;

  GET_FLOAT_WORD (xi, x);

  /* |x| */

  ix = xi & 0x7fffffff;

  /* If |x|< Pi/4.  */

  if (ix < 0x3f490fdb)

    {

      if (ix >= 0x3d000000) /* |x| >= 2^-5.  */

	{

	  __v2df v2x, v2sx, v2cx;

	  const __v2df v2theta = { theta, theta };

	  const __v2df v2theta2 = v2theta * v2theta;

	  /* Chebyshev polynomial of the form for sin and cos.  */

	  v2x = V3 + v2theta2 * V4;

	  v2x = V2 + v2theta2 * v2x;

	  v2x = V1 + v2theta2 * v2x;

	  v2x = V0 + v2theta2 * v2x;

	  v2x = v2theta2 * v2x;

	  v2cx = v2ones + v2x;

	  v2sx = v2theta + v2theta * v2x;

	  v2cx[0] = v2sx[0];

	  __v4sf v4sx = _mm_cvtpd_ps (v2cx);

	  *sinx = v4sx[0];

	  *cosx = v4sx[1];

	}

      else if (ix >= 0x32000000)     /* |x| >= 2^-27.  */

	{

	  /* A simpler Chebyshev approximation is close enough for this range:

	     for sin: x+x^3*(SS0+x^2*SS1)

	     for cos: 1.0+x^2*(CC0+x^3*CC1).  */

	  __v2df v2x, v2sx, v2cx;

	  const __v2df v2theta = { theta, theta };

	  const __v2df v2theta2 = v2theta * v2theta;

	  v2x = VC0 + v2theta * v2theta2 * VC1;

	  v2x = v2theta2 * v2x;

	  v2cx = v2ones + v2x;

	  v2sx = v2theta + v2theta * v2x;

	  v2cx[0] = v2sx[0];

	  __v4sf v4sx = _mm_cvtpd_ps (v2cx);

	  *sinx = v4sx[0];

	  *cosx = v4sx[1];

	}

      else

	{

	  /* Handle some special cases.  */

	  if (ix)

	    *sinx = theta - (theta * SMALL);

	  else

	    *sinx = theta;

	  *cosx = 1.0 - abstheta;

	}

    }

  else                          /* |x| >= Pi/4.  */

    {

      unsigned int signbit = xi >> 31;

      if (ix < 0x40e231d6) /* |x| < 9*Pi/4.  */

	{

	  /* There are cases where FE_UPWARD rounding mode can

	     produce a result of abstheta * inv_PI_4 == 9,

	     where abstheta < 9pi/4, so the domain for

	     pio2_table must go to 5 (9 / 2 + 1).  */

	  unsigned int n = (abstheta * inv_PI_4) + 1;

	  theta = abstheta - pio2_table[n / 2];

	  reduced_sincos (theta, n, signbit, sinx, cosx);

	}

      else if (ix < 0x7f800000)

	{

	  if (ix < 0x4b000000)     /* |x| < 2^23.  */

	    {

	      unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1;

	      double x = n / 2;

	      theta = (abstheta - x * PI_2_hi) - x * PI_2_lo;

	      /* Argument reduction needed.  */

	      reduced_sincos (theta, n, signbit, sinx, cosx);

	    }

	  else                  /* |x| >= 2^23.  */

	    {

	      x = fabsf (x);

	      int exponent

	        = (ix >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS;

	      exponent += 3;

	      exponent /= 28;

	      double a = invpio4_table[exponent] * x;

	      double b = invpio4_table[exponent + 1] * x;

	      double c = invpio4_table[exponent + 2] * x;

	      double d = invpio4_table[exponent + 3] * x;

	      uint64_t l = a;

	      l &= ~0x7;

	      a -= l;

	      double e = a + b;

	      l = e;

	      e = a - l;

	      if (l & 1)

	        {

	          e -= 1.0;

	          e += b;

	          e += c;

	          e += d;

	          e *= M_PI_4;

		  reduced_sincos (e, l + 1, signbit, sinx, cosx);

	        }

	      else

		{

		  e += b;

		  e += c;

		  e += d;

		  if (e <= 1.0)

		    {

		      e *= M_PI_4;

		      reduced_sincos (e, l + 1, signbit, sinx, cosx);

		    }

		  else

		    {

		      l++;

		      e -= 2.0;

		      e *= M_PI_4;

		      reduced_sincos (e, l + 1, signbit, sinx, cosx);

		    }

		}

	    }

	}

      else

	{

	  if (ix == 0x7f800000)

	    __set_errno (EDOM);

	  /* sin/cos(Inf or NaN) is NaN.  */

	  *sinx = *cosx = x - x;

	}

    }

}

#ifndef SINCOSF

libm_alias_float (__sincos, sincos)

#endif