text: /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunPro, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  
  /*
    Long double expansions are
    Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
    and are incorporated herein by permission of the author.  The author
    reserves the right to distribute this material elsewhere under different
    copying permissions.  These modifications are distributed here under
    the following terms:
  
      This 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.
  
      This 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 this library; if not, see
      <https://www.gnu.org/licenses/>.  */
  
  /* __kernel_tanl( x, y, k )
   * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
   * Input x is assumed to be bounded by ~pi/4 in magnitude.
   * Input y is the tail of x.
   * Input k indicates whether tan (if k=1) or
   * -1/tan (if k= -1) is returned.
   *
   * Algorithm
   *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
   *	2. if x < 2^-57, return x with inexact if x!=0.
   *	3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
   *          on [0,0.67433].
   *
   *	   Note: tan(x+y) = tan(x) + tan'(x)*y
   *		          ~ tan(x) + (1+x*x)*y
   *	   Therefore, for better accuracy in computing tan(x+y), let
   *		r = x^3 * R(x^2)
   *	   then
   *		tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
   *
   *      4. For x in [0.67433,pi/4],  let y = pi/4 - x, then
   *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
   *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
   */
  
  #include <float.h>
  #include <math.h>
  #include <math_private.h>
  #include <math-underflow.h>
  #include <libc-diag.h>
  
  static const long double
    one = 1.0L,
    pio4hi = 7.8539816339744830961566084581987569936977E-1L,
    pio4lo = 2.1679525325309452561992610065108379921906E-35L,
  
    /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
       0 <= x <= 0.6743316650390625
       Peak relative error 8.0e-36  */
   TH =  3.333333333333333333333333333333333333333E-1L,
   T0 = -1.813014711743583437742363284336855889393E7L,
   T1 =  1.320767960008972224312740075083259247618E6L,
   T2 = -2.626775478255838182468651821863299023956E4L,
   T3 =  1.764573356488504935415411383687150199315E2L,
   T4 = -3.333267763822178690794678978979803526092E-1L,
  
   U0 = -1.359761033807687578306772463253710042010E8L,
   U1 =  6.494370630656893175666729313065113194784E7L,
   U2 = -4.180787672237927475505536849168729386782E6L,
   U3 =  8.031643765106170040139966622980914621521E4L,
   U4 = -5.323131271912475695157127875560667378597E2L;
    /* 1.000000000000000000000000000000000000000E0 */
  
  
  long double
  __kernel_tanl (long double x, long double y, int iy)
  {
    long double z, r, v, w, s;
    int32_t ix, sign, hx, lx;
    double xhi;
  
    xhi = ldbl_high (x);
    EXTRACT_WORDS (hx, lx, xhi);
    ix = hx & 0x7fffffff;
    if (ix < 0x3c600000)		/* x < 2**-57 */
      {
        if ((int) x == 0)		/* generate inexact */
  	{
  	  if ((ix | lx | (iy + 1)) == 0)
  	    return one / fabs (x);
  	  else if (iy == 1)
  	    {
  	      math_check_force_underflow (x);
  	      return x;
  	    }
  	  else
  	    return -one / x;
  	}
      }
    if (ix >= 0x3fe59420) /* |x| >= 0.6743316650390625 */
      {
        if ((hx & 0x80000000) != 0)
  	{
  	  x = -x;
  	  y = -y;
  	  sign = -1;
  	}
        else
  	sign = 1;
        z = pio4hi - x;
        w = pio4lo - y;
        x = z + w;
        y = 0.0;
      }
    z = x * x;
    r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
    v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
    r = r / v;
  
    s = z * x;
    r = y + z * (s * r + y);
    r += TH * s;
    w = x + r;
    if (ix >= 0x3fe59420)
      {
        v = (long double) iy;
        w = (v - 2.0 * (x - (w * w / (w + v) - r)));
        /* SIGN is set for arguments that reach this code, but not
  	 otherwise, resulting in warnings that it may be used
  	 uninitialized although in the cases where it is used it has
  	 always been set.  */
        DIAG_PUSH_NEEDS_COMMENT;
        DIAG_IGNORE_NEEDS_COMMENT (5, "-Wmaybe-uninitialized");
        if (sign < 0)
  	w = -w;
        DIAG_POP_NEEDS_COMMENT;
        return w;
      }
    if (iy == 1)
      return w;
    else
      {				/* if allow error up to 2 ulp,
  				   simply return -1.0/(x+r) here */
        /*  compute -1.0/(x+r) accurately */
        long double u1, z1;
  
        u1 = ldbl_high (w);
        v = r - (u1 - x);		/* u1+v = r+x */
        z = -1.0 / w;
        z1 = ldbl_high (z);
        s = 1.0 + z1 * u1;
        return z1 + z * (s + z1 * v);
      }
  }
  