text: /* From: @(#)k_tan.c 1.5 04/04/22 SMI */
  
  /*
   * ====================================================
   * Copyright 2004 Sun Microsystems, Inc.  All Rights Reserved.
   * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
   *
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  
  
  /*
   * ld80 version of k_tan.c.  See ../src/k_tan.c for most comments.
   */
  
  #include "math.h"
  #include "../math_private.h"
  
  /*
   * Domain [-0.67434, 0.67434], range ~[-2.25e-22, 1.921e-22]
   * |tan(x)/x - t(x)| < 2**-71.9
   *
   * See k_cosl.c for more details about the polynomial.
   */
  #if defined(__amd64__) || defined(__i386__)
  /* Long double constants are slow on these arches, and broken on i386. */
  static const volatile double
  T3hi =  0.33333333333333331,		/*  0x15555555555555.0p-54 */
  T3lo =  1.8350121769317163e-17,		/*  0x15280000000000.0p-108 */
  T5hi =  0.13333333333333336,		/*  0x11111111111112.0p-55 */
  T5lo =  1.3051083651294260e-17,		/*  0x1e180000000000.0p-109 */
  T7hi =  0.053968253968250494,		/*  0x1ba1ba1ba1b827.0p-57 */
  T7lo =  3.1509625637859973e-18,		/*  0x1d100000000000.0p-111 */
  pio4_hi =  0.78539816339744828,		/*  0x1921fb54442d18.0p-53 */
  pio4_lo =  3.0628711372715500e-17,	/*  0x11a80000000000.0p-107 */
  pio4lo_hi = -1.2541394031670831e-20,	/* -0x1d9cceba3f91f2.0p-119 */
  pio4lo_lo =  6.1493048227390915e-37;	/*  0x1a280000000000.0p-173 */
  #define	T3	((long double)T3hi + T3lo)
  #define	T5	((long double)T5hi + T5lo)
  #define	T7	((long double)T7hi + T7lo)
  #define	pio4	((long double)pio4_hi + pio4_lo)
  #define	pio4lo	((long double)pio4lo_hi + pio4lo_lo)
  #else
  static const long double
  T3 =   0.333333333333333333180L,	/*  0xaaaaaaaaaaaaaaa5.0p-65 */
  T5 =   0.133333333333333372290L,	/*  0x88888888888893c3.0p-66 */
  T7 =   0.0539682539682504975744L,	/*  0xdd0dd0dd0dc13ba2.0p-68 */
  pio4 = 0.785398163397448309628L,	/*  0xc90fdaa22168c235.0p-64 */
  pio4lo = -1.25413940316708300586e-20L;	/* -0xece675d1fc8f8cbb.0p-130 */
  #endif
  
  static const double
  T9  =  0.021869488536312216,		/*  0x1664f4882cc1c2.0p-58 */
  T11 =  0.0088632355256619590,		/*  0x1226e355c17612.0p-59 */
  T13 =  0.0035921281113786528,		/*  0x1d6d3d185d7ff8.0p-61 */
  T15 =  0.0014558334756312418,		/*  0x17da354aa3f96b.0p-62 */
  T17 =  0.00059003538700862256,		/*  0x13559358685b83.0p-63 */
  T19 =  0.00023907843576635544,		/*  0x1f56242026b5be.0p-65 */
  T21 =  0.000097154625656538905,		/*  0x1977efc26806f4.0p-66 */
  T23 =  0.000038440165747303162,		/*  0x14275a09b3ceac.0p-67 */
  T25 =  0.000018082171885432524,		/*  0x12f5e563e5487e.0p-68 */
  T27 =  0.0000024196006108814377,	/*  0x144c0d80cc6896.0p-71 */
  T29 =  0.0000078293456938132840,	/*  0x106b59141a6cb3.0p-69 */
  T31 = -0.0000032609076735050182,	/* -0x1b5abef3ba4b59.0p-71 */
  T33 =  0.0000023261313142559411;	/*  0x13835436c0c87f.0p-71 */
  
  long double
  __kernel_tanl(long double x, long double y, int iy) {
  	long double z, r, v, w, s;
  	long double osign;
  	int i;
  
  	iy = (iy == 1 ? -1 : 1);	/* XXX recover original interface */
  	osign = (x >= 0 ? 1.0 : -1.0);	/* XXX slow, probably wrong for -0 */
  	if (fabsl(x) >= 0.67434) {
  		if (x < 0) {
  			x = -x;
  			y = -y;
  		}
  		z = pio4 - x;
  		w = pio4lo - y;
  		x = z + w;
  		y = 0.0;
  		i = 1;
  	} else
  		i = 0;
  	z = x * x;
  	w = z * z;
  	r = T5 + w * (T9 + w * (T13 + w * (T17 + w * (T21 +
  	    w * (T25 + w * (T29 + w * T33))))));
  	v = z * (T7 + w * (T11 + w * (T15 + w * (T19 + w * (T23 +
  	    w * (T27 + w * T31))))));
  	s = z * x;
  	r = y + z * (s * (r + v) + y);
  	r += T3 * s;
  	w = x + r;
  	if (i == 1) {
  		v = (long double) iy;
  		return osign *
  			(v - 2.0 * (x - (w * w / (w + v) - r)));
  	}
  	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 a, t;
  		z = w;
  		z = z + 0x1p32 - 0x1p32;
  		v = r - (z - x);	/* z+v = r+x */
  		t = a = -1.0 / w;	/* a = -1.0/w */
  		t = t + 0x1p32 - 0x1p32;
  		s = 1.0 + t * z;
  		return t + a * (s + t * v);
  	}
  }
  