glibc/sysdeps/ieee754/dbl-64/s_tan.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001 Free Software Foundation
 *
 * This program 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 of the License, or
 * (at your option) any later version.
 *
 * This program 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 General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
 */
/*********************************************************************/
/*  MODULE_NAME: utan.c                                              */
/*                                                                   */
/*  FUNCTIONS: utan                                                  */
/*             tanMp                                                 */
/*                                                                   */
/*  FILES NEEDED:dla.h endian.h mpa.h mydefs.h utan.h                */
/*               branred.c sincos32.c mptan.c                        */
/*               utan.tbl                                            */
/*                                                                   */
/* An ultimate tan routine. Given an IEEE double machine number x    */
/* it computes the correctly rounded (to nearest) value of tan(x).   */
/* Assumption: Machine arithmetic operations are performed in        */
/* round to nearest mode of IEEE 754 standard.                       */
/*                                                                   */
/*********************************************************************/
#include "endian.h"
#include "dla.h"
#include "mpa.h"
#include "MathLib.h"
#include "math.h"

static double tanMp(double);
void __mptan(double, mp_no *, int);

double tan(double x) {
#include "utan.h"
#include "utan.tbl"

  int ux,i,n;
  double a,da,a2,b,db,c,dc,c1,cc1,c2,cc2,c3,cc3,fi,ffi,gi,pz,s,sy,
  t,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,w,x2,xn,xx2,y,ya,yya,z0,z,zz,z2,zz2;
  int p;
  number num,v;
  mp_no mpa,mpt1,mpt2;
#if 0
  mp_no mpy;
#endif

  int __branred(double, double *, double *);
  int __mpranred(double, mp_no *, int);

  /* x=+-INF, x=NaN */
  num.d = x;  ux = num.i[HIGH_HALF];
  if ((ux&0x7ff00000)==0x7ff00000) return x-x;

  w=(x<ZERO) ? -x : x;

  /* (I) The case abs(x) <= 1.259e-8 */
  if (w<=g1.d)  return x;

  /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
  if (w<=g2.d) {

    /* First stage */
    x2 = x*x;
    t2 = x*x2*(d3.d+x2*(d5.d+x2*(d7.d+x2*(d9.d+x2*d11.d))));
    if ((y=x+(t2-u1.d*t2)) == x+(t2+u1.d*t2))  return y;

    /* Second stage */
    c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
         x2*a27.d))))));
    EMULV(x,x,x2,xx2,t1,t2,t3,t4,t5)
    ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    MUL2(x ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(x    ,zero.d,c2,cc2,c1,cc1,t1,t2)
    if ((y=c1+(cc1-u2.d*c1)) == c1+(cc1+u2.d*c1))  return y;
    return tanMp(x);
  }

  /* (III) The case 0.0608 < abs(x) <= 0.787 */
  if (w<=g3.d) {

    /* First stage */
    i = ((int) (mfftnhf.d+TWO8*w));
    z = w-xfg[i][0].d;  z2 = z*z;   s = (x<ZERO) ? MONE : ONE;
    pz = z+z*z2*(e0.d+z2*e1.d);
    fi = xfg[i][1].d;   gi = xfg[i][2].d;   t2 = pz*(gi+fi)/(gi-pz);
    if ((y=fi+(t2-fi*u3.d))==fi+(t2+fi*u3.d))  return (s*y);
    t3 = (t2<ZERO) ? -t2 : t2;
    if ((y=fi+(t2-(t4=fi*ua3.d+t3*ub3.d)))==fi+(t2+t4))  return (s*y);

    /* Second stage */
    ffi = xfg[i][3].d;
    c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
    EMULV(z,z,z2,zz2,t1,t2,t3,t4,t5)
    ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
    MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
    MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    MUL2(z ,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(z ,zero.d,c2,cc2,c1,cc1,t1,t2)

    ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
    MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
    SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)
    DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)

    if ((y=c3+(cc3-u4.d*c3))==c3+(cc3+u4.d*c3))  return (s*y);
    return tanMp(x);
  }

  /* (---) The case 0.787 < abs(x) <= 25 */
  if (w<=g4.d) {
    /* Range reduction by algorithm i */
    t = (x*hpinv.d + toint.d);
    xn = t - toint.d;
    v.d = t;
    t1 = (x - xn*mp1.d) - xn*mp2.d;
    n =v.i[LOW_HALF] & 0x00000001;
    da = xn*mp3.d;
    a=t1-da;
    da = (t1-a)-da;
    if (a<ZERO)  {ya=-a;  yya=-da;  sy=MONE;}
    else         {ya= a;  yya= da;  sy= ONE;}

    /* (IV),(V) The case 0.787 < abs(x) <= 25,    abs(y) <= 1e-7 */
    if (ya<=gy1.d)  return tanMp(x);

    /* (VI) The case 0.787 < abs(x) <= 25,    1e-7 < abs(y) <= 0.0608 */
    if (ya<=gy2.d) {
      a2 = a*a;
      t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
      if (n) {
        /* First stage -cot */
        EADD(a,t2,b,db)
        DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
        if ((y=c+(dc-u6.d*c))==c+(dc+u6.d*c))  return (-y); }
      else {
        /* First stage tan */
        if ((y=a+(t2-u5.d*a))==a+(t2+u5.d*a))  return y; }
      /* Second stage */
      /* Range reduction by algorithm ii */
      t = (x*hpinv.d + toint.d);
      xn = t - toint.d;
      v.d = t;
      t1 = (x - xn*mp1.d) - xn*mp2.d;
      n =v.i[LOW_HALF] & 0x00000001;
      da = xn*pp3.d;
      t=t1-da;
      da = (t1-t)-da;
      t1 = xn*pp4.d;
      a = t - t1;
      da = ((t-a)-t1)+da;

      /* Second stage */
      EADD(a,da,t1,t2)   a=t1;  da=t2;
      MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
      c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
           x2*a27.d))))));
      ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a  ,da  ,c2,cc2,c1,cc1,t1,t2)

      if (n) {
        /* Second stage -cot */
        DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
        if ((y=c2+(cc2-u8.d*c2)) == c2+(cc2+u8.d*c2))  return (-y); }
      else {
        /* Second stage tan */
        if ((y=c1+(cc1-u7.d*c1)) == c1+(cc1+u7.d*c1))  return y; }
      return tanMp(x);
    }

    /* (VII) The case 0.787 < abs(x) <= 25,    0.0608 < abs(y) <= 0.787 */

    /* First stage */
    i = ((int) (mfftnhf.d+TWO8*ya));
    z = (z0=(ya-xfg[i][0].d))+yya;  z2 = z*z;
    pz = z+z*z2*(e0.d+z2*e1.d);
    fi = xfg[i][1].d;   gi = xfg[i][2].d;

    if (n) {
      /* -cot */
      t2 = pz*(fi+gi)/(fi+pz);
      if ((y=gi-(t2-gi*u10.d))==gi-(t2+gi*u10.d))  return (-sy*y);
      t3 = (t2<ZERO) ? -t2 : t2;
      if ((y=gi-(t2-(t4=gi*ua10.d+t3*ub10.d)))==gi-(t2+t4))  return (-sy*y); }
    else   {
      /* tan */
      t2 = pz*(gi+fi)/(gi-pz);
      if ((y=fi+(t2-fi*u9.d))==fi+(t2+fi*u9.d))  return (sy*y);
      t3 = (t2<ZERO) ? -t2 : t2;
      if ((y=fi+(t2-(t4=fi*ua9.d+t3*ub9.d)))==fi+(t2+t4))  return (sy*y); }

    /* Second stage */
    ffi = xfg[i][3].d;
    EADD(z0,yya,z,zz)
    MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
    c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
    ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
    MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
    MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)

    ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
    MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
    SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)

    if (n) {
      /* -cot */
      DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
      if ((y=c3+(cc3-u12.d*c3))==c3+(cc3+u12.d*c3))  return (-sy*y); }
    else {
      /* tan */
      DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
      if ((y=c3+(cc3-u11.d*c3))==c3+(cc3+u11.d*c3))  return (sy*y); }

    return tanMp(x);
  }

  /* (---) The case 25 < abs(x) <= 1e8 */
  if (w<=g5.d) {
    /* Range reduction by algorithm ii */
    t = (x*hpinv.d + toint.d);
    xn = t - toint.d;
    v.d = t;
    t1 = (x - xn*mp1.d) - xn*mp2.d;
    n =v.i[LOW_HALF] & 0x00000001;
    da = xn*pp3.d;
    t=t1-da;
    da = (t1-t)-da;
    t1 = xn*pp4.d;
    a = t - t1;
    da = ((t-a)-t1)+da;
    EADD(a,da,t1,t2)   a=t1;  da=t2;
    if (a<ZERO)  {ya=-a;  yya=-da;  sy=MONE;}
    else         {ya= a;  yya= da;  sy= ONE;}

    /* (+++) The case 25 < abs(x) <= 1e8,    abs(y) <= 1e-7 */
    if (ya<=gy1.d)  return tanMp(x);

    /* (VIII) The case 25 < abs(x) <= 1e8,    1e-7 < abs(y) <= 0.0608 */
    if (ya<=gy2.d) {
      a2 = a*a;
      t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
      if (n) {
        /* First stage -cot */
        EADD(a,t2,b,db)
        DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
        if ((y=c+(dc-u14.d*c))==c+(dc+u14.d*c))  return (-y); }
      else {
        /* First stage tan */
        if ((y=a+(t2-u13.d*a))==a+(t2+u13.d*a))  return y; }

      /* Second stage */
      MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
      c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
           x2*a27.d))))));
      ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
      MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
      MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
      ADD2(a  ,da  ,c2,cc2,c1,cc1,t1,t2)

      if (n) {
        /* Second stage -cot */
        DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
        if ((y=c2+(cc2-u16.d*c2)) == c2+(cc2+u16.d*c2))  return (-y); }
      else {
        /* Second stage tan */
        if ((y=c1+(cc1-u15.d*c1)) == c1+(cc1+u15.d*c1))  return (y); }
      return tanMp(x);
    }

    /* (IX) The case 25 < abs(x) <= 1e8,    0.0608 < abs(y) <= 0.787 */
    /* First stage */
    i = ((int) (mfftnhf.d+TWO8*ya));
    z = (z0=(ya-xfg[i][0].d))+yya;  z2 = z*z;
    pz = z+z*z2*(e0.d+z2*e1.d);
    fi = xfg[i][1].d;   gi = xfg[i][2].d;

    if (n) {
      /* -cot */
      t2 = pz*(fi+gi)/(fi+pz);
      if ((y=gi-(t2-gi*u18.d))==gi-(t2+gi*u18.d))  return (-sy*y);
      t3 = (t2<ZERO) ? -t2 : t2;
      if ((y=gi-(t2-(t4=gi*ua18.d+t3*ub18.d)))==gi-(t2+t4))  return (-sy*y); }
    else   {
      /* tan */
      t2 = pz*(gi+fi)/(gi-pz);
      if ((y=fi+(t2-fi*u17.d))==fi+(t2+fi*u17.d))  return (sy*y);
      t3 = (t2<ZERO) ? -t2 : t2;
      if ((y=fi+(t2-(t4=fi*ua17.d+t3*ub17.d)))==fi+(t2+t4))  return (sy*y); }

    /* Second stage */
    ffi = xfg[i][3].d;
    EADD(z0,yya,z,zz)
    MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
    c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
    ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
    MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
    MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)

    ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
    MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
    SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)

    if (n) {
      /* -cot */
      DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
      if ((y=c3+(cc3-u20.d*c3))==c3+(cc3+u20.d*c3))  return (-sy*y); }
    else {
      /* tan */
      DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
      if ((y=c3+(cc3-u19.d*c3))==c3+(cc3+u19.d*c3))  return (sy*y); }
    return tanMp(x);
  }

  /* (---) The case 1e8 < abs(x) < 2**1024 */
  /* Range reduction by algorithm iii */
  n = (__branred(x,&a,&da)) & 0x00000001;
  EADD(a,da,t1,t2)   a=t1;  da=t2;
  if (a<ZERO)  {ya=-a;  yya=-da;  sy=MONE;}
  else         {ya= a;  yya= da;  sy= ONE;}

  /* (+++) The case 1e8 < abs(x) < 2**1024,    abs(y) <= 1e-7 */
  if (ya<=gy1.d)  return tanMp(x);

  /* (X) The case 1e8 < abs(x) < 2**1024,    1e-7 < abs(y) <= 0.0608 */
  if (ya<=gy2.d) {
    a2 = a*a;
    t2 = da+a*a2*(d3.d+a2*(d5.d+a2*(d7.d+a2*(d9.d+a2*d11.d))));
    if (n) {
      /* First stage -cot */
      EADD(a,t2,b,db)
      DIV2(one.d,zero.d,b,db,c,dc,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
      if ((y=c+(dc-u22.d*c))==c+(dc+u22.d*c))  return (-y); }
    else {
      /* First stage tan */
      if ((y=a+(t2-u21.d*a))==a+(t2+u21.d*a))  return y; }

    /* Second stage */
    /* Reduction by algorithm iv */
    p=10;    n = (__mpranred(x,&mpa,p)) & 0x00000001;
    __mp_dbl(&mpa,&a,p);        __dbl_mp(a,&mpt1,p);
    __sub(&mpa,&mpt1,&mpt2,p);  __mp_dbl(&mpt2,&da,p);

    MUL2(a,da,a,da,x2,xx2,t1,t2,t3,t4,t5,t6,t7,t8)
    c1 = x2*(a15.d+x2*(a17.d+x2*(a19.d+x2*(a21.d+x2*(a23.d+x2*(a25.d+
         x2*a27.d))))));
    ADD2(a13.d,aa13.d,c1,zero.d,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a11.d,aa11.d,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a9.d ,aa9.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a7.d ,aa7.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a5.d ,aa5.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a3.d ,aa3.d ,c1,cc1,c2,cc2,t1,t2)
    MUL2(x2,xx2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
    MUL2(a ,da ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
    ADD2(a    ,da    ,c2,cc2,c1,cc1,t1,t2)

    if (n) {
      /* Second stage -cot */
      DIV2(one.d,zero.d,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
      if ((y=c2+(cc2-u24.d*c2)) == c2+(cc2+u24.d*c2))  return (-y); }
    else {
      /* Second stage tan */
      if ((y=c1+(cc1-u23.d*c1)) == c1+(cc1+u23.d*c1))  return y; }
    return tanMp(x);
  }

  /* (XI) The case 1e8 < abs(x) < 2**1024,    0.0608 < abs(y) <= 0.787 */
  /* First stage */
  i = ((int) (mfftnhf.d+TWO8*ya));
  z = (z0=(ya-xfg[i][0].d))+yya;  z2 = z*z;
  pz = z+z*z2*(e0.d+z2*e1.d);
  fi = xfg[i][1].d;   gi = xfg[i][2].d;

  if (n) {
    /* -cot */
    t2 = pz*(fi+gi)/(fi+pz);
    if ((y=gi-(t2-gi*u26.d))==gi-(t2+gi*u26.d))  return (-sy*y);
    t3 = (t2<ZERO) ? -t2 : t2;
    if ((y=gi-(t2-(t4=gi*ua26.d+t3*ub26.d)))==gi-(t2+t4))  return (-sy*y); }
  else   {
    /* tan */
    t2 = pz*(gi+fi)/(gi-pz);
    if ((y=fi+(t2-fi*u25.d))==fi+(t2+fi*u25.d))  return (sy*y);
    t3 = (t2<ZERO) ? -t2 : t2;
    if ((y=fi+(t2-(t4=fi*ua25.d+t3*ub25.d)))==fi+(t2+t4))  return (sy*y); }

  /* Second stage */
  ffi = xfg[i][3].d;
  EADD(z0,yya,z,zz)
  MUL2(z,zz,z,zz,z2,zz2,t1,t2,t3,t4,t5,t6,t7,t8)
  c1 = z2*(a7.d+z2*(a9.d+z2*a11.d));
  ADD2(a5.d,aa5.d,c1,zero.d,c2,cc2,t1,t2)
  MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(a3.d,aa3.d,c1,cc1,c2,cc2,t1,t2)
  MUL2(z2,zz2,c2,cc2,c1,cc1,t1,t2,t3,t4,t5,t6,t7,t8)
  MUL2(z ,zz ,c1,cc1,c2,cc2,t1,t2,t3,t4,t5,t6,t7,t8)
  ADD2(z ,zz ,c2,cc2,c1,cc1,t1,t2)

  ADD2(fi ,ffi,c1,cc1,c2,cc2,t1,t2)
  MUL2(fi ,ffi,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8)
  SUB2(one.d,zero.d,c3,cc3,c1,cc1,t1,t2)

  if (n) {
    /* -cot */
    DIV2(c1,cc1,c2,cc2,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
    if ((y=c3+(cc3-u28.d*c3))==c3+(cc3+u28.d*c3))  return (-sy*y); }
  else {
    /* tan */
    DIV2(c2,cc2,c1,cc1,c3,cc3,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10)
    if ((y=c3+(cc3-u27.d*c3))==c3+(cc3+u27.d*c3))  return (sy*y); }
  return tanMp(x);
}


/* multiple precision stage                                              */
/* Convert x to multi precision number,compute tan(x) by mptan() routine */
/* and converts result back to double                                    */
static double tanMp(double x)
{
  int p;
  double y;
  mp_no mpy;
  p=32;
  __mptan(x, &mpy, p);
  __mp_dbl(&mpy,&y,p);
  return y;
}

#ifdef NO_LONG_DOUBLE
weak_alias (tan, tanl)
#endif