Update.

2001-03-11  Ulrich Drepper  <drepper@redhat.com>

	Last-bit accurate math library implementation by IBM Haifa.
	Contributed by Abraham Ziv <ziv@il.ibm.com>, Moshe Olshansky
	<olshansk@il.ibm.com>, Ealan Henis <ealan@il.ibm.com>, and
	Anna Reitman <reitman@il.ibm.com>.
	* math/Makefile (dbl-only-routines): New variable.
	(libm-routines): Add $(dbl-only-routines).
	* sysdeps/ieee754/dbl-64/e_acos.c: Empty, definition is in e_asin.c.
	* sysdeps/ieee754/dbl-64/e_asin.c: Replaced with accurate asin
	implementation.
	* sysdeps/ieee754/dbl-64/e_atan2.c: Replaced with accurate atan2
	implementation.
	* sysdeps/ieee754/dbl-64/e_exp.c: Replaced with accurate exp
	implementation.
	* sysdeps/ieee754/dbl-64/e_lgamma_r.c: Don't use __kernel_sin and
	__kernel_cos.
	* sysdeps/ieee754/dbl-64/e_log.c: Replaced with accurate log
	implementation.
	* sysdeps/ieee754/dbl-64/e_remainder.c: Replaced with accurate
	remainder implementation.
	* sysdeps/ieee754/dbl-64/e_pow.c: Replaced with accurate pow
	implementation.
	* sysdeps/ieee754/dbl-64/e_sqrt.c: Replaced with accurate sqrt
	implementation.
	* sysdeps/ieee754/dbl-64/k_cos.c: Empty, definition is in s_sin.c.
	* sysdeps/ieee754/dbl-64/k_sin.c: Empty, definition is in s_sin.c.
	* sysdeps/ieee754/dbl-64/s_atan.c: Replaced with accurate atan
	implementation.
	* sysdeps/ieee754/dbl-64/s_cos.c: Empty, definition is in s_sin.c.
	* sysdeps/ieee754/dbl-64/s_sin.c: Replaced with accurate sin/cos
	implementation.
	* sysdeps/ieee754/dbl-64/s_sincos.c: Rewritten to not use __kernel_sin
	and __kernel_cos.
	* sysdeps/ieee754/dbl-64/s_tan.c: Replaced with accurate tan
	implementation.
	* sysdeps/ieee754/dbl-64/Dist: Add new non-code files.
	* sysdeps/ieee754/dbl-64/MathLib.h: New file.
	* sysdeps/ieee754/dbl-64/asincos.tbl: New file.
	* sysdeps/ieee754/dbl-64/atnat.h: New file.
	* sysdeps/ieee754/dbl-64/atnat2.h: New file.
	* sysdeps/ieee754/dbl-64/branred.c: New file.
	* sysdeps/ieee754/dbl-64/branred.h: New file.
	* sysdeps/ieee754/dbl-64/dla.h: New file.
	* sysdeps/ieee754/dbl-64/doasin.c: New file.
	* sysdeps/ieee754/dbl-64/doasin.h: New file.
	* sysdeps/ieee754/dbl-64/dosincos.c: New file.
	* sysdeps/ieee754/dbl-64/dosincos.h: New file.
	* sysdeps/ieee754/dbl-64/endian.h: New file.
	* sysdeps/ieee754/dbl-64/halfulp.c: New file.
	* sysdeps/ieee754/dbl-64/mpa.c: New file.
	* sysdeps/ieee754/dbl-64/mpa.h: New file.
	* sysdeps/ieee754/dbl-64/mpa2.h: New file.
	* sysdeps/ieee754/dbl-64/mpatan.c: New file.
	* sysdeps/ieee754/dbl-64/mpatan.h: New file.
	* sysdeps/ieee754/dbl-64/mpatan2.c: New file.
	* sysdeps/ieee754/dbl-64/mpexp.c: New file.
	* sysdeps/ieee754/dbl-64/mpexp.h: New file.
	* sysdeps/ieee754/dbl-64/mplog.c: New file.
	* sysdeps/ieee754/dbl-64/mplog.h: New file.
	* sysdeps/ieee754/dbl-64/mpsqrt.c: New file.
	* sysdeps/ieee754/dbl-64/mpsqrt.h: New file.
	* sysdeps/ieee754/dbl-64/mptan.c: New file.
	* sysdeps/ieee754/dbl-64/mydefs.h: New file.
	* sysdeps/ieee754/dbl-64/powtwo.tbl: New file.
	* sysdeps/ieee754/dbl-64/root.tbl: New file.
	* sysdeps/ieee754/dbl-64/sincos.tbl: New file.
	* sysdeps/ieee754/dbl-64/sincos32.c: New file.
	* sysdeps/ieee754/dbl-64/sincos32.h: New file.
	* sysdeps/ieee754/dbl-64/slowexp.c: New file.
	* sysdeps/ieee754/dbl-64/slowpow.c: New file.
	* sysdeps/ieee754/dbl-64/uasncs.h: New file.
	* sysdeps/ieee754/dbl-64/uatan.tbl: New file.
	* sysdeps/ieee754/dbl-64/uexp.h: New file.
	* sysdeps/ieee754/dbl-64/uexp.tbl: New file.
	* sysdeps/ieee754/dbl-64/ulog.h: New file.
	* sysdeps/ieee754/dbl-64/ulog.tbl: New file.
	* sysdeps/ieee754/dbl-64/upow.h: New file.
	* sysdeps/ieee754/dbl-64/upow.tbl: New file.
	* sysdeps/ieee754/dbl-64/urem.h: New file.
	* sysdeps/ieee754/dbl-64/uroot.h: New file.
	* sysdeps/ieee754/dbl-64/usncs.h: New file.
	* sysdeps/ieee754/dbl-64/utan.h: New file.
	* sysdeps/ieee754/dbl-64/utan.tbl: New file.
	* sysdeps/i386/fpu/branred.c: New file.
	* sysdeps/i386/fpu/doasin.c: New file.
	* sysdeps/i386/fpu/dosincos.c: New file.
	* sysdeps/i386/fpu/halfulp.c: New file.
	* sysdeps/i386/fpu/mpa.c: New file.
	* sysdeps/i386/fpu/mpatan.c: New file.
	* sysdeps/i386/fpu/mpatan2.c: New file.
	* sysdeps/i386/fpu/mpexp.c: New file.
	* sysdeps/i386/fpu/mplog.c: New file.
	* sysdeps/i386/fpu/mpsqrt.c: New file.
	* sysdeps/i386/fpu/mptan.c: New file.
	* sysdeps/i386/fpu/sincos32.c: New file.
	* sysdeps/i386/fpu/slowexp.c: New file.
	* sysdeps/i386/fpu/slowpow.c: New file.
	* sysdeps/ia64/fpu/branred.c: New file.
	* sysdeps/ia64/fpu/doasin.c: New file.
	* sysdeps/ia64/fpu/dosincos.c: New file.
	* sysdeps/ia64/fpu/halfulp.c: New file.
	* sysdeps/ia64/fpu/mpa.c: New file.
	* sysdeps/ia64/fpu/mpatan.c: New file.
	* sysdeps/ia64/fpu/mpatan2.c: New file.
	* sysdeps/ia64/fpu/mpexp.c: New file.
	* sysdeps/ia64/fpu/mplog.c: New file.
	* sysdeps/ia64/fpu/mpsqrt.c: New file.
	* sysdeps/ia64/fpu/mptan.c: New file.
	* sysdeps/ia64/fpu/sincos32.c: New file.
	* sysdeps/ia64/fpu/slowexp.c: New file.
	* sysdeps/ia64/fpu/slowpow.c: New file.
	* sysdeps/m68k/fpu/branred.c: New file.
	* sysdeps/m68k/fpu/doasin.c: New file.
	* sysdeps/m68k/fpu/dosincos.c: New file.
	* sysdeps/m68k/fpu/halfulp.c: New file.
	* sysdeps/m68k/fpu/mpa.c: New file.
	* sysdeps/m68k/fpu/mpatan.c: New file.
	* sysdeps/m68k/fpu/mpatan2.c: New file.
	* sysdeps/m68k/fpu/mpexp.c: New file.
	* sysdeps/m68k/fpu/mplog.c: New file.
	* sysdeps/m68k/fpu/mpsqrt.c: New file.
	* sysdeps/m68k/fpu/mptan.c: New file.
	* sysdeps/m68k/fpu/sincos32.c: New file.
	* sysdeps/m68k/fpu/slowexp.c: New file.
	* sysdeps/m68k/fpu/slowpow.c: New file.

	* iconvdata/gconv-modules: Add a number of alias, mostly for IBM
	codepages.

1 files changed, 466 insertions, 67 deletions

diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c
index 714cf27dd2..2db8673389 100644
--- a/sysdeps/ieee754/dbl-64/s_tan.c
+++ b/sysdeps/ieee754/dbl-64/s_tan.c
@@ -1,81 +1,480 @@
-/* @(#)s_tan.c 5.1 93/09/24 */
 /*
- * ====================================================
- * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ * IBM Accurate Mathematical Library
+ * Copyright (c) International Business Machines Corp., 2001
  *
- * 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.
- * ====================================================
- */
-
-#if defined(LIBM_SCCS) && !defined(lint)
-static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $";
-#endif
-
-/* tan(x)
- * Return tangent function of x.
- *
- * kernel function:
- *	__kernel_tan		... tangent function on [-pi/4,pi/4]
- *	__ieee754_rem_pio2	... argument reduction routine
- *
- * Method.
- *      Let S,C and T denote the sin, cos and tan respectively on
- *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
- *	in [-pi/4 , +pi/4], and let n = k mod 4.
- *	We have
- *
- *          n        sin(x)      cos(x)        tan(x)
- *     ----------------------------------------------------------
- *	    0	       S	   C		 T
- *	    1	       C	  -S		-1/T
- *	    2	      -S	  -C		 T
- *	    3	      -C	   S		-1/T
- *     ----------------------------------------------------------
+ * 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.
  *
- * Special cases:
- *      Let trig be any of sin, cos, or tan.
- *      trig(+-INF)  is NaN, with signals;
- *      trig(NaN)    is that NaN;
+ * 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.
  *
- * Accuracy:
- *	TRIG(x) returns trig(x) nearly rounded
+ * 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"
+static double tanMp(double);
+void __mptan(double, mp_no *, int);
 
-#include "math.h"
-#include "math_private.h"
+double tan(double x) {
+#include "utan.h"
+#include "utan.tbl"
 
-#ifdef __STDC__
-	double __tan(double x)
-#else
-	double __tan(x)
-	double x;
-#endif
-{
-	double y[2],z=0.0;
-	int32_t n, ix;
+  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,mpy,mpt1,mpt2;
+
+  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;
 
-    /* High word of x. */
-	GET_HIGH_WORD(ix,x);
+    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); }
 
-    /* |x| ~< pi/4 */
-	ix &= 0x7fffffff;
-	if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
+    /* 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)
 
-    /* tan(Inf or NaN) is NaN */
-	else if (ix>=0x7ff00000) return x-x;		/* NaN */
+    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)
 
-    /* argument reduction needed */
-	else {
-	    n = __ieee754_rem_pio2(x,y);
-	    return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
-							-1 -- n odd */
-	}
+    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;
 }
-weak_alias (__tan, tan)
+
 #ifdef NO_LONG_DOUBLE
-strong_alias (__tan, __tanl)
-weak_alias (__tan, tanl)
+weak_alias (tan, tanl)
 #endif