math: Remove slow paths in tan [BZ #15267]

Remove slow paths in tan. Add ULP annotations. Merge 'number' into 'mynumber'.
Remove unused entries from tan constants.

Reviewed-By: Paul Zimmermann <Paul.Zimmermann@inria.fr>

1 files changed, 75 insertions, 535 deletions

diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c
index 6aa5a5a..a4f21fd 100644
--- a/sysdeps/ieee754/dbl-64/s_tan.c
+++ b/sysdeps/ieee754/dbl-64/s_tan.c
@@ -20,40 +20,30 @@
 /*  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                        */
+/*  FILES NEEDED:dla.h endian.h mydefs.h utan.h                      */
+/*               branred.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 <errno.h>
 #include <float.h>
 #include "endian.h"
 #include <dla.h>
-#include "mpa.h"
-#include "MathLib.h"
+#include "mydefs.h"
 #include <math.h>
 #include <math_private.h>
 #include <fenv_private.h>
 #include <math-underflow.h>
 #include <libm-alias-double.h>
 #include <fenv.h>
-#include <stap-probe.h>
 
 #ifndef SECTION
 # define SECTION
 #endif
 
-static double tanMp (double);
-void __mptan (double, mp_no *, int);
-
+/* tan with max ULP of ~0.619 based on random sampling.  */
 double
 SECTION
 __tan (double x)
@@ -62,17 +52,14 @@ __tan (double x)
 #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, w, x2, xn, xx2, y, ya,
-         yya, z0, z, zz, z2, zz2;
-  int p;
-  number num, v;
-  mp_no mpa, mpt1, mpt2;
+  double a, da, a2, b, db, c, dc, fi, gi, pz,
+	 s, sy, t, t1, t2, t3, t4, w, x2, xn, y, ya,
+         yya, z0, z, z2;
+  mynumber num, v;
 
   double retval;
 
   int __branred (double, double *, double *);
-  int __mpranred (double, mp_no *, int);
 
   SET_RESTORE_ROUND_53BIT (FE_TONEAREST);
 
@@ -100,7 +87,6 @@ __tan (double x)
   /* (II) The case 1.259e-8 < abs(x) <= 0.0608 */
   if (w <= g2.d)
     {
-      /* First stage */
       x2 = x * x;
 
       t2 = d9.d + x2 * d11.d;
@@ -109,50 +95,16 @@ __tan (double x)
       t2 = d3.d + x2 * t2;
       t2 *= x * x2;
 
-      if ((y = x + (t2 - u1.d * t2)) == x + (t2 + u1.d * t2))
-	{
-	  retval = y;
-	  goto ret;
-	}
-
-      /* Second stage */
-      c1 = a25.d + x2 * a27.d;
-      c1 = a23.d + x2 * c1;
-      c1 = a21.d + x2 * c1;
-      c1 = a19.d + x2 * c1;
-      c1 = a17.d + x2 * c1;
-      c1 = a15.d + x2 * c1;
-      c1 *= x2;
-
-      EMULV (x, x, x2, xx2);
-      ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      MUL2 (x, 0.0, c1, cc1, c2, cc2, t1, t2);
-      ADD2 (x, 0.0, c2, cc2, c1, cc1, t1, t2);
-      if ((y = c1 + (cc1 - u2.d * c1)) == c1 + (cc1 + u2.d * c1))
-	{
-	  retval = y;
-	  goto ret;
-	}
-      retval = tanMp (x);
+      y = x + t2;
+      retval = y;
+      /* Max ULP is 0.504.  */
       goto ret;
     }
 
   /* (III) The case 0.0608 < abs(x) <= 0.787 */
   if (w <= g3.d)
     {
-      /* First stage */
-      i = ((int) (mfftnhf.d + TWO8 * w));
+      i = ((int) (mfftnhf.d + 256 * w));
       z = w - xfg[i][0].d;
       z2 = z * z;
       s = (x < 0.0) ? -1 : 1;
@@ -160,41 +112,9 @@ __tan (double x)
       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))
-	{
-	  retval = (s * y);
-	  goto ret;
-	}
-      t3 = (t2 < 0.0) ? -t2 : t2;
-      t4 = fi * ua3.d + t3 * ub3.d;
-      if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
-	{
-	  retval = (s * y);
-	  goto ret;
-	}
-
-      /* Second stage */
-      ffi = xfg[i][3].d;
-      c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
-      EMULV (z, z, z2, zz2);
-      ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
-      MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-      MUL2 (z, 0.0, c1, cc1, c2, cc2, t1, t2);
-      ADD2 (z, 0.0, c2, cc2, c1, cc1, t1, t2);
-
-      ADD2 (fi, ffi, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (fi, ffi, c1, cc1, c3, cc3, t1, t2);
-      SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
-      DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
-
-      if ((y = c3 + (cc3 - u4.d * c3)) == c3 + (cc3 + u4.d * c3))
-	{
-	  retval = (s * y);
-	  goto ret;
-	}
-      retval = tanMp (x);
+      y = fi + t2;
+      retval = (s * y);
+      /* Max ULP is 0.60.  */
       goto ret;
     }
 
@@ -223,14 +143,7 @@ __tan (double x)
 	  sy = 1;
 	}
 
-      /* (IV),(V) The case 0.787 < abs(x) <= 25,    abs(y) <= 1e-7 */
-      if (ya <= gy1.d)
-	{
-	  retval = tanMp (x);
-	  goto ret;
-	}
-
-      /* (VI) The case 0.787 < abs(x) <= 25,    1e-7 < abs(y) <= 0.0608 */
+      /* (VI) The case 0.787 < abs(x) <= 25,    0 < abs(y) <= 0.0608 */
       if (ya <= gy2.d)
 	{
 	  a2 = a * a;
@@ -242,94 +155,27 @@ __tan (double x)
 
 	  if (n)
 	    {
-	      /* First stage -cot */
+	      /* -cot */
 	      EADD (a, t2, b, db);
 	      DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4);
-	      if ((y = c + (dc - u6.d * c)) == c + (dc + u6.d * c))
-		{
-		  retval = (-y);
-		  goto ret;
-		}
-	    }
-	  else
-	    {
-	      /* First stage tan */
-	      if ((y = a + (t2 - u5.d * a)) == a + (t2 + u5.d * a))
-		{
-		  retval = y;
-		  goto ret;
-		}
-	    }
-	  /* 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);
-
-	  c1 = a25.d + x2 * a27.d;
-	  c1 = a23.d + x2 * c1;
-	  c1 = a21.d + x2 * c1;
-	  c1 = a19.d + x2 * c1;
-	  c1 = a17.d + x2 * c1;
-	  c1 = a15.d + x2 * c1;
-	  c1 *= x2;
-
-	  ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
-	  ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
-
-	  if (n)
-	    {
-	      /* Second stage -cot */
-	      DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4);
-	      if ((y = c2 + (cc2 - u8.d * c2)) == c2 + (cc2 + u8.d * c2))
-		{
-		  retval = (-y);
-		  goto ret;
-		}
+	      y = c + dc;
+	      retval = (-y);
+	      /* Max ULP is 0.506.  */
+	      goto ret;
 	    }
 	  else
 	    {
-	      /* Second stage tan */
-	      if ((y = c1 + (cc1 - u7.d * c1)) == c1 + (cc1 + u7.d * c1))
-		{
-		  retval = y;
-		  goto ret;
-		}
+	      /* tan */
+	      y = a + t2;
+	      retval = y;
+	      /* Max ULP is 0.506.  */
+	      goto ret;
 	    }
-	  retval = tanMp (x);
-	  goto ret;
 	}
 
       /* (VII) The case 0.787 < abs(x) <= 25,    0.0608 < abs(y) <= 0.787 */
 
-      /* First stage */
-      i = ((int) (mfftnhf.d + TWO8 * ya));
+      i = ((int) (mfftnhf.d + 256 * ya));
       z = (z0 = (ya - xfg[i][0].d)) + yya;
       z2 = z * z;
       pz = z + z * z2 * (e0.d + z2 * e1.d);
@@ -340,76 +186,20 @@ __tan (double x)
 	{
 	  /* -cot */
 	  t2 = pz * (fi + gi) / (fi + pz);
-	  if ((y = gi - (t2 - gi * u10.d)) == gi - (t2 + gi * u10.d))
-	    {
-	      retval = (-sy * y);
-	      goto ret;
-	    }
-	  t3 = (t2 < 0.0) ? -t2 : t2;
-	  t4 = gi * ua10.d + t3 * ub10.d;
-	  if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
-	    {
-	      retval = (-sy * y);
-	      goto ret;
-	    }
+	  y = gi - t2;
+	  retval = (-sy * y);
+	  /* Max ULP is 0.62.  */
+	  goto ret;
 	}
       else
 	{
 	  /* tan */
 	  t2 = pz * (gi + fi) / (gi - pz);
-	  if ((y = fi + (t2 - fi * u9.d)) == fi + (t2 + fi * u9.d))
-	    {
-	      retval = (sy * y);
-	      goto ret;
-	    }
-	  t3 = (t2 < 0.0) ? -t2 : t2;
-	  t4 = fi * ua9.d + t3 * ub9.d;
-	  if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
-	    {
-	      retval = (sy * y);
-	      goto ret;
-	    }
-	}
-
-      /* Second stage */
-      ffi = xfg[i][3].d;
-      EADD (z0, yya, z, zz)
-      MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
-      c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
-      ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
-      MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-      MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
-      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);
-      SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
-
-      if (n)
-	{
-	  /* -cot */
-	  DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
-	  if ((y = c3 + (cc3 - u12.d * c3)) == c3 + (cc3 + u12.d * c3))
-	    {
-	      retval = (-sy * y);
-	      goto ret;
-	    }
-	}
-      else
-	{
-	  /* tan */
-	  DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
-	  if ((y = c3 + (cc3 - u11.d * c3)) == c3 + (cc3 + u11.d * c3))
-	    {
-	      retval = (sy * y);
-	      goto ret;
-	    }
+	  y = fi + t2;
+	  retval = (sy * y);
+	  /* Max ULP is 0.62.  */
+	  goto ret;
 	}
-
-      retval = tanMp (x);
-      goto ret;
     }
 
   /* (---) The case 25 < abs(x) <= 1e8 */
@@ -443,14 +233,7 @@ __tan (double x)
 	  sy = 1;
 	}
 
-      /* (+++) The case 25 < abs(x) <= 1e8,    abs(y) <= 1e-7 */
-      if (ya <= gy1.d)
-	{
-	  retval = tanMp (x);
-	  goto ret;
-	}
-
-      /* (VIII) The case 25 < abs(x) <= 1e8,    1e-7 < abs(y) <= 0.0608 */
+      /* (VIII) The case 25 < abs(x) <= 1e8,    0 < abs(y) <= 0.0608 */
       if (ya <= gy2.d)
 	{
 	  a2 = a * a;
@@ -462,76 +245,26 @@ __tan (double x)
 
 	  if (n)
 	    {
-	      /* First stage -cot */
+	      /* -cot */
 	      EADD (a, t2, b, db);
 	      DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4);
-	      if ((y = c + (dc - u14.d * c)) == c + (dc + u14.d * c))
-		{
-		  retval = (-y);
-		  goto ret;
-		}
-	    }
-	  else
-	    {
-	      /* First stage tan */
-	      if ((y = a + (t2 - u13.d * a)) == a + (t2 + u13.d * a))
-		{
-		  retval = y;
-		  goto ret;
-		}
-	    }
-
-	  /* Second stage */
-	  MUL2 (a, da, a, da, x2, xx2, t1, t2);
-	  c1 = a25.d + x2 * a27.d;
-	  c1 = a23.d + x2 * c1;
-	  c1 = a21.d + x2 * c1;
-	  c1 = a19.d + x2 * c1;
-	  c1 = a17.d + x2 * c1;
-	  c1 = a15.d + x2 * c1;
-	  c1 *= x2;
-
-	  ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-	  MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-	  MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
-	  ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
-
-	  if (n)
-	    {
-	      /* Second stage -cot */
-	      DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4);
-	      if ((y = c2 + (cc2 - u16.d * c2)) == c2 + (cc2 + u16.d * c2))
-		{
-		  retval = (-y);
-		  goto ret;
-		}
+	      y = c + dc;
+	      retval = (-y);
+	      /* Max ULP is 0.506.  */
+	      goto ret;
 	    }
 	  else
 	    {
-	      /* Second stage tan */
-	      if ((y = c1 + (cc1 - u15.d * c1)) == c1 + (cc1 + u15.d * c1))
-		{
-		  retval = (y);
-		  goto ret;
-		}
+	      /* tan */
+	      y = a + t2;
+	      retval = y;
+	      /* Max ULP is 0.506.  */
+	      goto ret;
 	    }
-	  retval = tanMp (x);
-	  goto ret;
 	}
 
       /* (IX) The case 25 < abs(x) <= 1e8,    0.0608 < abs(y) <= 0.787 */
-      /* First stage */
-      i = ((int) (mfftnhf.d + TWO8 * ya));
+      i = ((int) (mfftnhf.d + 256 * ya));
       z = (z0 = (ya - xfg[i][0].d)) + yya;
       z2 = z * z;
       pz = z + z * z2 * (e0.d + z2 * e1.d);
@@ -542,75 +275,20 @@ __tan (double x)
 	{
 	  /* -cot */
 	  t2 = pz * (fi + gi) / (fi + pz);
-	  if ((y = gi - (t2 - gi * u18.d)) == gi - (t2 + gi * u18.d))
-	    {
-	      retval = (-sy * y);
-	      goto ret;
-	    }
-	  t3 = (t2 < 0.0) ? -t2 : t2;
-	  t4 = gi * ua18.d + t3 * ub18.d;
-	  if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
-	    {
-	      retval = (-sy * y);
-	      goto ret;
-	    }
+	  y = gi - t2;
+	  retval = (-sy * y);
+	  /* Max ULP is 0.62.  */
+	  goto ret;
 	}
       else
 	{
 	  /* tan */
 	  t2 = pz * (gi + fi) / (gi - pz);
-	  if ((y = fi + (t2 - fi * u17.d)) == fi + (t2 + fi * u17.d))
-	    {
-	      retval = (sy * y);
-	      goto ret;
-	    }
-	  t3 = (t2 < 0.0) ? -t2 : t2;
-	  t4 = fi * ua17.d + t3 * ub17.d;
-	  if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
-	    {
-	      retval = (sy * y);
-	      goto ret;
-	    }
-	}
-
-      /* Second stage */
-      ffi = xfg[i][3].d;
-      EADD (z0, yya, z, zz);
-      MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
-      c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
-      ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
-      MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-      MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
-      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);
-      SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
-
-      if (n)
-	{
-	  /* -cot */
-	  DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
-	  if ((y = c3 + (cc3 - u20.d * c3)) == c3 + (cc3 + u20.d * c3))
-	    {
-	      retval = (-sy * y);
-	      goto ret;
-	    }
-	}
-      else
-	{
-	  /* tan */
-	  DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
-	  if ((y = c3 + (cc3 - u19.d * c3)) == c3 + (cc3 + u19.d * c3))
-	    {
-	      retval = (sy * y);
-	      goto ret;
-	    }
+	  y = fi + t2;
+	  retval = (sy * y);
+	  /* Max ULP is 0.62.  */
+	  goto ret;
 	}
-      retval = tanMp (x);
-      goto ret;
     }
 
   /* (---) The case 1e8 < abs(x) < 2**1024 */
@@ -632,14 +310,7 @@ __tan (double x)
       sy = 1;
     }
 
-  /* (+++) The case 1e8 < abs(x) < 2**1024,    abs(y) <= 1e-7 */
-  if (ya <= gy1.d)
-    {
-      retval = tanMp (x);
-      goto ret;
-    }
-
-  /* (X) The case 1e8 < abs(x) < 2**1024,    1e-7 < abs(y) <= 0.0608 */
+  /* (X) The case 1e8 < abs(x) < 2**1024,    0 < abs(y) <= 0.0608 */
   if (ya <= gy2.d)
     {
       a2 = a * a;
@@ -650,85 +321,26 @@ __tan (double x)
       t2 = da + a * a2 * t2;
       if (n)
 	{
-	  /* First stage -cot */
+	  /* -cot */
 	  EADD (a, t2, b, db);
 	  DIV2 (1.0, 0.0, b, db, c, dc, t1, t2, t3, t4);
-	  if ((y = c + (dc - u22.d * c)) == c + (dc + u22.d * c))
-	    {
-	      retval = (-y);
-	      goto ret;
-	    }
-	}
-      else
-	{
-	  /* First stage tan */
-	  if ((y = a + (t2 - u21.d * a)) == a + (t2 + u21.d * a))
-	    {
-	      retval = y;
-	      goto ret;
-	    }
-	}
-
-      /* 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);
-
-      c1 = a25.d + x2 * a27.d;
-      c1 = a23.d + x2 * c1;
-      c1 = a21.d + x2 * c1;
-      c1 = a19.d + x2 * c1;
-      c1 = a17.d + x2 * c1;
-      c1 = a15.d + x2 * c1;
-      c1 *= x2;
-
-      ADD2 (a13.d, aa13.d, c1, 0.0, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a11.d, aa11.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a9.d, aa9.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a7.d, aa7.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a5.d, aa5.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-      MUL2 (x2, xx2, c2, cc2, c1, cc1, t1, t2);
-      MUL2 (a, da, c1, cc1, c2, cc2, t1, t2);
-      ADD2 (a, da, c2, cc2, c1, cc1, t1, t2);
-
-      if (n)
-	{
-	  /* Second stage -cot */
-	  DIV2 (1.0, 0.0, c1, cc1, c2, cc2, t1, t2, t3, t4);
-	  if ((y = c2 + (cc2 - u24.d * c2)) == c2 + (cc2 + u24.d * c2))
-	    {
-	      retval = (-y);
-	      goto ret;
-	    }
+	  y = c + dc;
+	  retval = (-y);
+	  /* Max ULP is 0.506.  */
+	  goto ret;
 	}
       else
 	{
-	  /* Second stage tan */
-	  if ((y = c1 + (cc1 - u23.d * c1)) == c1 + (cc1 + u23.d * c1))
-	    {
-	      retval = y;
-	      goto ret;
-	    }
+	  /* tan */
+	  y = a + t2;
+	  retval = y;
+	  /* Max ULP is 0.507.  */
+	  goto ret;
 	}
-      retval = tanMp (x);
-      goto ret;
     }
 
   /* (XI) The case 1e8 < abs(x) < 2**1024,    0.0608 < abs(y) <= 0.787 */
-  /* First stage */
-  i = ((int) (mfftnhf.d + TWO8 * ya));
+  i = ((int) (mfftnhf.d + 256 * ya));
   z = (z0 = (ya - xfg[i][0].d)) + yya;
   z2 = z * z;
   pz = z + z * z2 * (e0.d + z2 * e1.d);
@@ -739,97 +351,25 @@ __tan (double x)
     {
       /* -cot */
       t2 = pz * (fi + gi) / (fi + pz);
-      if ((y = gi - (t2 - gi * u26.d)) == gi - (t2 + gi * u26.d))
-	{
-	  retval = (-sy * y);
-	  goto ret;
-	}
-      t3 = (t2 < 0.0) ? -t2 : t2;
-      t4 = gi * ua26.d + t3 * ub26.d;
-      if ((y = gi - (t2 - t4)) == gi - (t2 + t4))
-	{
-	  retval = (-sy * y);
-	  goto ret;
-	}
+      y = gi - t2;
+      retval = (-sy * y);
+      /* Max ULP is 0.62.  */
+      goto ret;
     }
   else
     {
       /* tan */
       t2 = pz * (gi + fi) / (gi - pz);
-      if ((y = fi + (t2 - fi * u25.d)) == fi + (t2 + fi * u25.d))
-	{
-	  retval = (sy * y);
-	  goto ret;
-	}
-      t3 = (t2 < 0.0) ? -t2 : t2;
-      t4 = fi * ua25.d + t3 * ub25.d;
-      if ((y = fi + (t2 - t4)) == fi + (t2 + t4))
-	{
-	  retval = (sy * y);
-	  goto ret;
-	}
-    }
-
-  /* Second stage */
-  ffi = xfg[i][3].d;
-  EADD (z0, yya, z, zz);
-  MUL2 (z, zz, z, zz, z2, zz2, t1, t2);
-  c1 = z2 * (a7.d + z2 * (a9.d + z2 * a11.d));
-  ADD2 (a5.d, aa5.d, c1, 0.0, c2, cc2, t1, t2);
-  MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-  ADD2 (a3.d, aa3.d, c1, cc1, c2, cc2, t1, t2);
-  MUL2 (z2, zz2, c2, cc2, c1, cc1, t1, t2);
-  MUL2 (z, zz, c1, cc1, c2, cc2, t1, t2);
-  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);
-  SUB2 (1.0, 0.0, c3, cc3, c1, cc1, t1, t2);
-
-  if (n)
-    {
-      /* -cot */
-      DIV2 (c1, cc1, c2, cc2, c3, cc3, t1, t2, t3, t4);
-      if ((y = c3 + (cc3 - u28.d * c3)) == c3 + (cc3 + u28.d * c3))
-	{
-	  retval = (-sy * y);
-	  goto ret;
-	}
-    }
-  else
-    {
-      /* tan */
-      DIV2 (c2, cc2, c1, cc1, c3, cc3, t1, t2, t3, t4);
-      if ((y = c3 + (cc3 - u27.d * c3)) == c3 + (cc3 + u27.d * c3))
-	{
-	  retval = (sy * y);
-	  goto ret;
-	}
+      y = fi + t2;
+      retval = (sy * y);
+      /* Max ULP is 0.62.  */
+      goto ret;
     }
-  retval = tanMp (x);
-  goto ret;
 
 ret:
   return retval;
 }
 
-/* multiple precision stage                                              */
-/* Convert x to multi precision number,compute tan(x) by mptan() routine */
-/* and converts result back to double                                    */
-static double
-SECTION
-tanMp (double x)
-{
-  int p;
-  double y;
-  mp_no mpy;
-  p = 32;
-  __mptan (x, &mpy, p);
-  __mp_dbl (&mpy, &y, p);
-  LIBC_PROBE (slowtan, 2, &x, &y);
-  return y;
-}
-
 #ifndef __tan
 libm_alias_double (__tan, tan)
 #endif