diff mbox series

[2/5] Remove slow paths in tan

Message ID VE1PR08MB55995238802DC3165A33665083D20@VE1PR08MB5599.eurprd08.prod.outlook.com
State Superseded
Headers show
Series Remove remaining slow paths from math functions | expand

Commit Message

Wilco Dijkstra Jan. 4, 2021, 12:17 p.m. UTC
Remove slow paths in tan. Add ULP annotations. Merge 'number' into 'mynumber'.
Remove unused entries from tan constants.

Passes GLIBC testsuite.

---

Comments

Paul Zimmermann Jan. 4, 2021, 4:36 p.m. UTC | #1
Dear Wilco,

about this second patch, in addition to the following remarks similar to
asin and acos:

- it would be nice to explain where the "Max ULP" come from, to allow
  future developers to debug the code if needed.

- it would be nice to have a summary with the maximal ulp error at the
  top of each function

I have only one further remark:

-typedef union { int4 i[2]; double x; } mynumber;
+typedef union { int4 i[2]; double x; double d; } mynumber;

Why did you add another 'double' field d? Only the 'd' field is used in
e_atan2.c, why not replace it by 'x'? Maybe to avoid a too large diff?

Best regards,
Paul
diff mbox series

Patch

diff --git a/sysdeps/ieee754/dbl-64/e_atan2.c b/sysdeps/ieee754/dbl-64/e_atan2.c
index 380d34368dbdf95138aed911677bdc29ac1e7d9b..7af2a4f495d39f6450699de1d0d9d2f7a33fdcf7 100644
--- a/sysdeps/ieee754/dbl-64/e_atan2.c
+++ b/sysdeps/ieee754/dbl-64/e_atan2.c
@@ -39,6 +39,7 @@ 
 #include <dla.h>
 #include "mpa.h"
 #include "MathLib.h"
+#include "mydefs.h"
 #include "uatan.tbl"
 #include "atnat2.h"
 #include <fenv.h>
diff --git a/sysdeps/ieee754/dbl-64/mydefs.h b/sysdeps/ieee754/dbl-64/mydefs.h
index 60aa2401e02d31524d0890c31987dfd9736ed25a..f17f4f593ca3819d3cbc03bb6138d483743982e8 100644
--- a/sysdeps/ieee754/dbl-64/mydefs.h
+++ b/sysdeps/ieee754/dbl-64/mydefs.h
@@ -28,7 +28,7 @@ 
 #define MY_H
 
 typedef int int4;
-typedef union { int4 i[2]; double x; } mynumber;
+typedef union { int4 i[2]; double x; double d; } mynumber;
 
 #define max(x, y)  (((y) > (x)) ? (y) : (x))
 #define min(x, y)  (((y) < (x)) ? (y) : (x))
diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c
index 086ae50458a3b1cd5826f61b736ea609d9d72ee9..1c5f32711eb31e99f2f1b4372b200bbe520efe57 100644
--- a/sysdeps/ieee754/dbl-64/s_tan.c
+++ b/sysdeps/ieee754/dbl-64/s_tan.c
@@ -20,40 +20,29 @@ 
 /*  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);
-
 double
 SECTION
 __tan (double x)
@@ -62,17 +51,14 @@  __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 +86,6 @@  __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 +94,16 @@  __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 +111,9 @@  __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 +142,7 @@  __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 +154,27 @@  __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 +185,20 @@  __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 +232,7 @@  __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 +244,26 @@  __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 +274,20 @@  __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 +309,7 @@  __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 +320,26 @@  __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 +350,25 @@  __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
diff --git a/sysdeps/ieee754/dbl-64/utan.h b/sysdeps/ieee754/dbl-64/utan.h
index ebe3e193a210280647f76564b6991f98bfe83a9b..8f1034eba855130258adb2aeb816c5722b3f9818 100644
--- a/sysdeps/ieee754/dbl-64/utan.h
+++ b/sysdeps/ieee754/dbl-64/utan.h
@@ -28,7 +28,7 @@ 
 #define UTAN_H
 
 #ifdef BIG_ENDI
-  static const number
+  static const mynumber
   /* polynomial I */
 /**/ d3             = {{0x3FD55555, 0x55555555} }, /*  0.333... */
 /**/ d5             = {{0x3FC11111, 0x111107C6} }, /*  0.133... */
@@ -36,46 +36,6 @@ 
 /**/ d9             = {{0x3F9664ED, 0x49CFC666} }, /*    .      */
 /**/ d11            = {{0x3F82385A, 0x3CF2E4EA} }, /*    .      */
   /* polynomial II */
-/**/ a3             = {{0x3fd55555, 0x55555555} }, /*  1/3      */
-/**/ aa3            = {{0x3c755555, 0x55555555} }, /*  1/3-a3   */
-/**/ a5             = {{0x3fc11111, 0x11111111} }, /*  2/15     */
-/**/ aa5            = {{0x3c411111, 0x11111111} }, /*  2/15-a5  */
-/**/ a7             = {{0x3faba1ba, 0x1ba1ba1c} }, /*  17/315   */
-/**/ aa7            = {{0xbc479179, 0x17917918} }, /*   ()-a7   */
-/**/ a9             = {{0x3f9664f4, 0x882c10fa} }, /*  62/2835  */
-/**/ aa9            = {{0xbc09a528, 0x8b6c44fd} }, /*   ()-a9   */
-/**/ a11            = {{0x3f8226e3, 0x55e6c23d} }, /*    .      */
-/**/ aa11           = {{0xbc2c292b, 0x8f1a2c13} }, /*    .      */
-/**/ a13            = {{0x3f6d6d3d, 0x0e157de0} }, /*    .      */
-/**/ aa13           = {{0xbc0280cf, 0xc968d971} }, /*    .      */
-/**/ a15            = {{0x3f57da36, 0x452b75e3} }, /*    .      */
-#if 0
-/**/ aa15           = {{0xbbf25789, 0xb285d2ed} }, /*    .      */
-#endif
-/**/ a17            = {{0x3f435582, 0x48036744} }, /*    .      */
-#if 0
-/**/ aa17           = {{0x3be488d9, 0x563f1f23} }, /*    .      */
-#endif
-/**/ a19            = {{0x3f2f57d7, 0x734d1664} }, /*    .      */
-#if 0
-/**/ aa19           = {{0x3bb0d55a, 0x913ccb50} }, /*    .      */
-#endif
-/**/ a21            = {{0x3f1967e1, 0x8afcafad} }, /*    .      */
-#if 0
-/**/ aa21           = {{0xbbbd7614, 0xa42d44e6} }, /*    .      */
-#endif
-/**/ a23            = {{0x3f0497d8, 0xeea25259} }, /*    .      */
-#if 0
-/**/ aa23           = {{0x3b99f2d0, 0x2e4d2863} }, /*    .      */
-#endif
-/**/ a25            = {{0x3ef0b132, 0xd39a6050} }, /*    .      */
-#if 0
-/**/ aa25           = {{0x3b93b274, 0xc2c19614} }, /*    .      */
-#endif
-/**/ a27            = {{0x3edb0f72, 0xd3ee24e9} }, /*    .      */
-#if 0
-/**/ aa27           = {{0x3b61688d, 0xdd595609} }, /*    .      */
-#endif
   /* polynomial III */
 /**/ e0             = {{0x3FD55555, 0x55554DBD} }, /*    .      */
 /**/ e1             = {{0x3FC11112, 0xE0A6B45F} }, /*    .      */
@@ -88,52 +48,8 @@ 
 /**/ g3             = {{0x3fe92f1a, 0x00000000} }, /* 0.787     */
 /**/ g4             = {{0x40390000, 0x00000000} }, /* 25.0      */
 /**/ g5             = {{0x4197d784, 0x00000000} }, /* 1e8       */
-/**/ gy1            = {{0x3e7ad7f2, 0x9abcaf48} }, /* 1e-7      */
 /**/ gy2            = {{0x3faf212d, 0x00000000} }, /* 0.0608    */
 
-/**/ u1             = {{0x3cc8c33a, 0x00000000} }, /* 6.873e-16 */
-/**/ u2             = {{0x3983dc4d, 0x00000000} }, /* 1.224e-31 */
-/**/ u3             = {{0x3c78e14b, 0x00000000} }, /* 2.158e-17 */
-/**/ ua3            = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
-/**/ ub3            = {{0x3cc81898, 0x00000000} }, /* 6.688e-16 */
-/**/ u4             = {{0x399856c2, 0x00000000} }, /* 3e-31     */
-/**/ u5             = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */
-/**/ u6             = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */
-/**/ u7             = {{0x39903beb, 0x00000000} }, /* 2.001e-31 */
-/**/ u8             = {{0x399c56ae, 0x00000000} }, /* 3.493e-31 */
-/**/ u9             = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */
-/**/ ua9            = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
-/**/ ub9            = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */
-/**/ u10            = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */
-/**/ ua10           = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
-/**/ ub10           = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */
-/**/ u11            = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */
-/**/ u12            = {{0x39e509b6, 0x00000000} }, /* 8.298e-30 */
-/**/ u13            = {{0x3c39d80a, 0x00000000} }, /* 1.401e-18 */
-/**/ u14            = {{0x3c374c5a, 0x00000000} }, /* 1.263e-18 */
-/**/ u15            = {{0x3ab5767a, 0x00000000} }, /* 6.935e-26 */
-/**/ u16            = {{0x3ab57744, 0x00000000} }, /* 6.936e-26 */
-/**/ u17            = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */
-/**/ ua17           = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */
-/**/ ub17           = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */
-/**/ u18            = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */
-/**/ ua18           = {{0x3bfdb11f, 0x00000000} }, /* 1.006e-19 */
-/**/ ub18           = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */
-/**/ u19            = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */
-/**/ u20            = {{0x39a13b61, 0x00000000} }, /* 4.248e-31 */
-/**/ u21            = {{0x3c3bb9b8, 0x00000000} }, /* 1.503e-18 */
-/**/ u22            = {{0x3c392e08, 0x00000000} }, /* 1.365e-18 */
-/**/ u23            = {{0x3a0ce706, 0x00000000} }, /* 4.560e-29 */
-/**/ u24            = {{0x3a0cff5d, 0x00000000} }, /* 4.575e-29 */
-/**/ u25            = {{0x3c7d0ac7, 0x00000000} }, /* 2.519e-17 */
-/**/ ua25           = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
-/**/ ub25           = {{0x3ccc2375, 0x00000000} }, /* 7.810e-16 */
-/**/ u26            = {{0x3c7e40af, 0x00000000} }, /* 2.624e-17 */
-/**/ ua26           = {{0x3bfd8b58, 0x00000000} }, /* 1.001e-19 */
-/**/ ub26           = {{0x3ccc6405, 0x00000000} }, /* 7.880e-16 */
-/**/ u27            = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */
-/**/ u28            = {{0x3ad421cb, 0x00000000} }, /* 2.602e-25 */
-
 /**/            mp1 = {{0x3FF921FB, 0x58000000} },
 /**/            mp2 = {{0xBE4DDE97, 0x3C000000} },
 /**/            mp3 = {{0xBC8CB3B3, 0x99D747F2} },
@@ -145,7 +61,7 @@ 
 #else
 #ifdef LITTLE_ENDI
 
-  static const number
+  static const mynumber
   /* polynomial I */
 /**/ d3             = {{0x55555555, 0x3FD55555} }, /*  0.333... */
 /**/ d5             = {{0x111107C6, 0x3FC11111} }, /*  0.133... */
@@ -153,46 +69,6 @@ 
 /**/ d9             = {{0x49CFC666, 0x3F9664ED} }, /*    .      */
 /**/ d11            = {{0x3CF2E4EA, 0x3F82385A} }, /*    .      */
   /* polynomial II */
-/**/ a3             = {{0x55555555, 0x3fd55555} }, /*  1/3      */
-/**/ aa3            = {{0x55555555, 0x3c755555} }, /*  1/3-a3   */
-/**/ a5             = {{0x11111111, 0x3fc11111} }, /*  2/15     */
-/**/ aa5            = {{0x11111111, 0x3c411111} }, /*  2/15-a5  */
-/**/ a7             = {{0x1ba1ba1c, 0x3faba1ba} }, /*  17/315   */
-/**/ aa7            = {{0x17917918, 0xbc479179} }, /*   ()-a7   */
-/**/ a9             = {{0x882c10fa, 0x3f9664f4} }, /*  62/2835  */
-/**/ aa9            = {{0x8b6c44fd, 0xbc09a528} }, /*   ()-a9   */
-/**/ a11            = {{0x55e6c23d, 0x3f8226e3} }, /*    .      */
-/**/ aa11           = {{0x8f1a2c13, 0xbc2c292b} }, /*    .      */
-/**/ a13            = {{0x0e157de0, 0x3f6d6d3d} }, /*    .      */
-/**/ aa13           = {{0xc968d971, 0xbc0280cf} }, /*    .      */
-/**/ a15            = {{0x452b75e3, 0x3f57da36} }, /*    .      */
-#if 0
-/**/ aa15           = {{0xb285d2ed, 0xbbf25789} }, /*    .      */
-#endif
-/**/ a17            = {{0x48036744, 0x3f435582} }, /*    .      */
-#if 0
-/**/ aa17           = {{0x563f1f23, 0x3be488d9} }, /*    .      */
-#endif
-/**/ a19            = {{0x734d1664, 0x3f2f57d7} }, /*    .      */
-#if 0
-/**/ aa19           = {{0x913ccb50, 0x3bb0d55a} }, /*    .      */
-#endif
-/**/ a21            = {{0x8afcafad, 0x3f1967e1} }, /*    .      */
-#if 0
-/**/ aa21           = {{0xa42d44e6, 0xbbbd7614} }, /*    .      */
-#endif
-/**/ a23            = {{0xeea25259, 0x3f0497d8} }, /*    .      */
-#if 0
-/**/ aa23           = {{0x2e4d2863, 0x3b99f2d0} }, /*    .      */
-#endif
-/**/ a25            = {{0xd39a6050, 0x3ef0b132} }, /*    .      */
-#if 0
-/**/ aa25           = {{0xc2c19614, 0x3b93b274} }, /*    .      */
-#endif
-/**/ a27            = {{0xd3ee24e9, 0x3edb0f72} }, /*    .      */
-#if 0
-/**/ aa27           = {{0xdd595609, 0x3b61688d} }, /*    .      */
-#endif
   /* polynomial III */
 /**/ e0             = {{0x55554DBD, 0x3FD55555} }, /*    .      */
 /**/ e1             = {{0xE0A6B45F, 0x3FC11112} }, /*    .      */
@@ -205,52 +81,8 @@ 
 /**/ g3             = {{0x00000000, 0x3fe92f1a} }, /* 0.787     */
 /**/ g4             = {{0x00000000, 0x40390000} }, /* 25.0      */
 /**/ g5             = {{0x00000000, 0x4197d784} }, /* 1e8       */
-/**/ gy1            = {{0x9abcaf48, 0x3e7ad7f2} }, /* 1e-7      */
 /**/ gy2            = {{0x00000000, 0x3faf212d} }, /* 0.0608    */
 
-/**/ u1             = {{0x00000000, 0x3cc8c33a} }, /* 6.873e-16 */
-/**/ u2             = {{0x00000000, 0x3983dc4d} }, /* 1.224e-31 */
-/**/ u3             = {{0x00000000, 0x3c78e14b} }, /* 2.158e-17 */
-/**/ ua3            = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
-/**/ ub3            = {{0x00000000, 0x3cc81898} }, /* 6.688e-16 */
-/**/ u4             = {{0x00000000, 0x399856c2} }, /* 3e-31     */
-/**/ u5             = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */
-/**/ u6             = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */
-/**/ u7             = {{0x00000000, 0x39903beb} }, /* 2.001e-31 */
-/**/ u8             = {{0x00000000, 0x399c56ae} }, /* 3.493e-31 */
-/**/ u9             = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */
-/**/ ua9            = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
-/**/ ub9            = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */
-/**/ u10            = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */
-/**/ ua10           = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
-/**/ ub10           = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */
-/**/ u11            = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */
-/**/ u12            = {{0x00000000, 0x39e509b6} }, /* 8.298e-30 */
-/**/ u13            = {{0x00000000, 0x3c39d80a} }, /* 1.401e-18 */
-/**/ u14            = {{0x00000000, 0x3c374c5a} }, /* 1.263e-18 */
-/**/ u15            = {{0x00000000, 0x3ab5767a} }, /* 6.935e-26 */
-/**/ u16            = {{0x00000000, 0x3ab57744} }, /* 6.936e-26 */
-/**/ u17            = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */
-/**/ ua17           = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */
-/**/ ub17           = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */
-/**/ u18            = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */
-/**/ ua18           = {{0x00000000, 0x3bfdb11f} }, /* 1.006e-19 */
-/**/ ub18           = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */
-/**/ u19            = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */
-/**/ u20            = {{0x00000000, 0x39a13b61} }, /* 4.248e-31 */
-/**/ u21            = {{0x00000000, 0x3c3bb9b8} }, /* 1.503e-18 */
-/**/ u22            = {{0x00000000, 0x3c392e08} }, /* 1.365e-18 */
-/**/ u23            = {{0x00000000, 0x3a0ce706} }, /* 4.560e-29 */
-/**/ u24            = {{0x00000000, 0x3a0cff5d} }, /* 4.575e-29 */
-/**/ u25            = {{0x00000000, 0x3c7d0ac7} }, /* 2.519e-17 */
-/**/ ua25           = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
-/**/ ub25           = {{0x00000000, 0x3ccc2375} }, /* 7.810e-16 */
-/**/ u26            = {{0x00000000, 0x3c7e40af} }, /* 2.624e-17 */
-/**/ ua26           = {{0x00000000, 0x3bfd8b58} }, /* 1.001e-19 */
-/**/ ub26           = {{0x00000000, 0x3ccc6405} }, /* 7.880e-16 */
-/**/ u27            = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */
-/**/ u28            = {{0x00000000, 0x3ad421cb} }, /* 2.602e-25 */
-
 /**/            mp1 = {{0x58000000, 0x3FF921FB} },
 /**/            mp2 = {{0x3C000000, 0xBE4DDE97} },
 /**/            mp3 = {{0x99D747F2, 0xBC8CB3B3} },
diff --git a/sysdeps/ieee754/dbl-64/utan.tbl b/sysdeps/ieee754/dbl-64/utan.tbl
index b094d164b8189c26145083a5dbe86454c10ec754..80796293de54d676fefdfa23e302bce254b8f7bc 100644
--- a/sysdeps/ieee754/dbl-64/utan.tbl
+++ b/sysdeps/ieee754/dbl-64/utan.tbl
@@ -23,7 +23,7 @@ 
 
 
 #ifdef BIG_ENDI
-static const number
+static const mynumber
       xfg[186][4] = {                             /* xi,Fi,Gi,FFi, i=16..201 */
 /**/                 {{{0x3fb00000, 0x1e519d60} },
 /**/                  {{0x3fb00557, 0x96c4e240} },
@@ -773,7 +773,7 @@  static const number
 
 #else
 #ifdef LITTLE_ENDI
-static const number
+static const mynumber
       xfg[186][4] = {                             /* xi,Fi,Gi,FFi, i=16..201 */
 /**/                 {{{0x1e519d60, 0x3fb00000} },
 /**/                  {{0x96c4e240, 0x3fb00557} },