Fix tan, tanl for large inputs.

13 files changed, 221 insertions, 168 deletions

diff --git a/ChangeLog b/ChangeLog
index 05c3bfee9a..91b04a2587 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,22 @@
+2012-03-16  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #13851]
+	[BZ #13854]
+	* sysdeps/ieee754/dbl-64/s_tan.c (tan): Use
+	libc_feholdexcept_setround_53bit and libc_feupdateenv_53bit.
+	* sysdeps/ieee754/ldbl-96/k_tanl.c: New file.
+	* sysdeps/ieee754/ldbl-96/s_tanl.c: Include <errno.h>.
+	(__tanl): Set errno for infinite argument.
+	* sysdeps/i386/fpu/mptan.c: Remove.
+	* sysdeps/i386/fpu/s_tan.S: Likewise.
+	* sysdeps/i386/fpu/s_tanl.S: Likewise.
+	* sysdeps/x86_64/fpu/k_tanl.c: Likewise.
+	* sysdeps/x86_64/fpu/s_tanl.S: Likewise.
+	* math/libm-test.inc (tan_test): Add more tests and enable more
+	tests for double and long double.
+	* sysdeps/i386/fpu/libm-test-ulps: Update.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 2012-03-16  Jan Kratochvil  <jan.kratochvil@redhat.com>
 
 	* sysdeps/x86_64/elf/start.S: Include <sysdep.h>.
diff --git a/NEWS b/NEWS
index 2328480d28..cbccc7b458 100644
--- a/NEWS
+++ b/NEWS
@@ -15,7 +15,7 @@ Version 2.16
   13526, 13527, 13528, 13529, 13530, 13531, 13532, 13533, 13547, 13551,
   13552, 13553, 13555, 13559, 13566, 13583, 13618, 13637, 13656, 13658,
   13673, 13695, 13704, 13706, 13726, 13738, 13786, 13792, 13806, 13840,
-  13841, 13844, 13846, 13851, 13852
+  13841, 13844, 13846, 13851, 13852, 13854
 
 * ISO C11 support:
 
diff --git a/math/libm-test.inc b/math/libm-test.inc
index fb82926183..8bcaa8869f 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -6796,11 +6796,16 @@ tan_test (void)
   TEST_f_f (tan, M_PI_4l, 1);
   TEST_f_f (tan, 0.75L, 0.931596459944072461165202756573936428L);
 
-#ifdef TEST_FLOAT
-  /* Enable for double and long double once x86 and x86-64
-     implementations are fixed.  */
   TEST_f_f (tan, 0x1p65, -0.0472364872359047946798414219288370688827L);
   TEST_f_f (tan, -0x1p65, 0.0472364872359047946798414219288370688827L);
+
+#ifndef TEST_FLOAT
+  TEST_f_f (tan, 1e22, -1.628778225606898878549375936939548513545L);
+  TEST_f_f (tan, 0x1p1023, -0.6814476476066215012854144040167365190368L);
+#endif
+
+#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384
+  TEST_f_f (tan, 0x1p16383L, 0.422722393732022337800504160054440141575L);
 #endif
 
   END (tan);
diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps
index 6f090e1417..d83b2339ca 100644
--- a/sysdeps/i386/fpu/libm-test-ulps
+++ b/sysdeps/i386/fpu/libm-test-ulps
@@ -1539,6 +1539,12 @@ idouble: 1
 ldouble: 7
 
 # tan
+Test "tan (0x1p16383) == 0.422722393732022337800504160054440141575":
+ildouble: 1
+ldouble: 1
+Test "tan (1e22) == -1.628778225606898878549375936939548513545":
+ildouble: 1
+ldouble: 1
 Test "tan (pi/4) == 1":
 double: 1
 float: 1
@@ -1551,9 +1557,13 @@ double: 1
 float: 2
 idouble: 1
 ifloat: 2
+ildouble: 1
+ldouble: 1
 Test "tan_downward (10) == 0.6483608274590866712591249330098086768169":
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "tan_downward (2) == -2.1850398632615189916433061023136825434320":
 double: 1
 float: 1
@@ -1614,9 +1624,13 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "tan_towardzero (10) == 0.6483608274590866712591249330098086768169":
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "tan_towardzero (2) == -2.1850398632615189916433061023136825434320":
 ildouble: 1
 ldouble: 1
@@ -1681,8 +1695,8 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 1
-ldouble: 1
+ildouble: 2
+ldouble: 2
 Test "tan_upward (6) == -0.2910061913847491570536995888681755428312":
 ildouble: 1
 ldouble: 1
@@ -2366,6 +2380,8 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 
 Function: "tan_downward":
 double: 1
diff --git a/sysdeps/i386/fpu/mptan.c b/sysdeps/i386/fpu/mptan.c
deleted file mode 100644
index 1cc8931700..0000000000
--- a/sysdeps/i386/fpu/mptan.c
+++ /dev/null
@@ -1 +0,0 @@
-/* Not needed.  */
diff --git a/sysdeps/i386/fpu/s_tan.S b/sysdeps/i386/fpu/s_tan.S
deleted file mode 100644
index b35bb835de..0000000000
--- a/sysdeps/i386/fpu/s_tan.S
+++ /dev/null
@@ -1,55 +0,0 @@
-/*
- * Written by J.T. Conklin <jtc@netbsd.org>.
- * Fixed errno handling by Ulrich Drepper <drepper@redhat.com>.
- * Public domain.
- */
-
-#define __need_Emath
-#include <bits/errno.h>
-#include <machine/asm.h>
-
-RCSID("$NetBSD: s_tan.S,v 1.5 1995/05/09 00:30:00 jtc Exp $")
-
-ENTRY(__tan)
-	fldl	4(%esp)
-	fxam
-	fstsw	%ax
-	movb	$0x45, %dh
-	andb	%ah, %dh
-	cmpb	$0x05, %dh
-	je	3f
-4:	fptan
-	fnstsw	%ax
-	testl	$0x400,%eax
-	jnz	1f
-	fstp	%st(0)
-	ret
-1:	fldpi
-	fadd	%st(0)
-	fxch	%st(1)
-2:	fprem1
-	fstsw	%ax
-	testl	$0x400,%eax
-	jnz	2b
-	fstp	%st(1)
-	fptan
-	fstp	%st(0)
-	ret
-3:
-#ifdef PIC
-	pushl	%ebx
-	cfi_adjust_cfa_offset (4)
-	cfi_rel_offset (ebx, 0)
-	LOAD_PIC_REG (bx)
-	call	__errno_location@PLT
-	movl	$EDOM, (%eax)
-	popl	%ebx
-	cfi_adjust_cfa_offset (-4)
-	cfi_restore (ebx)
-#else
-	call	__errno_location@PLT
-	movl	$EDOM, (%eax)
-#endif
-	jmp	4b
-END (__tan)
-weak_alias (__tan, tan)
diff --git a/sysdeps/i386/fpu/s_tanl.S b/sysdeps/i386/fpu/s_tanl.S
deleted file mode 100644
index 151b77113f..0000000000
--- a/sysdeps/i386/fpu/s_tanl.S
+++ /dev/null
@@ -1,55 +0,0 @@
-/*
- * Written by J.T. Conklin <jtc@netbsd.org>.
- * Public domain.
- *
- * Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
- * Fixed errno handling by Ulrich Drepper <drepper@redhat.com>.
- */
-
-#define __need_Emath
-#include <bits/errno.h>
-#include <machine/asm.h>
-
-ENTRY(__tanl)
-	fldt	4(%esp)
-	fxam
-	fstsw	%ax
-	movb	$0x45, %dh
-	andb	%ah, %dh
-	cmpb	$0x05, %dh
-	je	3f
-4:	fptan
-	fnstsw	%ax
-	testl	$0x400,%eax
-	jnz	1f
-	fstp	%st(0)
-	ret
-1:	fldpi
-	fadd	%st(0)
-	fxch	%st(1)
-2:	fprem1
-	fstsw	%ax
-	testl	$0x400,%eax
-	jnz	2b
-	fstp	%st(1)
-	fptan
-	fstp	%st(0)
-	ret
-3:
-#ifdef PIC
-	pushl	%ebx
-	cfi_adjust_cfa_offset (4)
-	cfi_rel_offset (ebx, 0)
-	LOAD_PIC_REG (bx)
-	call	__errno_location@PLT
-	movl	$EDOM, (%eax)
-	popl	%ebx
-	cfi_adjust_cfa_offset (-4)
-	cfi_restore (ebx)
-#else
-	call	__errno_location@PLT
-	movl	$EDOM, (%eax)
-#endif
-	jmp	4b
-END (__tanl)
-weak_alias (__tanl, tanl)
diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c
index acff67c987..8eee383933 100644
--- a/sysdeps/ieee754/dbl-64/s_tan.c
+++ b/sysdeps/ieee754/dbl-64/s_tan.c
@@ -74,7 +74,7 @@ tan(double x) {
   int __branred(double, double *, double *);
   int __mpranred(double, mp_no *, int);
 
-  libc_feholdexcept_setround (&env, FE_TONEAREST);
+  libc_feholdexcept_setround_53bit (&env, FE_TONEAREST);
 
   /* x=+-INF, x=NaN */
   num.d = x;  ux = num.i[HIGH_HALF];
@@ -503,7 +503,7 @@ tan(double x) {
   goto ret;
 
  ret:
-  libc_feupdateenv (&env);
+  libc_feupdateenv_53bit (&env);
   return retval;
 }
 
diff --git a/sysdeps/ieee754/ldbl-96/k_tanl.c b/sysdeps/ieee754/ldbl-96/k_tanl.c
new file mode 100644
index 0000000000..31cd236aa2
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/k_tanl.c
@@ -0,0 +1,137 @@
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * 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.
+ * ====================================================
+ */
+
+/*
+  Long double expansions are
+  Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
+  and are incorporated herein by permission of the author.  The author
+  reserves the right to distribute this material elsewhere under different
+  copying permissions.  These modifications are distributed here under
+  the following terms:
+
+    This library 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 2.1 of the License, or (at your option) any later version.
+
+    This library 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
+    Lesser General Public License for more details.
+
+    You should have received a copy of the GNU Lesser General Public
+    License along with this library; if not, see
+    <http://www.gnu.org/licenses/>.  */
+
+/* __kernel_tanl( x, y, k )
+ * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
+ * Input x is assumed to be bounded by ~pi/4 in magnitude.
+ * Input y is the tail of x.
+ * Input k indicates whether tan (if k=1) or
+ * -1/tan (if k= -1) is returned.
+ *
+ * Algorithm
+ *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
+ *	2. if x < 2^-33, return x with inexact if x!=0.
+ *	3. tan(x) is approximated by a rational form x + x^3 / 3 + x^5 R(x^2)
+ *          on [0,0.67433].
+ *
+ *	   Note: tan(x+y) = tan(x) + tan'(x)*y
+ *		          ~ tan(x) + (1+x*x)*y
+ *	   Therefore, for better accuracy in computing tan(x+y), let
+ *		r = x^3 * R(x^2)
+ *	   then
+ *		tan(x+y) = x + (x^3 / 3 + (x^2 *(r+y)+y))
+ *
+ *      4. For x in [0.67433,pi/4],  let y = pi/4 - x, then
+ *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
+ *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
+ */
+
+#include <math.h>
+#include <math_private.h>
+static const long double
+  one = 1.0L,
+  pio4hi = 0xc.90fdaa22168c235p-4L,
+  pio4lo = -0x3.b399d747f23e32ecp-68L,
+
+  /* tan x = x + x^3 / 3 + x^5 T(x^2)/U(x^2)
+     0 <= x <= 0.6743316650390625
+     Peak relative error 8.0e-36  */
+ TH =  3.333333333333333333333333333333333333333E-1L,
+ T0 = -1.813014711743583437742363284336855889393E7L,
+ T1 =  1.320767960008972224312740075083259247618E6L,
+ T2 = -2.626775478255838182468651821863299023956E4L,
+ T3 =  1.764573356488504935415411383687150199315E2L,
+ T4 = -3.333267763822178690794678978979803526092E-1L,
+
+ U0 = -1.359761033807687578306772463253710042010E8L,
+ U1 =  6.494370630656893175666729313065113194784E7L,
+ U2 = -4.180787672237927475505536849168729386782E6L,
+ U3 =  8.031643765106170040139966622980914621521E4L,
+ U4 = -5.323131271912475695157127875560667378597E2L;
+  /* 1.000000000000000000000000000000000000000E0 */
+
+
+long double
+__kernel_tanl (long double x, long double y, int iy)
+{
+  long double z, r, v, w, s;
+  long double absx = fabsl (x);
+  int sign;
+
+  if (absx < 0x1p-33)
+    {
+      if ((int) x == 0)
+	{			/* generate inexact */
+	  if (x == 0 && iy == -1)
+	    return one / fabsl (x);
+	  else
+	    return (iy == 1) ? x : -one / x;
+	}
+    }
+  if (absx >= 0.6743316650390625L)
+    {
+      if (signbit (x))
+	{
+	  x = -x;
+	  y = -y;
+	  sign = -1;
+	}
+      else
+	sign = 1;
+      z = pio4hi - x;
+      w = pio4lo - y;
+      x = z + w;
+      y = 0.0;
+    }
+  z = x * x;
+  r = T0 + z * (T1 + z * (T2 + z * (T3 + z * T4)));
+  v = U0 + z * (U1 + z * (U2 + z * (U3 + z * (U4 + z))));
+  r = r / v;
+
+  s = z * x;
+  r = y + z * (s * r + y);
+  r += TH * s;
+  w = x + r;
+  if (absx >= 0.6743316650390625L)
+    {
+      v = (long double) iy;
+      w = (v - 2.0 * (x - (w * w / (w + v) - r)));
+      if (sign < 0)
+	w = -w;
+      return w;
+    }
+  if (iy == 1)
+    return w;
+  else
+    return -1.0 / (x + r);
+}
diff --git a/sysdeps/ieee754/ldbl-96/s_tanl.c b/sysdeps/ieee754/ldbl-96/s_tanl.c
index 3054601a50..3fbe4a8f6b 100644
--- a/sysdeps/ieee754/ldbl-96/s_tanl.c
+++ b/sysdeps/ieee754/ldbl-96/s_tanl.c
@@ -48,23 +48,28 @@ static char rcsid[] = "$NetBSD: $";
  *	TRIG(x) returns trig(x) nearly rounded
  */
 
+#include <errno.h>
 #include <math.h>
 #include <math_private.h>
 
 long double __tanl(long double x)
 {
 	long double y[2],z=0.0;
-	int32_t n, se;
+	int32_t n, se, i0, i1;
 
     /* High word of x. */
-	GET_LDOUBLE_EXP(se,x);
+	GET_LDOUBLE_WORDS(se,i0,i1,x);
 
     /* |x| ~< pi/4 */
 	se &= 0x7fff;
 	if(se <= 0x3ffe) return __kernel_tanl(x,z,1);
 
     /* tan(Inf or NaN) is NaN */
-	else if (se==0x7fff) return x-x;		/* NaN */
+	else if (se==0x7fff) {
+	  if (i1 == 0 && i0 == 0x80000000)
+	    __set_errno (EDOM);
+	  return x-x;
+	}
 
     /* argument reduction needed */
 	else {
diff --git a/sysdeps/x86_64/fpu/k_tanl.c b/sysdeps/x86_64/fpu/k_tanl.c
deleted file mode 100644
index eea55a98d2..0000000000
--- a/sysdeps/x86_64/fpu/k_tanl.c
+++ /dev/null
@@ -1 +0,0 @@
-/*  Not needed.  */
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 9a3fd6f8be..613ae579e9 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -1539,6 +1539,12 @@ ildouble: 7
 ldouble: 7
 
 # tan
+Test "tan (0x1p16383) == 0.422722393732022337800504160054440141575":
+ildouble: 1
+ldouble: 1
+Test "tan (1e22) == -1.628778225606898878549375936939548513545":
+ildouble: 1
+ldouble: 1
 Test "tan (pi/4) == 1":
 double: 1
 idouble: 1
@@ -1547,12 +1553,19 @@ idouble: 1
 Test "tan_downward (1) == 1.5574077246549022305069748074583601730873":
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "tan_downward (10) == 0.6483608274590866712591249330098086768169":
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "tan_downward (2) == -2.1850398632615189916433061023136825434320":
 float: 1
 ifloat: 1
+Test "tan_downward (3) == -0.1425465430742778052956354105339134932261":
+ildouble: 1
+ldouble: 1
 Test "tan_downward (4) == 1.1578212823495775831373424182673239231198":
 ildouble: 1
 ldouble: 1
@@ -1572,6 +1585,12 @@ float: 1
 ifloat: 1
 
 # tan_tonearest
+Test "tan_tonearest (1) == 1.5574077246549022305069748074583601730873":
+ildouble: 1
+ldouble: 1
+Test "tan_tonearest (2) == -2.1850398632615189916433061023136825434320":
+ildouble: 1
+ldouble: 1
 Test "tan_tonearest (6) == -0.2910061913847491570536995888681755428312":
 ildouble: 1
 ldouble: 1
@@ -1583,9 +1602,14 @@ ildouble: 1
 ldouble: 1
 
 # tan_towardzero
+Test "tan_towardzero (1) == 1.5574077246549022305069748074583601730873":
+ildouble: 1
+ldouble: 1
 Test "tan_towardzero (10) == 0.6483608274590866712591249330098086768169":
 float: 1
 ifloat: 1
+ildouble: 1
+ldouble: 1
 Test "tan_towardzero (2) == -2.1850398632615189916433061023136825434320":
 ildouble: 1
 ldouble: 1
@@ -1636,6 +1660,8 @@ ldouble: 1
 Test "tan_upward (5) == -3.3805150062465856369827058794473439087096":
 float: 1
 ifloat: 1
+ildouble: 2
+ldouble: 2
 Test "tan_upward (6) == -0.2910061913847491570536995888681755428312":
 ildouble: 1
 ldouble: 1
@@ -2308,6 +2334,8 @@ ldouble: 27
 Function: "tan":
 double: 1
 idouble: 1
+ildouble: 1
+ldouble: 1
 
 Function: "tan_downward":
 float: 1
diff --git a/sysdeps/x86_64/fpu/s_tanl.S b/sysdeps/x86_64/fpu/s_tanl.S
deleted file mode 100644
index 6427e3f6f0..0000000000
--- a/sysdeps/x86_64/fpu/s_tanl.S
+++ /dev/null
@@ -1,45 +0,0 @@
-/*
- * Written by J.T. Conklin <jtc@netbsd.org>.
- * Public domain.
- *
- * Adapted for `long double' by Ulrich Drepper <drepper@cygnus.com>.
- * Adapted for x86-64 by Andreas Jaeger <aj@suse.de>.
- * Fixed errno handling by Ulrich Drepper <drepper@redhat.com>.
- */
-
-#define __need_Emath
-#include <bits/errno.h>
-#include <machine/asm.h>
-
-RCSID("$NetBSD: $")
-
-ENTRY(__tanl)
-	fldt	8(%rsp)
-	fxam
-	fstsw	%ax
-	movb	$0x45, %dh
-	andb	%ah, %dh
-	cmpb	$0x05, %dh
-	je	3f
-4:	fptan
-	fnstsw	%ax
-	testl	$0x400,%eax
-	jnz	1f
-	fstp	%st(0)
-	ret
-1:	fldpi
-	fadd	%st(0)
-	fxch	%st(1)
-2:	fprem1
-	fstsw	%ax
-	testl	$0x400,%eax
-	jnz	2b
-	fstp	%st(1)
-	fptan
-	fstp	%st(0)
-	ret
-3:	call	__errno_location@PLT
-	movl	$EDOM, (%rax)
-	jmp	4b
-END (__tanl)
-weak_alias (__tanl, tanl)