+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>.
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:
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);
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
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
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
float: 1
idouble: 1
ifloat: 1
-ildouble: 1
-ldouble: 1
+ildouble: 2
+ldouble: 2
Test "tan_upward (6) == -0.2910061913847491570536995888681755428312":
ildouble: 1
ldouble: 1
float: 1
idouble: 1
ifloat: 1
+ildouble: 1
+ldouble: 1
Function: "tan_downward":
double: 1
+++ /dev/null
-/* Not needed. */
+++ /dev/null
-/*
- * 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)
+++ /dev/null
-/*
- * 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)
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];
goto ret;
ret:
- libc_feupdateenv (&env);
+ libc_feupdateenv_53bit (&env);
return retval;
}
--- /dev/null
+/*
+ * ====================================================
+ * 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);
+}
* 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 {
+++ /dev/null
-/* Not needed. */
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
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
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
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
Test "tan_upward (5) == -3.3805150062465856369827058794473439087096":
float: 1
ifloat: 1
+ildouble: 2
+ldouble: 2
Test "tan_upward (6) == -0.2910061913847491570536995888681755428312":
ildouble: 1
ldouble: 1
Function: "tan":
double: 1
idouble: 1
+ildouble: 1
+ldouble: 1
Function: "tan_downward":
float: 1
+++ /dev/null
-/*
- * 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)
git://sourceware.org / glibc.git / commitdiff