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Fix tan, tanl for large inputs.

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This commit is contained in:
Joseph Myers 2012-03-16 20:05:04 +00:00
parent 6a1bd2a100
commit 11b90b9f50
13 changed files with 221 additions and 168 deletions
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19
ChangeLog
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@ -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>.

2
NEWS
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@ -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:

11
math/libm-test.inc
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@ -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);

20
sysdeps/i386/fpu/libm-test-ulps
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@ -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

1
sysdeps/i386/fpu/mptan.c
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@ -1 +0,0 @@
/* Not needed. */

55
sysdeps/i386/fpu/s_tan.S
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@ -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)

55
sysdeps/i386/fpu/s_tanl.S
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@ -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)

4
sysdeps/ieee754/dbl-64/s_tan.c
View File

@ -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;
}

137
sysdeps/ieee754/ldbl-96/k_tanl.c Normal file
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@ -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);
}

11
sysdeps/ieee754/ldbl-96/s_tanl.c
View File

@ -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 {

1
sysdeps/x86_64/fpu/k_tanl.c
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@ -1 +0,0 @@
/* Not needed. */

28
sysdeps/x86_64/fpu/libm-test-ulps
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@ -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

45
sysdeps/x86_64/fpu/s_tanl.S
View File

@ -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)