mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-26 15:00:06 +00:00
4629c866ad
This patch fixes bug 15319, missing underflows from atan / atan2 when the result of atan is very close to its small argument (or that of atan2 is very close to the ratio of its arguments, which may be an exact division). The usual approach of doing an underflowing computation if the computed result is subnormal is followed. For 32-bit x86, there are extra complications: the inline __ieee754_atan2 in bits/mathinline.h needs to be disabled for float and double because other libm functions using it generally rely on getting proper underflow exceptions from it, while the out-of-line functions have to remove excess range and precision from the underflowing result so as to return an exact 0 in the case where errno should be set for underflow to 0. (The failures I saw without that are similar to those Carlos reported for other functions, where I haven't seen a response to <https://sourceware.org/ml/libc-alpha/2015-01/msg00485.html> confirming if my diagnosis is correct. Arguably all libm functions with float and double returns should remove excess range and precision, but that's a separate matter.) The x86_64 long double case reported in a comment in bug 15319 is not a bug (it's an argument of LDBL_MIN, and x86_64 is an after-rounding architecture so the correct IEEE result is not to raise underflow in the given rounding mode, in addition to treating the result as an exact LDBL_MIN being within the newly clarified documentation of accuracy goals). I'm presuming that the fpatan instruction can be trusted to raise appropriate exceptions when the (long double) result underflows (after rounding) and so no changes are needed for x86 / x86_64 long double functions here; empirically this is the case for the cases covered in the testsuite, on my system. Tested for x86_64, x86, powerpc and mips64. Only 32-bit x86 needs ulps updates (for the changes to inlines meaning some functions no longer get excess precision from their __ieee754_atan2* calls). [BZ #15319] * sysdeps/i386/fpu/e_atan2.S (dbl_min): New object. (MO): New macro. (__ieee754_atan2): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/i386/fpu/e_atan2f.S (flt_min): New object. (MO): New macro. (__ieee754_atan2f): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/i386/fpu/s_atan.S (dbl_min): New object. (MO): New macro. (__atan): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/i386/fpu/s_atanf.S (flt_min): New object. (MO): New macro. (__atanf): For results with small absolute value, force underflow exception and remove excess range and precision from return value. * sysdeps/ieee754/dbl-64/e_atan2.c: Include <float.h> and <math.h>. (__ieee754_atan2): Force underflow exception for results with small absolute value. * sysdeps/ieee754/dbl-64/s_atan.c: Include <float.h> and <math_private.h>. (atan): Force underflow exception for results with small absolute value. * sysdeps/ieee754/flt-32/s_atanf.c: Include <float.h>. (__atanf): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128/s_atanl.c: Include <float.h> and <math.h>. (__atanl): Force underflow exception for results with small absolute value. * sysdeps/ieee754/ldbl-128ibm/s_atanl.c: Include <float.h>. (__atanl): Force underflow exception for results with small absolute value. * sysdeps/x86/fpu/bits/mathinline.h [!__SSE2_MATH__ && !__x86_64__ && __LIBC_INTERNAL_MATH_INLINES] (__ieee754_atan2): Only define inline for long double. * sysdeps/x86_64/fpu/multiarch/e_atan2.c [HAVE_FMA4_SUPPORT || HAVE_AVX_SUPPORT]: Include <math.h>. * math/auto-libm-test-in: Do not mark underflow exceptions as possibly missing for bug 15319. Add more tests of atan2. * math/auto-libm-test-out: Regenerated. * math/libm-test.inc (casin_test_data): Do not mark underflow exceptions as possibly missing for bug 15319. (casinh_test_data): Likewise. * sysdeps/i386/fpu/libm-test-ulps: Update.
331 lines
10 KiB
C
331 lines
10 KiB
C
/*
|
|
* IBM Accurate Mathematical Library
|
|
* written by International Business Machines Corp.
|
|
* Copyright (C) 2001-2015 Free Software Foundation, Inc.
|
|
*
|
|
* This program 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 program 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 program; if not, see <http://www.gnu.org/licenses/>.
|
|
*/
|
|
/************************************************************************/
|
|
/* MODULE_NAME: atnat.c */
|
|
/* */
|
|
/* FUNCTIONS: uatan */
|
|
/* atanMp */
|
|
/* signArctan */
|
|
/* */
|
|
/* */
|
|
/* FILES NEEDED: dla.h endian.h mpa.h mydefs.h atnat.h */
|
|
/* mpatan.c mpatan2.c mpsqrt.c */
|
|
/* uatan.tbl */
|
|
/* */
|
|
/* An ultimate atan() routine. Given an IEEE double machine number x */
|
|
/* it computes the correctly rounded (to nearest) value of atan(x). */
|
|
/* */
|
|
/* Assumption: Machine arithmetic operations are performed in */
|
|
/* round to nearest mode of IEEE 754 standard. */
|
|
/* */
|
|
/************************************************************************/
|
|
|
|
#include <dla.h>
|
|
#include "mpa.h"
|
|
#include "MathLib.h"
|
|
#include "uatan.tbl"
|
|
#include "atnat.h"
|
|
#include <float.h>
|
|
#include <math.h>
|
|
#include <math_private.h>
|
|
#include <stap-probe.h>
|
|
|
|
void __mpatan (mp_no *, mp_no *, int); /* see definition in mpatan.c */
|
|
static double atanMp (double, const int[]);
|
|
|
|
/* Fix the sign of y and return */
|
|
static double
|
|
__signArctan (double x, double y)
|
|
{
|
|
return __copysign (y, x);
|
|
}
|
|
|
|
|
|
/* An ultimate atan() routine. Given an IEEE double machine number x, */
|
|
/* routine computes the correctly rounded (to nearest) value of atan(x). */
|
|
double
|
|
atan (double x)
|
|
{
|
|
double cor, s1, ss1, s2, ss2, t1, t2, t3, t7, t8, t9, t10, u, u2, u3,
|
|
v, vv, w, ww, y, yy, z, zz;
|
|
#ifndef DLA_FMS
|
|
double t4, t5, t6;
|
|
#endif
|
|
int i, ux, dx;
|
|
static const int pr[M] = { 6, 8, 10, 32 };
|
|
number num;
|
|
|
|
num.d = x;
|
|
ux = num.i[HIGH_HALF];
|
|
dx = num.i[LOW_HALF];
|
|
|
|
/* x=NaN */
|
|
if (((ux & 0x7ff00000) == 0x7ff00000)
|
|
&& (((ux & 0x000fffff) | dx) != 0x00000000))
|
|
return x + x;
|
|
|
|
/* Regular values of x, including denormals +-0 and +-INF */
|
|
u = (x < 0) ? -x : x;
|
|
if (u < C)
|
|
{
|
|
if (u < B)
|
|
{
|
|
if (u < A)
|
|
{
|
|
if (u < DBL_MIN)
|
|
{
|
|
double force_underflow = x * x;
|
|
math_force_eval (force_underflow);
|
|
}
|
|
return x;
|
|
}
|
|
else
|
|
{ /* A <= u < B */
|
|
v = x * x;
|
|
yy = d11.d + v * d13.d;
|
|
yy = d9.d + v * yy;
|
|
yy = d7.d + v * yy;
|
|
yy = d5.d + v * yy;
|
|
yy = d3.d + v * yy;
|
|
yy *= x * v;
|
|
|
|
if ((y = x + (yy - U1 * x)) == x + (yy + U1 * x))
|
|
return y;
|
|
|
|
EMULV (x, x, v, vv, t1, t2, t3, t4, t5); /* v+vv=x^2 */
|
|
|
|
s1 = f17.d + v * f19.d;
|
|
s1 = f15.d + v * s1;
|
|
s1 = f13.d + v * s1;
|
|
s1 = f11.d + v * s1;
|
|
s1 *= v;
|
|
|
|
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
MUL2 (x, 0, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7,
|
|
t8);
|
|
ADD2 (x, 0, s2, ss2, s1, ss1, t1, t2);
|
|
if ((y = s1 + (ss1 - U5 * s1)) == s1 + (ss1 + U5 * s1))
|
|
return y;
|
|
|
|
return atanMp (x, pr);
|
|
}
|
|
}
|
|
else
|
|
{ /* B <= u < C */
|
|
i = (TWO52 + TWO8 * u) - TWO52;
|
|
i -= 16;
|
|
z = u - cij[i][0].d;
|
|
yy = cij[i][5].d + z * cij[i][6].d;
|
|
yy = cij[i][4].d + z * yy;
|
|
yy = cij[i][3].d + z * yy;
|
|
yy = cij[i][2].d + z * yy;
|
|
yy *= z;
|
|
|
|
t1 = cij[i][1].d;
|
|
if (i < 112)
|
|
{
|
|
if (i < 48)
|
|
u2 = U21; /* u < 1/4 */
|
|
else
|
|
u2 = U22;
|
|
} /* 1/4 <= u < 1/2 */
|
|
else
|
|
{
|
|
if (i < 176)
|
|
u2 = U23; /* 1/2 <= u < 3/4 */
|
|
else
|
|
u2 = U24;
|
|
} /* 3/4 <= u <= 1 */
|
|
if ((y = t1 + (yy - u2 * t1)) == t1 + (yy + u2 * t1))
|
|
return __signArctan (x, y);
|
|
|
|
z = u - hij[i][0].d;
|
|
|
|
s1 = hij[i][14].d + z * hij[i][15].d;
|
|
s1 = hij[i][13].d + z * s1;
|
|
s1 = hij[i][12].d + z * s1;
|
|
s1 = hij[i][11].d + z * s1;
|
|
s1 *= z;
|
|
|
|
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (z, 0, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
|
|
if ((y = s2 + (ss2 - U6 * s2)) == s2 + (ss2 + U6 * s2))
|
|
return __signArctan (x, y);
|
|
|
|
return atanMp (x, pr);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
if (u < D)
|
|
{ /* C <= u < D */
|
|
w = 1 / u;
|
|
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
|
|
ww = w * ((1 - t1) - t2);
|
|
i = (TWO52 + TWO8 * w) - TWO52;
|
|
i -= 16;
|
|
z = (w - cij[i][0].d) + ww;
|
|
|
|
yy = cij[i][5].d + z * cij[i][6].d;
|
|
yy = cij[i][4].d + z * yy;
|
|
yy = cij[i][3].d + z * yy;
|
|
yy = cij[i][2].d + z * yy;
|
|
yy = HPI1 - z * yy;
|
|
|
|
t1 = HPI - cij[i][1].d;
|
|
if (i < 112)
|
|
u3 = U31; /* w < 1/2 */
|
|
else
|
|
u3 = U32; /* w >= 1/2 */
|
|
if ((y = t1 + (yy - u3)) == t1 + (yy + u3))
|
|
return __signArctan (x, y);
|
|
|
|
DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8, t9,
|
|
t10);
|
|
t1 = w - hij[i][0].d;
|
|
EADD (t1, ww, z, zz);
|
|
|
|
s1 = hij[i][14].d + z * hij[i][15].d;
|
|
s1 = hij[i][13].d + z * s1;
|
|
s1 = hij[i][12].d + z * s1;
|
|
s1 = hij[i][11].d + z * s1;
|
|
s1 *= z;
|
|
|
|
ADD2 (hij[i][9].d, hij[i][10].d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][7].d, hij[i][8].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][5].d, hij[i][6].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][3].d, hij[i][4].d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (z, zz, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (hij[i][1].d, hij[i][2].d, s1, ss1, s2, ss2, t1, t2);
|
|
SUB2 (HPI, HPI1, s2, ss2, s1, ss1, t1, t2);
|
|
if ((y = s1 + (ss1 - U7)) == s1 + (ss1 + U7))
|
|
return __signArctan (x, y);
|
|
|
|
return atanMp (x, pr);
|
|
}
|
|
else
|
|
{
|
|
if (u < E)
|
|
{ /* D <= u < E */
|
|
w = 1 / u;
|
|
v = w * w;
|
|
EMULV (w, u, t1, t2, t3, t4, t5, t6, t7);
|
|
|
|
yy = d11.d + v * d13.d;
|
|
yy = d9.d + v * yy;
|
|
yy = d7.d + v * yy;
|
|
yy = d5.d + v * yy;
|
|
yy = d3.d + v * yy;
|
|
yy *= w * v;
|
|
|
|
ww = w * ((1 - t1) - t2);
|
|
ESUB (HPI, w, t3, cor);
|
|
yy = ((HPI1 + cor) - ww) - yy;
|
|
if ((y = t3 + (yy - U4)) == t3 + (yy + U4))
|
|
return __signArctan (x, y);
|
|
|
|
DIV2 (1, 0, u, 0, w, ww, t1, t2, t3, t4, t5, t6, t7, t8,
|
|
t9, t10);
|
|
MUL2 (w, ww, w, ww, v, vv, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
|
|
s1 = f17.d + v * f19.d;
|
|
s1 = f15.d + v * s1;
|
|
s1 = f13.d + v * s1;
|
|
s1 = f11.d + v * s1;
|
|
s1 *= v;
|
|
|
|
ADD2 (f9.d, ff9.d, s1, 0, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f7.d, ff7.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f5.d, ff5.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (f3.d, ff3.d, s1, ss1, s2, ss2, t1, t2);
|
|
MUL2 (v, vv, s2, ss2, s1, ss1, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
MUL2 (w, ww, s1, ss1, s2, ss2, t1, t2, t3, t4, t5, t6, t7, t8);
|
|
ADD2 (w, ww, s2, ss2, s1, ss1, t1, t2);
|
|
SUB2 (HPI, HPI1, s1, ss1, s2, ss2, t1, t2);
|
|
|
|
if ((y = s2 + (ss2 - U8)) == s2 + (ss2 + U8))
|
|
return __signArctan (x, y);
|
|
|
|
return atanMp (x, pr);
|
|
}
|
|
else
|
|
{
|
|
/* u >= E */
|
|
if (x > 0)
|
|
return HPI;
|
|
else
|
|
return MHPI;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* Final stages. Compute atan(x) by multiple precision arithmetic */
|
|
static double
|
|
atanMp (double x, const int pr[])
|
|
{
|
|
mp_no mpx, mpy, mpy2, mperr, mpt1, mpy1;
|
|
double y1, y2;
|
|
int i, p;
|
|
|
|
for (i = 0; i < M; i++)
|
|
{
|
|
p = pr[i];
|
|
__dbl_mp (x, &mpx, p);
|
|
__mpatan (&mpx, &mpy, p);
|
|
__dbl_mp (u9[i].d, &mpt1, p);
|
|
__mul (&mpy, &mpt1, &mperr, p);
|
|
__add (&mpy, &mperr, &mpy1, p);
|
|
__sub (&mpy, &mperr, &mpy2, p);
|
|
__mp_dbl (&mpy1, &y1, p);
|
|
__mp_dbl (&mpy2, &y2, p);
|
|
if (y1 == y2)
|
|
{
|
|
LIBC_PROBE (slowatan, 3, &p, &x, &y1);
|
|
return y1;
|
|
}
|
|
}
|
|
LIBC_PROBE (slowatan_inexact, 3, &p, &x, &y1);
|
|
return y1; /*if impossible to do exact computing */
|
|
}
|
|
|
|
#ifdef NO_LONG_DOUBLE
|
|
weak_alias (atan, atanl)
|
|
#endif
|