glibc/sysdeps/ieee754/ldbl-128ibm/e_asinl.c
Wilco Dijkstra 220622dde5 Add libm_alias_finite for _finite symbols
This patch adds a new macro, libm_alias_finite, to define all _finite
symbol.  It sets all _finite symbol as compat symbol based on its first
version (obtained from the definition at built generated first-versions.h).

The <fn>f128_finite symbols were introduced in GLIBC 2.26 and so need
special treatment in code that is shared between long double and float128.
It is done by adding a list, similar to internal symbol redifinition,
on sysdeps/ieee754/float128/float128_private.h.

Alpha also needs some tricky changes to ensure we still emit 2 compat
symbols for sqrt(f).

Passes buildmanyglibc.

Co-authored-by: Adhemerval Zanella <adhemerval.zanella@linaro.org>
Reviewed-by: Siddhesh Poyarekar <siddhesh@sourceware.org>
2020-01-03 10:02:04 -03:00

253 lines
7.2 KiB
C

/*
* ====================================================
* 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
<https://www.gnu.org/licenses/>. */
/* __ieee754_asin(x)
* Method :
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
* we approximate asin(x) on [0,0.5] by
* asin(x) = x + x*x^2*R(x^2)
* Between .5 and .625 the approximation is
* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
* For x in [0.625,1]
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
* then for x>0.98
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
* For x<=0.98, let pio4_hi = pio2_hi/2, then
* f = hi part of s;
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
* and
* asin(x) = pi/2 - 2*(s+s*z*R(z))
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
*/
#include <float.h>
#include <math.h>
#include <math-barriers.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-finite.h>
static const long double
one = 1.0L,
huge = 1.0e+300L,
pio2_hi = 1.5707963267948966192313216916397514420986L,
pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
/* coefficient for R(x^2) */
/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
0 <= x <= 0.5
peak relative error 1.9e-35 */
pS0 = -8.358099012470680544198472400254596543711E2L,
pS1 = 3.674973957689619490312782828051860366493E3L,
pS2 = -6.730729094812979665807581609853656623219E3L,
pS3 = 6.643843795209060298375552684423454077633E3L,
pS4 = -3.817341990928606692235481812252049415993E3L,
pS5 = 1.284635388402653715636722822195716476156E3L,
pS6 = -2.410736125231549204856567737329112037867E2L,
pS7 = 2.219191969382402856557594215833622156220E1L,
pS8 = -7.249056260830627156600112195061001036533E-1L,
pS9 = 1.055923570937755300061509030361395604448E-3L,
qS0 = -5.014859407482408326519083440151745519205E3L,
qS1 = 2.430653047950480068881028451580393430537E4L,
qS2 = -4.997904737193653607449250593976069726962E4L,
qS3 = 5.675712336110456923807959930107347511086E4L,
qS4 = -3.881523118339661268482937768522572588022E4L,
qS5 = 1.634202194895541569749717032234510811216E4L,
qS6 = -4.151452662440709301601820849901296953752E3L,
qS7 = 5.956050864057192019085175976175695342168E2L,
qS8 = -4.175375777334867025769346564600396877176E1L,
/* 1.000000000000000000000000000000000000000E0 */
/* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
-0.0625 <= x <= 0.0625
peak relative error 3.3e-35 */
rS0 = -5.619049346208901520945464704848780243887E0L,
rS1 = 4.460504162777731472539175700169871920352E1L,
rS2 = -1.317669505315409261479577040530751477488E2L,
rS3 = 1.626532582423661989632442410808596009227E2L,
rS4 = -3.144806644195158614904369445440583873264E1L,
rS5 = -9.806674443470740708765165604769099559553E1L,
rS6 = 5.708468492052010816555762842394927806920E1L,
rS7 = 1.396540499232262112248553357962639431922E1L,
rS8 = -1.126243289311910363001762058295832610344E1L,
rS9 = -4.956179821329901954211277873774472383512E-1L,
rS10 = 3.313227657082367169241333738391762525780E-1L,
sS0 = -4.645814742084009935700221277307007679325E0L,
sS1 = 3.879074822457694323970438316317961918430E1L,
sS2 = -1.221986588013474694623973554726201001066E2L,
sS3 = 1.658821150347718105012079876756201905822E2L,
sS4 = -4.804379630977558197953176474426239748977E1L,
sS5 = -1.004296417397316948114344573811562952793E2L,
sS6 = 7.530281592861320234941101403870010111138E1L,
sS7 = 1.270735595411673647119592092304357226607E1L,
sS8 = -1.815144839646376500705105967064792930282E1L,
sS9 = -7.821597334910963922204235247786840828217E-2L,
/* 1.000000000000000000000000000000000000000E0 */
asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
long double
__ieee754_asinl (long double x)
{
long double a, t, w, p, q, c, r, s;
int flag;
if (__glibc_unlikely (isnan (x)))
return x + x;
flag = 0;
a = __builtin_fabsl (x);
if (a == 1.0L) /* |x|>= 1 */
return x * pio2_hi + x * pio2_lo; /* asin(1)=+-pi/2 with inexact */
else if (a >= 1.0L)
return (x - x) / (x - x); /* asin(|x|>1) is NaN */
else if (a < 0.5L)
{
if (a < 6.938893903907228e-18L) /* |x| < 2**-57 */
{
math_check_force_underflow (x);
long double force_inexact = huge + x;
math_force_eval (force_inexact);
return x; /* return x with inexact if x!=0 */
}
else
{
t = x * x;
/* Mark to use pS, qS later on. */
flag = 1;
}
}
else if (a < 0.625L)
{
t = a - 0.5625;
p = ((((((((((rS10 * t
+ rS9) * t
+ rS8) * t
+ rS7) * t
+ rS6) * t
+ rS5) * t
+ rS4) * t
+ rS3) * t
+ rS2) * t
+ rS1) * t
+ rS0) * t;
q = ((((((((( t
+ sS9) * t
+ sS8) * t
+ sS7) * t
+ sS6) * t
+ sS5) * t
+ sS4) * t
+ sS3) * t
+ sS2) * t
+ sS1) * t
+ sS0;
t = asinr5625 + p / q;
if (x > 0.0L)
return t;
else
return -t;
}
else
{
/* 1 > |x| >= 0.625 */
w = one - a;
t = w * 0.5;
}
p = (((((((((pS9 * t
+ pS8) * t
+ pS7) * t
+ pS6) * t
+ pS5) * t
+ pS4) * t
+ pS3) * t
+ pS2) * t
+ pS1) * t
+ pS0) * t;
q = (((((((( t
+ qS8) * t
+ qS7) * t
+ qS6) * t
+ qS5) * t
+ qS4) * t
+ qS3) * t
+ qS2) * t
+ qS1) * t
+ qS0;
if (flag) /* 2^-57 < |x| < 0.5 */
{
w = p / q;
return x + x * w;
}
s = sqrtl (t);
if (a > 0.975L)
{
w = p / q;
t = pio2_hi - (2.0 * (s + s * w) - pio2_lo);
}
else
{
w = ldbl_high (s);
c = (t - w * w) / (s + w);
r = p / q;
p = 2.0 * s * r - (pio2_lo - 2.0 * c);
q = pio4_hi - 2.0 * w;
t = pio4_hi - (p - q);
}
if (x > 0.0L)
return t;
else
return -t;
}
libm_alias_finite (__ieee754_asinl, __asinl)