glibc/sysdeps/ieee754/ldbl-96/e_atanhl.c
Joseph Myers 2ca725c594 Fix ldbl-96, ldbl-128ibm atanhl inaccuracy (bug 18046, bug 18047).
The threshold in ldbl-96 atanhl for when to return the argument,
0x1p-28, is a bit too big, and that in ldbl-128ibm atanhl is much too
big (the relevant condition being x^3/3 being < 0.5ulp of x),
resulting in errors a bit above the limits of those considered
acceptable in glibc in the ldbl-96 case, and in large errors in the
ldbl-128ibm case.  This patch changes those implementations to use
more appropriate thresholds and adds tests around the thresholds for
various formats.

Tested for x86_64, x86 and powerpc.  x86_64 and x86 ulps updated
accordingly.

	[BZ #18046]
	[BZ #18047]
	* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl): Use
	0x1p-56L as threshold for just returning the argument.
	* sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Use
	0x1p-32L as threshold for just returning the argument.
	* math/auto-libm-test-in: Add more tests of atanh.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/fpu/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulp: Likewise.
2015-02-27 17:48:37 +00:00

68 lines
1.8 KiB
C

/* s_atanhl.c -- long double version of s_atan.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/*
* ====================================================
* 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.
* ====================================================
*/
/* __ieee754_atanhl(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
*
* Special cases:
* atanhl(x) is NaN if |x| > 1 with signal;
* atanhl(NaN) is that NaN with no signal;
* atanhl(+-1) is +-INF with signal.
*
*/
#include <math.h>
#include <math_private.h>
static const long double one = 1.0, huge = 1e4900L;
static const long double zero = 0.0;
long double
__ieee754_atanhl(long double x)
{
long double t;
int32_t ix;
u_int32_t se,i0,i1;
GET_LDOUBLE_WORDS(se,i0,i1,x);
ix = se&0x7fff;
if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff)
/* |x|>1 */
return (x-x)/(x-x);
if(ix==0x3fff)
return x/zero;
if(ix<0x3fdf) {
math_force_eval(huge+x);
return x; /* x<2**-32 */
}
SET_LDOUBLE_EXP(x,ix);
if(ix<0x3ffe) { /* x < 0.5 */
t = x+x;
t = 0.5*__log1pl(t+t*x/(one-x));
} else
t = 0.5*__log1pl((x+x)/(one-x));
if(se<=0x7fff) return t; else return -t;
}
strong_alias (__ieee754_atanhl, __atanhl_finite)