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2ca725c594
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.
67 lines
1.7 KiB
C
67 lines
1.7 KiB
C
/* @(#)e_atanh.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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/* __ieee754_atanh(x)
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* Method :
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* 1.Reduced x to positive by atanh(-x) = -atanh(x)
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* 2.For x>=0.5
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* 1 2x x
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* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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* 2 1 - x 1 - x
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*
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* For x<0.5
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* atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
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*
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* Special cases:
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* atanh(x) is NaN if |x| > 1 with signal;
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* atanh(NaN) is that NaN with no signal;
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* atanh(+-1) is +-INF with signal.
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*
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*/
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#include <math.h>
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#include <math_private.h>
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static const long double one = 1.0L, huge = 1e300L;
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static const long double zero = 0.0L;
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long double
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__ieee754_atanhl(long double x)
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{
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long double t;
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int64_t hx,ix;
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double xhi;
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xhi = ldbl_high (x);
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EXTRACT_WORDS64 (hx, xhi);
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ix = hx&0x7fffffffffffffffLL;
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if (ix >= 0x3ff0000000000000LL) { /* |x|>=1 */
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if (ix > 0x3ff0000000000000LL)
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return (x-x)/(x-x);
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t = fabsl (x);
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if (t > one)
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return (x-x)/(x-x);
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if (t == one)
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return x/zero;
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}
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if(ix<0x3c70000000000000LL&&(huge+x)>zero) return x; /* x<2**-56 */
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x = fabsl (x);
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if(ix<0x3fe0000000000000LL) { /* x < 0.5 */
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t = x+x;
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t = 0.5*__log1pl(t+t*x/(one-x));
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} else
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t = 0.5*__log1pl((x+x)/(one-x));
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if(hx>=0) return t; else return -t;
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}
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strong_alias (__ieee754_atanhl, __atanhl_finite)
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