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137cef7d43
The ldbl-128ibm implementation of asinhl uses cut-offs of 0x1p28 and 0x1p-29 to determine when to use simpler formulas that avoid possible overflow / underflow. Both those cut-offs are inappropriate for this format, resulting in large errors. This patch changes the code to use more appropriate cut-offs of 0x1p56 and 0x1p-56, adding tests around the cut-offs for various floating-point formats. Tested for powerpc. Also tested for x86_64 and x86 and updated ulps. [BZ #18020] * sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Use 2**56 and 2**-56 not 2**28 and 2**-29 as thresholds for simpler formulas. * math/auto-libm-test-in: Add more tests of asinh. * math/auto-libm-test-out: Regenerated. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
62 lines
1.9 KiB
C
62 lines
1.9 KiB
C
/* @(#)s_asinh.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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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] = "$NetBSD: s_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
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#endif
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/* asinh(x)
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* Method :
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* Based on
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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* we have
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* asinh(x) := x if 1+x*x=1,
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* := sign(x)*(log(x)+ln2)) for large |x|, else
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* := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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* := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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*/
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#include <math.h>
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#include <math_private.h>
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#include <math_ldbl_opt.h>
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static const long double
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one = 1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */
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ln2 = 0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */
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huge= 1.00000000000000000000e+300L;
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long double __asinhl(long double x)
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{
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long double t,w;
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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>=0x7ff0000000000000LL) return x+x; /* x is inf or NaN */
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if(ix< 0x3c70000000000000LL) { /* |x|<2**-56 */
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if(huge+x>one) return x; /* return x inexact except 0 */
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}
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if(ix>0x4370000000000000LL) { /* |x| > 2**56 */
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w = __ieee754_logl(fabsl(x))+ln2;
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} else if (ix>0x4000000000000000LL) { /* 2**56 >= |x| > 2.0 */
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t = fabs(x);
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w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
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} else { /* 2.0 >= |x| >= 2**-56 */
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t = x*x;
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w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
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}
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if(hx>0) return w; else return -w;
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}
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long_double_symbol (libm, __asinhl, asinhl);
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