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According to C99 and C11 Annex F, acosh (1) should be +0 in all rounding modes. However, some implementations in glibc wrongly return -0 in round-downward mode (which is what you get if you end up computing log1p (-0), via 1 - 1 being -0 in round-downward mode). This patch fixes the problem implementations, by correcting the test for an exact 1 value in the ldbl-96 implementation to allow for the explicit high bit of the mantissa, and by inserting fabs instructions in the i386 implementations; tests of acosh are duly converted to ALL_RM_TEST. I believe all the other sysdeps/ieee754 implementations are already OK (I haven't checked the ia64 versions, but if buggy then that will be obvious from the results of test runs after this patch is in). Tested x86_64 and x86 and ulps updated accordingly. [BZ #16927] * sysdeps/i386/fpu/e_acosh.S (__ieee754_acosh): Use fabs on x-1 value. * sysdeps/i386/fpu/e_acoshf.S (__ieee754_acoshf): Likewise. * sysdeps/i386/fpu/e_acoshl.S (__ieee754_acoshl): Likewise. * sysdeps/ieee754/ldbl-96/e_acoshl.c (__ieee754_acoshl): Correct for explicit high bit of mantissa when testing for argument equal to 1. * math/libm-test.inc (acosh_test): Use ALL_RM_TEST. * sysdeps/i386/fpu/libm-test-ulps: Update. * sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
62 lines
1.7 KiB
C
62 lines
1.7 KiB
C
/* e_acoshl.c -- long double version of e_acosh.c.
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* Conversion to long double by Ulrich Drepper,
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* Cygnus Support, drepper@cygnus.com.
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*/
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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_acoshl(x)
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* Method :
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* Based on
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* acoshl(x) = logl [ x + sqrtl(x*x-1) ]
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* we have
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* acoshl(x) := logl(x)+ln2, if x is large; else
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* acoshl(x) := logl(2x-1/(sqrtl(x*x-1)+x)) if x>2; else
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* acoshl(x) := log1pl(t+sqrtl(2.0*t+t*t)); where t=x-1.
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*
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* Special cases:
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* acoshl(x) is NaN with signal if x<1.
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* acoshl(NaN) is NaN without signal.
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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
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one = 1.0,
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ln2 = 6.931471805599453094287e-01L; /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
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long double
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__ieee754_acoshl(long double x)
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{
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long double t;
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u_int32_t se,i0,i1;
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GET_LDOUBLE_WORDS(se,i0,i1,x);
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if(se<0x3fff || se & 0x8000) { /* x < 1 */
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return (x-x)/(x-x);
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} else if(se >=0x401d) { /* x > 2**30 */
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if(se >=0x7fff) { /* x is inf of NaN */
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return x+x;
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} else
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return __ieee754_logl(x)+ln2; /* acoshl(huge)=logl(2x) */
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} else if(((se-0x3fff)|(i0^0x80000000)|i1)==0) {
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return 0.0; /* acosh(1) = 0 */
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} else if (se > 0x4000) { /* 2**28 > x > 2 */
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t=x*x;
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return __ieee754_logl(2.0*x-one/(x+__ieee754_sqrtl(t-one)));
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} else { /* 1<x<2 */
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t = x-one;
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return __log1pl(t+__ieee754_sqrtl(2.0*t+t*t));
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}
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}
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strong_alias (__ieee754_acoshl, __acoshl_finite)
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