affd78d50b
at compile time regardless of the dynamic precision, and there's no way to disable this misfeature at compile time. Hence, it's impossible to generate the appropriate tables of constants for the long double inverse trig functions in a straightforward way on i386; this change hacks around the problem by encoding the underlying bits in the table. Note that these functions won't pass the regression test on i386, even with the FPU set to extended precision, because the regression test is similarly damaged by gcc. However, the tests all pass when compiled with a modified version of gcc. Reported by: bde
115 lines
3.1 KiB
C
115 lines
3.1 KiB
C
/*-
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* Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*
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* $FreeBSD$
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*/
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#include <float.h>
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#include "fpmath.h"
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#define BIAS (LDBL_MAX_EXP - 1)
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#define MANH_SIZE LDBL_MANH_SIZE
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/* Approximation thresholds. */
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#define ASIN_LINEAR (BIAS - 32) /* 2**-32 */
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#define ACOS_CONST (BIAS - 65) /* 2**-65 */
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#define ATAN_CONST (BIAS + 65) /* 2**65 */
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#define ATAN_LINEAR (BIAS - 32) /* 2**-32 */
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/* 0.95 */
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#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
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/* Constants shared by the long double inverse trig functions. */
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#define pS0 _ItL_pS0
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#define pS1 _ItL_pS1
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#define pS2 _ItL_pS2
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#define pS3 _ItL_pS3
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#define pS4 _ItL_pS4
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#define pS5 _ItL_pS5
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#define pS6 _ItL_pS6
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#define qS1 _ItL_qS1
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#define qS2 _ItL_qS2
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#define qS3 _ItL_qS3
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#define qS4 _ItL_qS4
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#define qS5 _ItL_qS5
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#define atanhi _ItL_atanhi
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#define atanlo _ItL_atanlo
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#define aT _ItL_aT
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#define pi_lo _ItL_pi_lo
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#define pio2_hi atanhi[3]
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#define pio2_lo atanlo[3]
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#define pio4_hi atanhi[1]
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#ifdef STRUCT_DECLS
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typedef struct longdouble {
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uint64_t mant;
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uint16_t expsign;
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} LONGDOUBLE;
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#else
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typedef long double LONGDOUBLE;
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#endif
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extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
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extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
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extern const LONGDOUBLE atanhi[], atanlo[], aT[];
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extern const LONGDOUBLE pi_lo;
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#ifndef STRUCT_DECLS
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static inline long double
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P(long double x)
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{
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return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
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(pS4 + x * (pS5 + x * pS6)))))));
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}
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static inline long double
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Q(long double x)
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{
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return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
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}
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static inline long double
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T_even(long double x)
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{
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return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
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(aT[8] + x * (aT[10] + x * aT[12]))))));
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}
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static inline long double
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T_odd(long double x)
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{
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return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
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(aT[9] + x * aT[11])))));
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}
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#endif
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