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114 lines
3.5 KiB
C
114 lines
3.5 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 + 1)
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/* Approximation thresholds. */
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#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */
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#define ACOS_CONST (BIAS - 113) /* 2**-113 */
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#define ATAN_CONST (BIAS + 113) /* 2**113 */
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#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */
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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 pS7 _ItL_pS7
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#define pS8 _ItL_pS8
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#define pS9 _ItL_pS9
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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 qS6 _ItL_qS6
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#define qS7 _ItL_qS7
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#define qS8 _ItL_qS8
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#define qS9 _ItL_qS9
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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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/* Constants shared by the long double inverse trig functions. */
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extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
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extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
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extern const long double atanhi[], atanlo[], aT[];
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extern const long double pi_lo;
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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 + x * (pS7 + x * (pS8 + x * \
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pS9))))))))));
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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 * \
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(qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
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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] + x * (aT[14] + x * \
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(aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
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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] + x * (aT[13] + x * (aT[15] + x * \
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(aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
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}
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