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/*-
* Copyright (c) 2008 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* $FreeBSD$
*/
#include <float.h>
#include "fpmath.h"
#define BIAS (LDBL_MAX_EXP - 1)
#define MANH_SIZE (LDBL_MANH_SIZE + 1)
/* Approximation thresholds. */
#define ASIN_LINEAR (BIAS - 56) /* 2**-56 */
#define ACOS_CONST (BIAS - 113) /* 2**-113 */
#define ATAN_CONST (BIAS + 113) /* 2**113 */
#define ATAN_LINEAR (BIAS - 56) /* 2**-56 */
/* 0.95 */
#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)
/* Constants shared by the long double inverse trig functions. */
#define pS0 _ItL_pS0
#define pS1 _ItL_pS1
#define pS2 _ItL_pS2
#define pS3 _ItL_pS3
#define pS4 _ItL_pS4
#define pS5 _ItL_pS5
#define pS6 _ItL_pS6
#define pS7 _ItL_pS7
#define pS8 _ItL_pS8
#define pS9 _ItL_pS9
#define qS1 _ItL_qS1
#define qS2 _ItL_qS2
#define qS3 _ItL_qS3
#define qS4 _ItL_qS4
#define qS5 _ItL_qS5
#define qS6 _ItL_qS6
#define qS7 _ItL_qS7
#define qS8 _ItL_qS8
#define qS9 _ItL_qS9
#define atanhi _ItL_atanhi
#define atanlo _ItL_atanlo
#define aT _ItL_aT
#define pi_lo _ItL_pi_lo
#define pio2_hi atanhi[3]
#define pio2_lo atanlo[3]
#define pio4_hi atanhi[1]
/* Constants shared by the long double inverse trig functions. */
extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6, pS7, pS8, pS9;
extern const long double qS1, qS2, qS3, qS4, qS5, qS6, qS7, qS8, qS9;
extern const long double atanhi[], atanlo[], aT[];
extern const long double pi_lo;
static inline long double
P(long double x)
{
return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
(pS4 + x * (pS5 + x * (pS6 + x * (pS7 + x * (pS8 + x * \
pS9))))))))));
}
static inline long double
Q(long double x)
{
return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * \
(qS5 + x * (qS6 + x * (qS7 + x * (qS8 + x * qS9)))))))));
}
static inline long double
T_even(long double x)
{
return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \
(aT[8] + x * (aT[10] + x * (aT[12] + x * (aT[14] + x * \
(aT[16] + x * (aT[18] + x * (aT[20] + x * aT[22])))))))))));
}
static inline long double
T_odd(long double x)
{
return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \
(aT[9] + x * (aT[11] + x * (aT[13] + x * (aT[15] + x * \
(aT[17] + x * (aT[19] + x * (aT[21] + x * aT[23])))))))))));
}
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