musl/src/math/__invtrigl.h

/* origin: FreeBSD /usr/src/lib/msun/src/ld80/invtrig.h */
/*-
 * Copyright (c) 2008 David Schultz <[email protected]>
 * 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.
 */

#include "libm.h"

#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384

#define BIAS            (LDBL_MAX_EXP - 1)
#define MANH_SIZE       LDBL_MANH_SIZE

/* Approximation thresholds. */
#define ASIN_LINEAR     (BIAS - 32)     /* 2**-32 */
#define ACOS_CONST      (BIAS - 65)     /* 2**-65 */
#define ATAN_CONST      (BIAS + 65)     /* 2**65 */
#define ATAN_LINEAR     (BIAS - 32)     /* 2**-32 */

/* 0.95 */
#define THRESH  ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|LDBL_NBIT)

/* Constants shared by the long double inverse trig functions. */
#define pS0     __pS0
#define pS1     __pS1
#define pS2     __pS2
#define pS3     __pS3
#define pS4     __pS4
#define pS5     __pS5
#define pS6     __pS6
#define qS1     __qS1
#define qS2     __qS2
#define qS3     __qS3
#define qS4     __qS4
#define qS5     __qS5
#define atanhi  __atanhi
#define atanlo  __atanlo
#define aT      __aT
#define pi_lo   __pi_lo

#define pio2_hi atanhi[3]
#define pio2_lo atanlo[3]
#define pio4_hi atanhi[1]

#ifdef STRUCT_DECLS
typedef struct longdouble {
	uint64_t mant;
	uint16_t expsign;
} LONGDOUBLE;
#else
typedef long double LONGDOUBLE;
#endif

extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6;
extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5;
extern const LONGDOUBLE atanhi[], atanlo[], aT[];
extern const LONGDOUBLE pi_lo;

#ifndef STRUCT_DECLS
static inline long double
P(long double x)
{
	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \
		(pS4 + x * (pS5 + x * pS6)))))));
}

static inline long double
Q(long double x)
{
	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5)))));
}

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]))))));
}

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])))));
}
#endif

#endif