| 1 |  |  | /*	$OpenBSD: invtrig.h,v 1.2 2016/09/12 19:47:03 guenther Exp $	*/ | 
    
    | 2 |  |  | /*- | 
    
    | 3 |  |  |  * Copyright (c) 2008 David Schultz <das@FreeBSD.ORG> | 
    
    | 4 |  |  |  * All rights reserved. | 
    
    | 5 |  |  |  * | 
    
    | 6 |  |  |  * Redistribution and use in source and binary forms, with or without | 
    
    | 7 |  |  |  * modification, are permitted provided that the following conditions | 
    
    | 8 |  |  |  * are met: | 
    
    | 9 |  |  |  * 1. Redistributions of source code must retain the above copyright | 
    
    | 10 |  |  |  *    notice, this list of conditions and the following disclaimer. | 
    
    | 11 |  |  |  * 2. Redistributions in binary form must reproduce the above copyright | 
    
    | 12 |  |  |  *    notice, this list of conditions and the following disclaimer in the | 
    
    | 13 |  |  |  *    documentation and/or other materials provided with the distribution. | 
    
    | 14 |  |  |  * | 
    
    | 15 |  |  |  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND | 
    
    | 16 |  |  |  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | 
    
    | 17 |  |  |  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | 
    
    | 18 |  |  |  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE | 
    
    | 19 |  |  |  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL | 
    
    | 20 |  |  |  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS | 
    
    | 21 |  |  |  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) | 
    
    | 22 |  |  |  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT | 
    
    | 23 |  |  |  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY | 
    
    | 24 |  |  |  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF | 
    
    | 25 |  |  |  * SUCH DAMAGE. | 
    
    | 26 |  |  |  * | 
    
    | 27 |  |  |  * $FreeBSD: src/lib/msun/ld80/invtrig.h,v 1.2 2008/08/02 03:56:22 das Exp $ | 
    
    | 28 |  |  |  */ | 
    
    | 29 |  |  |  | 
    
    | 30 |  |  | #include <sys/types.h> | 
    
    | 31 |  |  | #include <machine/ieee.h> | 
    
    | 32 |  |  | #include <float.h> | 
    
    | 33 |  |  |  | 
    
    | 34 |  |  | #define	BIAS		(LDBL_MAX_EXP - 1) | 
    
    | 35 |  |  | #define	MANH_SIZE	EXT_FRACHBITS | 
    
    | 36 |  |  |  | 
    
    | 37 |  |  | /* Approximation thresholds. */ | 
    
    | 38 |  |  | #define	ASIN_LINEAR	(BIAS - 32)	/* 2**-32 */ | 
    
    | 39 |  |  | #define	ACOS_CONST	(BIAS - 65)	/* 2**-65 */ | 
    
    | 40 |  |  | #define	ATAN_CONST	(BIAS + 65)	/* 2**65 */ | 
    
    | 41 |  |  | #define	ATAN_LINEAR	(BIAS - 32)	/* 2**-32 */ | 
    
    | 42 |  |  |  | 
    
    | 43 |  |  | /* 0.95 */ | 
    
    | 44 |  |  | #ifdef EXT_IMPLICIT_NBIT | 
    
    | 45 |  |  | #define	THRESH	(0xe666666666666666ULL>>(64-(MANH_SIZE-1))) | 
    
    | 46 |  |  | #else /* EXT_IMPLICIT_NBIT */ | 
    
    | 47 |  |  | #define	THRESH	((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|0x80000000) | 
    
    | 48 |  |  | #endif /* EXT_IMPLICIT_NBIT */ | 
    
    | 49 |  |  |  | 
    
    | 50 |  |  | /* Constants shared by the long double inverse trig functions. */ | 
    
    | 51 |  |  | #define	pS0	_ItL_pS0 | 
    
    | 52 |  |  | #define	pS1	_ItL_pS1 | 
    
    | 53 |  |  | #define	pS2	_ItL_pS2 | 
    
    | 54 |  |  | #define	pS3	_ItL_pS3 | 
    
    | 55 |  |  | #define	pS4	_ItL_pS4 | 
    
    | 56 |  |  | #define	pS5	_ItL_pS5 | 
    
    | 57 |  |  | #define	pS6	_ItL_pS6 | 
    
    | 58 |  |  | #define	qS1	_ItL_qS1 | 
    
    | 59 |  |  | #define	qS2	_ItL_qS2 | 
    
    | 60 |  |  | #define	qS3	_ItL_qS3 | 
    
    | 61 |  |  | #define	qS4	_ItL_qS4 | 
    
    | 62 |  |  | #define	qS5	_ItL_qS5 | 
    
    | 63 |  |  | #define	atanhi	_ItL_atanhi | 
    
    | 64 |  |  | #define	atanlo	_ItL_atanlo | 
    
    | 65 |  |  | #define	aT	_ItL_aT | 
    
    | 66 |  |  | #define	pi_lo	_ItL_pi_lo | 
    
    | 67 |  |  |  | 
    
    | 68 |  |  | #define	pio2_hi	atanhi[3] | 
    
    | 69 |  |  | #define	pio2_lo	atanlo[3] | 
    
    | 70 |  |  | #define	pio4_hi	atanhi[1] | 
    
    | 71 |  |  |  | 
    
    | 72 |  |  | #ifdef STRUCT_DECLS | 
    
    | 73 |  |  | typedef struct longdouble { | 
    
    | 74 |  |  | 	uint64_t mant; | 
    
    | 75 |  |  | 	uint16_t expsign; | 
    
    | 76 |  |  | } LONGDOUBLE; | 
    
    | 77 |  |  | #else | 
    
    | 78 |  |  | typedef long double LONGDOUBLE; | 
    
    | 79 |  |  | #endif | 
    
    | 80 |  |  |  | 
    
    | 81 |  |  | __BEGIN_HIDDEN_DECLS | 
    
    | 82 |  |  | extern const LONGDOUBLE pS0, pS1, pS2, pS3, pS4, pS5, pS6; | 
    
    | 83 |  |  | extern const LONGDOUBLE qS1, qS2, qS3, qS4, qS5; | 
    
    | 84 |  |  | extern const LONGDOUBLE atanhi[], atanlo[], aT[]; | 
    
    | 85 |  |  | extern const LONGDOUBLE pi_lo; | 
    
    | 86 |  |  | __END_HIDDEN_DECLS | 
    
    | 87 |  |  |  | 
    
    | 88 |  |  | #ifndef STRUCT_DECLS | 
    
    | 89 |  |  |  | 
    
    | 90 |  |  | static inline long double | 
    
    | 91 |  |  | P(long double x) | 
    
    | 92 |  |  | { | 
    
    | 93 |  |  |  | 
    
    | 94 |  |  | 	return (x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 + x * \ | 
    
    | 95 |  |  | 		(pS4 + x * (pS5 + x * pS6))))))); | 
    
    | 96 |  |  | } | 
    
    | 97 |  |  |  | 
    
    | 98 |  |  | static inline long double | 
    
    | 99 |  |  | Q(long double x) | 
    
    | 100 |  |  | { | 
    
    | 101 |  |  |  | 
    
    | 102 |  |  | 	return (1.0 + x * (qS1 + x * (qS2 + x * (qS3 + x * (qS4 + x * qS5))))); | 
    
    | 103 |  |  | } | 
    
    | 104 |  |  |  | 
    
    | 105 |  |  | static inline long double | 
    
    | 106 |  |  | T_even(long double x) | 
    
    | 107 |  |  | { | 
    
    | 108 |  |  |  | 
    
    | 109 |  |  | 	return (aT[0] + x * (aT[2] + x * (aT[4] + x * (aT[6] + x * \ | 
    
    | 110 |  |  | 		(aT[8] + x * (aT[10] + x * aT[12])))))); | 
    
    | 111 |  |  | } | 
    
    | 112 |  |  |  | 
    
    | 113 |  |  | static inline long double | 
    
    | 114 |  |  | T_odd(long double x) | 
    
    | 115 |  |  | { | 
    
    | 116 |  |  |  | 
    
    | 117 |  |  | 	return (aT[1] + x * (aT[3] + x * (aT[5] + x * (aT[7] + x * \ | 
    
    | 118 |  |  | 		(aT[9] + x * aT[11]))))); | 
    
    | 119 |  |  | } | 
    
    | 120 |  |  |  | 
    
    | 121 |  |  | #endif |