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/* $OpenBSD: invtrig.h,v 1.2 2016/09/12 19:47:03 guenther Exp $ */ |
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/*- |
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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: src/lib/msun/ld80/invtrig.h,v 1.2 2008/08/02 03:56:22 das Exp $ |
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*/ |
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#include <sys/types.h> |
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#include <machine/ieee.h> |
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#include <float.h> |
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#define BIAS (LDBL_MAX_EXP - 1) |
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#define MANH_SIZE EXT_FRACHBITS |
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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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#ifdef EXT_IMPLICIT_NBIT |
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#define THRESH (0xe666666666666666ULL>>(64-(MANH_SIZE-1))) |
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#else /* EXT_IMPLICIT_NBIT */ |
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#define THRESH ((0xe666666666666666ULL>>(64-(MANH_SIZE-1)))|0x80000000) |
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#endif /* EXT_IMPLICIT_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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__BEGIN_HIDDEN_DECLS |
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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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__END_HIDDEN_DECLS |
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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 |