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math: clean up inverse trigonometric functions
modifications: * avoid unsigned->signed conversions * removed various volatile hacks * use FORCE_EVAL when evaluating only for side-effects * factor out R() rational approximation instead of manual inline * __invtrigl.h now only provides __invtrigl_R, __pio2_hi and __pio2_lo * use 2*pio2_hi, 2*pio2_lo instead of pi_hi, pi_lo otherwise the logic is not changed, long double versions will need a revisit when a genaral long double cleanup happens
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/* origin: FreeBSD /usr/src/lib/msun/src/ld80/invtrig.h */
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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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#include "libm.h"
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#include <float.h>
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#if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
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#define BIAS (LDBL_MAX_EXP - 1)
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#define MANH_SIZE LDBL_MANH_SIZE
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/* Constants shared by the long double inverse trig functions. */
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#define pS0 __pS0
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#define pS1 __pS1
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#define pS2 __pS2
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#define pS3 __pS3
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#define pS4 __pS4
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#define pS5 __pS5
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#define pS6 __pS6
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#define qS1 __qS1
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#define qS2 __qS2
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#define qS3 __qS3
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#define qS4 __qS4
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#define qS5 __qS5
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#define pi_hi __pi_hi
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#define pi_lo __pi_lo
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/* shared by acosl, asinl and atan2l */
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#define pio2_hi __pio2_hi
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#define pio2_lo __pio2_lo
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extern const long double pio2_hi, pio2_lo;
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extern const long double pS0, pS1, pS2, pS3, pS4, pS5, pS6;
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extern const long double qS1, qS2, qS3, qS4, qS5;
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extern const long double pi_hi, pi_lo, pio2_hi, pio2_lo;
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static long double P(long double x)
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{
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return x * (pS0 + x * (pS1 + x * (pS2 + x * (pS3 +
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x * (pS4 + x * (pS5 + x * pS6))))));
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}
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static long double 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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long double __invtrigl_R(long double z);
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#endif
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