190 lines
8.6 KiB
C
190 lines
8.6 KiB
C
/* -------------------------------------------------------------- */
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/* (C)Copyright 2006,2007, */
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/* International Business Machines Corporation */
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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 */
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/* without modification, are permitted provided that the */
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/* following conditions are met: */
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/* */
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/* - 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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/* */
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/* - Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* - Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* 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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/* */
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/* Redistributions in binary form must reproduce the above */
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/* copyright notice, this list of conditions and the following */
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/* disclaimer in the documentation and/or other materials */
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/* provided with the distribution. */
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/* */
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/* Neither the name of IBM Corporation nor the names of its */
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/* contributors may be used to endorse or promote products */
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/* derived from this software without specific prior written */
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/* permission. */
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/* */
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/* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND */
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/* CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, */
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/* INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF */
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/* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE */
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/* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR */
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/* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, */
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/* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT */
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/* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; */
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/* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) */
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/* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN */
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/* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR */
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/* OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, */
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/* EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
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/* -------------------------------------------------------------- */
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/* PROLOG END TAG zYx */
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#ifdef __SPU__
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#ifndef _ASINHD2_H_
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#define _ASINHD2_H_ 1
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#include <spu_intrinsics.h>
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#include "logd2.h"
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#include "sqrtd2.h"
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/*
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* FUNCTION
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* vector double _asinhd2(vector double x)
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*
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* DESCRIPTION
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* The asinhd2 function returns a vector containing the hyperbolic
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* arcsines of the corresponding elements of the input vector.
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*
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* We are using the formula:
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* asinh = ln(|x| + sqrt(x^2 + 1))
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* and the anti-symmetry of asinh.
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*
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* For x near zero, we use the Taylor series:
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*
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* infinity
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* ------
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* - ' P (0)
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* - k-1 k
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* asinh x = - ----- x
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* - k
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* - ,
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* ------
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* k = 1
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*
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* Special Cases:
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* asinh(+0) returns +0
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* asinh(-0) returns -0
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* asinh(+infinity) returns +infinity
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* asinh(-infinity) returns -infinity
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* asinh(NaN) returns NaN
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*
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*/
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/*
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* Maclaurin Series Coefficients
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* for x near 0.
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*/
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#define ASINH_MAC01 1.0000000000000000000000000000000000000000000000000000000000000000000000E0
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#define ASINH_MAC03 -1.6666666666666666666666666666666666666666666666666666666666666666666667E-1
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#define ASINH_MAC05 7.5000000000000000000000000000000000000000000000000000000000000000000000E-2
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#define ASINH_MAC07 -4.4642857142857142857142857142857142857142857142857142857142857142857143E-2
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#define ASINH_MAC09 3.0381944444444444444444444444444444444444444444444444444444444444444444E-2
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#define ASINH_MAC11 -2.2372159090909090909090909090909090909090909090909090909090909090909091E-2
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#define ASINH_MAC13 1.7352764423076923076923076923076923076923076923076923076923076923076923E-2
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#define ASINH_MAC15 -1.3964843750000000000000000000000000000000000000000000000000000000000000E-2
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#define ASINH_MAC17 1.1551800896139705882352941176470588235294117647058823529411764705882353E-2
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#if 0
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#define ASINH_MAC19 -9.7616095291940789473684210526315789473684210526315789473684210526315789E-3
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#define ASINH_MAC21 8.3903358096168154761904761904761904761904761904761904761904761904761905E-3
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#define ASINH_MAC23 -7.3125258735988451086956521739130434782608695652173913043478260869565217E-3
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#define ASINH_MAC25 6.4472103118896484375000000000000000000000000000000000000000000000000000E-3
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#define ASINH_MAC27 -5.7400376708419234664351851851851851851851851851851851851851851851851852E-3
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#define ASINH_MAC29 5.1533096823199041958512931034482758620689655172413793103448275862068966E-3
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#define ASINH_MAC31 -4.6601434869150961599042338709677419354838709677419354838709677419354839E-3
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#define ASINH_MAC33 4.2409070936793630773370916193181818181818181818181818181818181818181818E-3
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#define ASINH_MAC35 -3.8809645588376692363194056919642857142857142857142857142857142857142857E-3
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#define ASINH_MAC37 3.5692053938259345454138678473395270270270270270270270270270270270270270E-3
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#define ASINH_MAC39 -3.2970595034734847453924325796274038461538461538461538461538461538461538E-3
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#define ASINH_MAC41 3.0578216492580306693548109473251714939024390243902439024390243902439024E-3
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#define ASINH_MAC43 -2.8461784011089421678767647854117460029069767441860465116279069767441860E-3
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#endif
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static __inline vector double _asinhd2(vector double x)
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{
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vec_double2 sign_mask = spu_splats(-0.0);
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vec_double2 oned = spu_splats(1.0);
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vec_uchar16 dup_even = ((vec_uchar16) { 0,1,2,3, 0,1,2,3, 8,9,10,11, 8,9,10,11 });
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vec_uint4 infminus1 = spu_splats(0x7FEFFFFFU);
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vec_uint4 isinfnan;
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vec_double2 xabs, xsqu;
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vec_uint4 xabshigh;
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/* Where we switch from maclaurin to formula */
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vec_float4 switch_approx = spu_splats(0.165f);
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vec_uint4 use_form;
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vec_float4 xf;
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vec_double2 result, fresult, mresult;
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xabs = spu_andc(x, sign_mask);
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xsqu = spu_mul(x, x);
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xf = spu_roundtf(xabs);
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xf = spu_shuffle(xf, xf, dup_even);
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/*
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* Formula:
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* asinh = ln(|x| + sqrt(x^2 + 1))
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*/
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fresult = _sqrtd2(spu_add(xsqu, oned));
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fresult = spu_add(xabs, fresult);
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fresult = _logd2(fresult);
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/*
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* Maclaurin Series approximation
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*/
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mresult = spu_madd(xsqu, spu_splats(ASINH_MAC17), spu_splats(ASINH_MAC15));
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mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC13));
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mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC11));
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mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC09));
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mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC07));
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mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC05));
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mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC03));
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mresult = spu_madd(xsqu, mresult, spu_splats(ASINH_MAC01));
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mresult = spu_mul(xabs, mresult);
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/*
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* Choose between series and formula
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*/
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use_form = spu_cmpgt(xf, switch_approx);
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result = spu_sel(mresult, fresult, (vec_ullong2)use_form);
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/* Special Cases */
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/* Infinity and NaN */
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xabshigh = (vec_uint4)spu_shuffle(xabs, xabs, dup_even);
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isinfnan = spu_cmpgt(xabshigh, infminus1);
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result = spu_sel(result, x, (vec_ullong2)isinfnan);
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/* Restore sign - asinh is an anti-symmetric */
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result = spu_sel(result, x, (vec_ullong2)sign_mask);
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return result;
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}
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#endif /* _ASINHD2_H_ */
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#endif /* __SPU__ */
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