353 lines
14 KiB
C
353 lines
14 KiB
C
/* Accurate tables for exp2f().
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Copyright (C) 1998 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, write to the Free
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Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 USA. */
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/* This table has the property that, for all integers -128 <= i <= 127,
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exp(i/256.0 + __exp2f_deltatable[i-128]) == __exp2f_atable[i+128] + r
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for some -2^-35 < r < 2^-35 (abs(r) < 2^-36 if i <= 0); and that
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__exp2f_deltatable[i+128] == t * 2^-30
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for integer t so that abs(t) <= 43447 * 2^0. */
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#define W30 (9.31322575e-10)
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static const float __exp2f_deltatable[256] = {
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-810*W30, 283*W30, -1514*W30, 1304*W30,
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-1148*W30, -98*W30, -744*W30, -156*W30,
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-419*W30, -155*W30, 474*W30, 167*W30,
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-1984*W30, -826*W30, 692*W30, 781*W30,
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-578*W30, -411*W30, -129*W30, -1500*W30,
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654*W30, -141*W30, -816*W30, -53*W30,
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148*W30, 493*W30, -2214*W30, 760*W30,
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260*W30, 750*W30, -1300*W30, 1424*W30,
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-1445*W30, -339*W30, -680*W30, -349*W30,
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-922*W30, 531*W30, 193*W30, -2892*W30,
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290*W30, -2145*W30, -276*W30, 485*W30,
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-695*W30, 215*W30, -7093*W30, 412*W30,
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-4596*W30, 367*W30, 592*W30, -615*W30,
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-97*W30, -1066*W30, 972*W30, -226*W30,
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-625*W30, -374*W30, -5647*W30, -180*W30,
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20349*W30, -447*W30, 111*W30, -4164*W30,
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-87*W30, -21*W30, -251*W30, 66*W30,
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-517*W30, 2093*W30, -263*W30, 182*W30,
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-601*W30, 475*W30, -483*W30, -1251*W30,
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-373*W30, 1471*W30, -92*W30, -215*W30,
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-97*W30, -190*W30, 0*W30, -290*W30,
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-2647*W30, 1940*W30, -582*W30, 28*W30,
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833*W30, 1493*W30, 34*W30, 321*W30,
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3327*W30, -35*W30, 177*W30, -135*W30,
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-796*W30, -428*W30, 129*W30, 9332*W30,
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-12*W30, -69*W30, -1743*W30, 6508*W30,
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-60*W30, 359*W30, 43447*W30, 15*W30,
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-23*W30, -305*W30, -375*W30, -652*W30,
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667*W30, 269*W30, -1575*W30, 185*W30,
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-329*W30, 200*W30, 6002*W30, 163*W30,
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-647*W30, 19*W30, -603*W30, -755*W30,
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742*W30, -438*W30, 3587*W30, 2560*W30,
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0*W30, -520*W30, -241*W30, -299*W30,
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-1270*W30, -991*W30, -1138*W30, 255*W30,
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-1192*W30, 1722*W30, 1023*W30, 3700*W30,
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-1388*W30, -1551*W30, -2549*W30, 27*W30,
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282*W30, 673*W30, 113*W30, 1561*W30,
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72*W30, 873*W30, 87*W30, -395*W30,
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-433*W30, 629*W30, 3440*W30, -284*W30,
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-592*W30, -103*W30, -46*W30, -3844*W30,
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1712*W30, 303*W30, 1555*W30, -631*W30,
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-1400*W30, -961*W30, -854*W30, -276*W30,
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407*W30, 833*W30, -345*W30, -1501*W30,
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121*W30, -1581*W30, 400*W30, 150*W30,
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1224*W30, -139*W30, -563*W30, 879*W30,
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933*W30, 2939*W30, 788*W30, 211*W30,
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530*W30, -192*W30, 706*W30, -13347*W30,
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1065*W30, 3*W30, 111*W30, -208*W30,
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-360*W30, -532*W30, -291*W30, 483*W30,
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987*W30, -33*W30, -1373*W30, -166*W30,
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-1174*W30, -3955*W30, 1601*W30, -280*W30,
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1405*W30, 600*W30, -1659*W30, -23*W30,
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390*W30, 449*W30, 570*W30, -13143*W30,
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-9*W30, -1646*W30, 1201*W30, 294*W30,
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2181*W30, -1173*W30, 1388*W30, -4504*W30,
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190*W30, -2304*W30, 211*W30, 239*W30,
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48*W30, -817*W30, 1018*W30, 1828*W30,
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-663*W30, 1408*W30, 408*W30, -36*W30,
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1295*W30, -230*W30, 1341*W30, 9*W30,
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40*W30, 705*W30, 186*W30, 376*W30,
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557*W30, 5866*W30, 363*W30, -1558*W30,
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718*W30, 669*W30, 1369*W30, -2972*W30,
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-468*W30, -121*W30, -219*W30, 667*W30,
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29954*W30, 366*W30, 48*W30, -203*W30
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};
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static const float __exp2f_atable[256] /* __attribute__((mode(SF))) */ = {
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0.707106411447, /* 0x0.b504ecfff */
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0.709024071690, /* 0x0.b58299fff */
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0.710945606239, /* 0x0.b60088000 */
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0.712874472142, /* 0x0.b67ef1000 */
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0.714806139464, /* 0x0.b6fd88fff */
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0.716744661340, /* 0x0.b77c94000 */
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0.718687653549, /* 0x0.b7fbea000 */
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0.720636486992, /* 0x0.b87ba1fff */
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0.722590208040, /* 0x0.b8fbabfff */
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0.724549472323, /* 0x0.b97c12fff */
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0.726514220228, /* 0x0.b9fcd5fff */
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0.728483855735, /* 0x0.ba7deb000 */
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0.730457961549, /* 0x0.baff4afff */
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0.732438981522, /* 0x0.bb811efff */
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0.734425544748, /* 0x0.bc0350000 */
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0.736416816713, /* 0x0.bc85d0000 */
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0.738412797450, /* 0x0.bd089efff */
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0.740414917465, /* 0x0.bd8bd4fff */
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0.742422521111, /* 0x0.be0f66fff */
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0.744434773914, /* 0x0.be9346fff */
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0.746454179287, /* 0x0.bf179f000 */
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0.748477637755, /* 0x0.bf9c3afff */
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0.750506639473, /* 0x0.c02133fff */
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0.752541840064, /* 0x0.c0a694fff */
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0.754582285889, /* 0x0.c12c4e000 */
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0.756628334525, /* 0x0.c1b265000 */
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0.758678436269, /* 0x0.c238bffff */
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0.760736882681, /* 0x0.c2bfa6fff */
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0.762799203401, /* 0x0.c346cf000 */
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0.764867603790, /* 0x0.c3ce5d000 */
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0.766940355298, /* 0x0.c45633fff */
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0.769021093841, /* 0x0.c4de90fff */
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0.771104693409, /* 0x0.c5671dfff */
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0.773195922364, /* 0x0.c5f02afff */
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0.775292098512, /* 0x0.c6798afff */
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0.777394294745, /* 0x0.c70350000 */
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0.779501736166, /* 0x0.c78d6d000 */
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0.781615912910, /* 0x0.c817fafff */
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0.783734917628, /* 0x0.c8a2d9fff */
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0.785858273516, /* 0x0.c92e02000 */
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0.787990570071, /* 0x0.c9b9c0000 */
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0.790125787245, /* 0x0.ca45aefff */
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0.792268991467, /* 0x0.cad223fff */
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0.794417440881, /* 0x0.cb5ef0fff */
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0.796570718287, /* 0x0.cbec0efff */
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0.798730909811, /* 0x0.cc79a0fff */
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0.800892710672, /* 0x0.cd074dfff */
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0.803068041795, /* 0x0.cd95ddfff */
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0.805242776881, /* 0x0.ce2464000 */
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0.807428598393, /* 0x0.ceb3a3fff */
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0.809617877002, /* 0x0.cf431dfff */
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0.811812341211, /* 0x0.cfd2eefff */
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0.814013659956, /* 0x0.d06333000 */
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0.816220164311, /* 0x0.d0f3ce000 */
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0.818434238424, /* 0x0.d184e7fff */
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0.820652604094, /* 0x0.d21649fff */
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0.822877407074, /* 0x0.d2a818000 */
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0.825108587751, /* 0x0.d33a51000 */
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0.827342867839, /* 0x0.d3ccbdfff */
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0.829588949684, /* 0x0.d45ff1000 */
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0.831849217401, /* 0x0.d4f411fff */
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0.834093391880, /* 0x0.d58724fff */
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0.836355149750, /* 0x0.d61b5f000 */
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0.838620424257, /* 0x0.d6afd3fff */
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0.840896368027, /* 0x0.d744fc000 */
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0.843176305293, /* 0x0.d7da66fff */
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0.845462262643, /* 0x0.d87037000 */
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0.847754716864, /* 0x0.d90673fff */
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0.850052893157, /* 0x0.d99d10fff */
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0.852359056469, /* 0x0.da3433fff */
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0.854668736446, /* 0x0.dacb91fff */
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0.856986224651, /* 0x0.db6373000 */
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0.859309315673, /* 0x0.dbfbb1fff */
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0.861639738080, /* 0x0.dc946bfff */
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0.863975346095, /* 0x0.dd2d7d000 */
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0.866317391394, /* 0x0.ddc6f9fff */
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0.868666708472, /* 0x0.de60f1000 */
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0.871022939695, /* 0x0.defb5c000 */
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0.873383641229, /* 0x0.df9611fff */
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0.875751554968, /* 0x0.e03141000 */
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0.878126025200, /* 0x0.e0ccde000 */
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0.880506813521, /* 0x0.e168e4fff */
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0.882894217966, /* 0x0.e2055afff */
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0.885287821299, /* 0x0.e2a239000 */
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0.887686729423, /* 0x0.e33f6ffff */
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0.890096127973, /* 0x0.e3dd56fff */
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0.892507970338, /* 0x0.e47b67000 */
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0.894928157336, /* 0x0.e51a03000 */
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0.897355020043, /* 0x0.e5b90efff */
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0.899788379682, /* 0x0.e65888000 */
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0.902227103705, /* 0x0.e6f85afff */
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0.904673457151, /* 0x0.e798ae000 */
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0.907128036008, /* 0x0.e8398afff */
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0.909585535528, /* 0x0.e8da99000 */
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0.912051796915, /* 0x0.e97c3a000 */
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0.914524436003, /* 0x0.ea1e46000 */
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0.917003571999, /* 0x0.eac0bf000 */
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0.919490039339, /* 0x0.eb63b2fff */
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0.921983361257, /* 0x0.ec071a000 */
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0.924488604054, /* 0x0.ecab48fff */
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0.926989555360, /* 0x0.ed4f30000 */
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0.929502844812, /* 0x0.edf3e6000 */
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0.932021975503, /* 0x0.ee98fdfff */
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0.934553921208, /* 0x0.ef3eecfff */
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0.937083780759, /* 0x0.efe4b8fff */
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0.939624726786, /* 0x0.f08b3f000 */
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0.942198514924, /* 0x0.f133ebfff */
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0.944726586343, /* 0x0.f1d99a000 */
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0.947287976728, /* 0x0.f28176fff */
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0.949856162070, /* 0x0.f329c5fff */
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0.952431440345, /* 0x0.f3d28bfff */
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0.955013573175, /* 0x0.f47bc5000 */
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0.957603693021, /* 0x0.f52584000 */
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0.960199773321, /* 0x0.f5cfa7000 */
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0.962801992906, /* 0x0.f67a31000 */
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0.965413510788, /* 0x0.f72556fff */
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0.968030691152, /* 0x0.f7d0dc000 */
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0.970655620084, /* 0x0.f87ce2fff */
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0.973290979849, /* 0x0.f92998fff */
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0.975926160805, /* 0x0.f9d64bfff */
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0.978571653370, /* 0x0.fa83ac000 */
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0.981225252139, /* 0x0.fb3193fff */
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0.983885228626, /* 0x0.fbdfe6fff */
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0.986552715296, /* 0x0.fc8eb7fff */
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0.989228487027, /* 0x0.fd3e14000 */
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0.991909801964, /* 0x0.fdedcd000 */
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0.994601726545, /* 0x0.fe9e38000 */
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0.997297704209, /* 0x0.ff4ee6fff */
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1.000000000000, /* 0x1.000000000 */
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1.002710938457, /* 0x1.00b1aa000 */
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1.005429744692, /* 0x1.0163d7ffe */
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1.008155703526, /* 0x1.02167dffe */
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1.010888457284, /* 0x1.02c995fff */
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1.013629436498, /* 0x1.037d38000 */
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1.016377568250, /* 0x1.043152000 */
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1.019134163841, /* 0x1.04e5f9ffe */
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1.021896362316, /* 0x1.059b00000 */
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1.024668931945, /* 0x1.0650b3ffe */
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1.027446627635, /* 0x1.0706be001 */
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1.030234098408, /* 0x1.07bd6bffe */
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1.033023953416, /* 0x1.087441ffe */
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1.035824656494, /* 0x1.092bce000 */
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1.038632392900, /* 0x1.09e3d0001 */
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1.041450142840, /* 0x1.0a9c79ffe */
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1.044273972530, /* 0x1.0b558a001 */
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1.047105550795, /* 0x1.0c0f1c001 */
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1.049944162390, /* 0x1.0cc924001 */
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1.052791833895, /* 0x1.0d83c4001 */
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1.055645227426, /* 0x1.0e3ec3fff */
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1.058507919326, /* 0x1.0efa60001 */
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1.061377286898, /* 0x1.0fb66bfff */
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1.064254641510, /* 0x1.1072fdffe */
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1.067140102389, /* 0x1.113018000 */
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1.070034146304, /* 0x1.11edc1fff */
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1.072937250162, /* 0x1.12ac04001 */
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1.075843691823, /* 0x1.136a7dfff */
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1.078760385496, /* 0x1.1429a3ffe */
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1.081685543070, /* 0x1.14e958000 */
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1.084618330005, /* 0x1.15a98c000 */
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1.087556362176, /* 0x1.166a18001 */
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1.090508937863, /* 0x1.172b98001 */
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1.093464612954, /* 0x1.17ed4bfff */
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1.096430182434, /* 0x1.18afa5ffe */
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1.099401354802, /* 0x1.19725e000 */
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1.102381587017, /* 0x1.1a35adfff */
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1.105370759965, /* 0x1.1af994000 */
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1.108367800686, /* 0x1.1bbdfdffe */
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1.111373305331, /* 0x1.1c82f6000 */
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1.114387035385, /* 0x1.1d4878001 */
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1.117408752440, /* 0x1.1e0e7ffff */
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1.120437502874, /* 0x1.1ed4fe000 */
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1.123474478729, /* 0x1.1f9c06000 */
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1.126521706601, /* 0x1.2063ba001 */
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1.129574775716, /* 0x1.212bd0001 */
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1.132638812065, /* 0x1.21f49e000 */
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1.135709524130, /* 0x1.22bddbffe */
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1.138789534565, /* 0x1.2387b5fff */
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1.141876101508, /* 0x1.2451fe000 */
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1.144971728301, /* 0x1.251cddffe */
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1.148077130296, /* 0x1.25e861ffe */
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1.151189923305, /* 0x1.26b462001 */
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1.154312610610, /* 0x1.278107ffe */
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1.157440662410, /* 0x1.284e08001 */
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1.160578370109, /* 0x1.291baa001 */
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1.163725256932, /* 0x1.29e9e6000 */
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1.166879892324, /* 0x1.2ab8a3ffe */
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1.170044302935, /* 0x1.2b8805fff */
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1.173205971694, /* 0x1.2c5739ffe */
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1.176397800428, /* 0x1.2d2867ffe */
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1.179586529747, /* 0x1.2df962001 */
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1.182784795737, /* 0x1.2ecafbffe */
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1.185991406414, /* 0x1.2f9d21ffe */
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1.189206838636, /* 0x1.306fdc001 */
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1.192430973067, /* 0x1.314328000 */
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1.195664167430, /* 0x1.32170c001 */
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1.198906540890, /* 0x1.32eb8a001 */
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1.202157497408, /* 0x1.33c098000 */
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1.205416083326, /* 0x1.349625fff */
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1.208683252332, /* 0x1.356c43fff */
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1.211961269402, /* 0x1.364318001 */
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1.215246438983, /* 0x1.371a64000 */
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1.218539118740, /* 0x1.37f22dffe */
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1.221847295770, /* 0x1.38cafc000 */
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1.225158572187, /* 0x1.39a3fdfff */
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1.228481650325, /* 0x1.3a7dc5ffe */
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1.231811761846, /* 0x1.3b5803fff */
|
|
1.235149741144, /* 0x1.3c32c5ffe */
|
|
1.238499879811, /* 0x1.3d0e53ffe */
|
|
1.241858124726, /* 0x1.3dea69fff */
|
|
1.245225191102, /* 0x1.3ec713fff */
|
|
1.248601436624, /* 0x1.3fa458000 */
|
|
1.251975655584, /* 0x1.40817a001 */
|
|
1.255380749731, /* 0x1.4160a2001 */
|
|
1.258783102010, /* 0x1.423f9bffe */
|
|
1.262198328973, /* 0x1.431f6e000 */
|
|
1.265619754780, /* 0x1.43ffa7fff */
|
|
1.269052743928, /* 0x1.44e0a4001 */
|
|
1.272490739830, /* 0x1.45c1f4000 */
|
|
1.275942921659, /* 0x1.46a432001 */
|
|
1.279397487615, /* 0x1.478697ffe */
|
|
1.282870173427, /* 0x1.486a2dffe */
|
|
1.286346316319, /* 0x1.494dfdffe */
|
|
1.289836049094, /* 0x1.4a32b2001 */
|
|
1.293333172770, /* 0x1.4b17e1ffe */
|
|
1.296839594835, /* 0x1.4bfdadfff */
|
|
1.300354957560, /* 0x1.4ce40fffe */
|
|
1.303882122055, /* 0x1.4dcb38001 */
|
|
1.307417988757, /* 0x1.4eb2f1ffe */
|
|
1.310960650439, /* 0x1.4f9b1dfff */
|
|
1.314516782746, /* 0x1.50842bfff */
|
|
1.318079948424, /* 0x1.516daffff */
|
|
1.321653246888, /* 0x1.5257de000 */
|
|
1.325237751030, /* 0x1.5342c8001 */
|
|
1.328829526907, /* 0x1.542e2c000 */
|
|
1.332433700535, /* 0x1.551a5fffe */
|
|
1.336045145966, /* 0x1.56070dffe */
|
|
1.339667558645, /* 0x1.56f473ffe */
|
|
1.343300342533, /* 0x1.57e287ffe */
|
|
1.346941947961, /* 0x1.58d130001 */
|
|
1.350594043714, /* 0x1.59c087ffe */
|
|
1.354256033883, /* 0x1.5ab085fff */
|
|
1.357932448365, /* 0x1.5ba175ffe */
|
|
1.361609339707, /* 0x1.5c926dfff */
|
|
1.365299344044, /* 0x1.5d8441ffe */
|
|
1.369003057507, /* 0x1.5e76fc001 */
|
|
1.372714757920, /* 0x1.5f6a3c000 */
|
|
1.376437187179, /* 0x1.605e2fffe */
|
|
1.380165219333, /* 0x1.615282001 */
|
|
1.383909463864, /* 0x1.6247e3ffe */
|
|
1.387661933907, /* 0x1.633dd0000 */
|
|
1.391424179060, /* 0x1.64345fffe */
|
|
1.395197510706, /* 0x1.652ba9fff */
|
|
1.399006724329, /* 0x1.66254dffe */
|
|
1.402773022651, /* 0x1.671c22000 */
|
|
1.406576037403, /* 0x1.68155dfff */
|
|
1.410389423392, /* 0x1.690f48001 */
|
|
};
|