author | William Roberts <williamr@symbian.org> |
Thu, 22 Jul 2010 16:48:56 +0100 | |
branch | GCC_SURGE |
changeset 45 | 4b03adbd26ca |
parent 0 | e4d67989cc36 |
permissions | -rw-r--r-- |
0
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/*-------------------------------------------------------------------- |
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*© Portions copyright (c) 2006 Nokia Corporation. All rights reserved. |
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*-------------------------------------------------------------------- |
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*/ |
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/*- |
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* Copyright (c) 2005 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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|
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#include <sys/cdefs.h> |
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#ifndef __SYMBIAN32__ |
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__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2.c,v 1.1 2005/04/05 02:57:15 das Exp $"); |
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#endif //__SYMBIAN32__ |
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#include <math.h> |
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#include "math_private.h" |
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#define TBLBITS 8 |
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#define TBLSIZE (1 << TBLBITS) |
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#ifdef __CW32__ |
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static const double |
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huge = 1.07150860718626732094842504906e+301, |
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twom1000 = 9.3326361850321887899008954472382e-302, |
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redux = 6755399441055744.0/ TBLSIZE, |
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P1 = 6.9314718246459960e-1, |
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P2 = 2.4022650718688965e-1, |
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P3 = 5.5504109710454940e-2, |
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P4 = 9.6181295812129970e-3, |
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P5 = 1.3333559036254882e-3; |
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|
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|
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static const double tbl[TBLSIZE * 2] = { |
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/* exp2(z + eps) eps */ |
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0.707106781186592, 9.070522111187529e-14, |
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0.7090239421602083, 1.332267629550188e-15, |
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0.7109463010845614, -4.346523141407488e-14, |
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0.7128738720527606, 2.731148640577885e-14, |
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0.7148066691959843, -1.332267629550188e-15, |
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0.7167447066838942, -3.885780586188048e-16, |
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0.718687998724463, -5.656586310465173e-14, |
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0.7206365595642875, -5.06816810741384e-14, |
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0.7225904034885321, 1.754152378907747e-14, |
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0.7245495448209743, -8.593126210598712e-14, |
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0.7265139979245225, -7.438494264988549e-15, |
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0.7284837772007502, 5.601075159233915e-14, |
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0.730458897090328, 8.826273045769994e-15, |
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0.7324393720731814, -4.229949723821846e-14, |
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0.7344252166684901, -1.609823385706477e-15, |
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0.7364164454346849, 2.109423746787797e-15, |
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0.738413072969748, -3.219646771412954e-15, |
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0.7404151139112507, 2.886579864025407e-14, |
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0.7424225829363763, 1.110223024625157e-16, |
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0.7444354947621779, -4.007905118896815e-14, |
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0.7464538641456281, -8.382183835919932e-15, |
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0.748477705883599, -3.613775945154885e-14, |
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0.7505070348132479, 6.750155989720952e-14, |
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0.7525418658117105, 1.376676550535194e-14, |
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0.7586795205991935, 1.638689184346731e-13, |
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1.269050957191729, -5.051514762044462e-15, |
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1.272491703389392, -1.232347557333924e-14, |
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1.275941778396378, -1.643130076445232e-14, |
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1.279401207505722, 5.995204332975845e-14, |
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1.282870016078732, -5.195843755245733e-14, |
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1.286348229546037, 1.249000902703301e-14, |
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1.289835873406642, -2.692290834716005e-14, |
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1.293332973229099, 1.043609643147647e-14, |
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1.296839554650994, -1.731947918415244e-14, |
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1.300355643379657, 7.327471962526033e-15, |
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1.303881265191982, 5.051514762044462e-14, |
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1.307416445934654, -2.564615186884112e-14, |
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1.310961211524785, 2.231548279496565e-14, |
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1.314515587949345, -1.099120794378905e-14, |
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1.318079601266059, -5.773159728050814e-15, |
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1.321653277603327, 1.849631559025511e-13, |
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1.325236643159704, -4.057865155004947e-14, |
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1.328829724205895, -6.48925357893404e-14, |
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1.33243254708332, 1.721955911193618e-13, |
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1.33604513820418, 3.674838211509268e-14, |
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1.339667524053417, 1.232902668846236e-13, |
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1.343299731186792, -4.596323321948148e-14, |
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1.346941786232914, -3.380629109983602e-14, |
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1.350593715892233, 2.126077092157175e-13, |
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1.354255546936892, -5.551115123125783e-16, |
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1.357927306212955, 5.695444116327053e-14, |
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1.361609020638187, -4.046762924758696e-14, |
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1.365300717204164, 1.605937605120289e-13, |
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1.369002422974568, -2.420286193682841e-14, |
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1.372714165087688, 2.081668171172169e-14, |
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1.376435970754569, 4.08006961549745e-14, |
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1.380167867260245, 7.549516567451064e-15, |
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1.383909881963813, -1.937339177970898e-14, |
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1.387662042298513, -1.670885652060861e-14, |
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1.391424375771923, -2.942091015256665e-15, |
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1.395196909966158, -4.329869796038111e-14, |
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1.398979672539303, 1.022737450284694e-12, |
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1.402772691220125, -8.215650382226158e-14, |
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1.406575993819018, 2.498001805406602e-15, |
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1.410389608217226, -4.524158825347513e-14 |
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}; |
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|
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#else |
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static const double |
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huge = 0x1p1000, |
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twom1000 = 0x1p-1000, |
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redux = 0x1.8p52 / TBLSIZE, |
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P1 = 0x1.62e42fefa39efp-1, |
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P2 = 0x1.ebfbdff82c575p-3, |
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P3 = 0x1.c6b08d704a0a6p-5, |
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P4 = 0x1.3b2ab88f70400p-7, |
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P5 = 0x1.5d88003875c74p-10; |
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|
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static const double tbl[TBLSIZE * 2] = { |
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/* exp2(z + eps) eps */ |
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0x1.6a09e667f3d5dp-1, 0x1.9880p-44, |
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328 |
0x1.6b052fa751744p-1, 0x1.8000p-50, |
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0x1.6c012750bd9fep-1, -0x1.8780p-45, |
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330 |
0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, |
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0x1.6dfb23c651a29p-1, -0x1.8000p-50, |
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0x1.6ef9298593ae3p-1, -0x1.c000p-52, |
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0x1.6ff7df9519386p-1, -0x1.fd80p-45, |
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0x1.70f7466f42da3p-1, -0x1.c880p-45, |
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0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, |
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0x1.72f8286eacf05p-1, -0x1.8300p-44, |
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0x1.73f9a48a58152p-1, -0x1.0c00p-47, |
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0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, |
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0x1.75feb564267f1p-1, 0x1.3e00p-47, |
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0x1.77024b1ab6d48p-1, -0x1.7d00p-45, |
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0x1.780694fde5d38p-1, -0x1.d000p-50, |
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342 |
0x1.790b938ac1d00p-1, 0x1.3000p-49, |
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0x1.7a11473eb0178p-1, -0x1.d000p-49, |
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0x1.7b17b0976d060p-1, 0x1.0400p-45, |
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0x1.7c1ed0130c133p-1, 0x1.0000p-53, |
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0x1.7d26a62ff8636p-1, -0x1.6900p-45, |
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0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, |
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0x1.7f3878491c3e8p-1, -0x1.4580p-45, |
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0x1.80427543e1b4ep-1, 0x1.3000p-44, |
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0x1.814d2add1071ap-1, 0x1.f000p-47, |
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0x1.82589994ccd7ep-1, -0x1.1c00p-45, |
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0x1.8364c1eb942d0p-1, 0x1.9d00p-45, |
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353 |
0x1.8471a4623cab5p-1, 0x1.7100p-43, |
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354 |
0x1.857f4179f5bbcp-1, 0x1.2600p-45, |
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355 |
0x1.868d99b4491afp-1, -0x1.2c40p-44, |
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0x1.879cad931a395p-1, -0x1.3000p-45, |
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0x1.88ac7d98a65b8p-1, -0x1.a800p-45, |
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0x1.89bd0a4785800p-1, -0x1.d000p-49, |
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359 |
0x1.8ace5422aa223p-1, 0x1.3280p-44, |
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529 |
0x1.38cae6d05d838p+0, -0x1.ae00p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
530 |
0x1.39a401b713ec3p+0, -0x1.4720p-43, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
531 |
0x1.3a7db34e5a020p+0, 0x1.8200p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
532 |
0x1.3b57fbfec6e95p+0, 0x1.e800p-44, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
533 |
0x1.3c32dc313a8f2p+0, 0x1.f800p-49, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
534 |
0x1.3d0e544ede122p+0, -0x1.7a00p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
535 |
0x1.3dea64c1234bbp+0, 0x1.6300p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
536 |
0x1.3ec70df1c4eccp+0, -0x1.8a60p-43, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
537 |
0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
538 |
0x1.40822c367a0bbp+0, 0x1.5b80p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
539 |
0x1.4160a21f72e95p+0, 0x1.ec00p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
540 |
0x1.423fb27094646p+0, -0x1.3600p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
541 |
0x1.431f5d950a920p+0, 0x1.3980p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
542 |
0x1.43ffa3f84b9ebp+0, 0x1.a000p-48, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
543 |
0x1.44e0860618919p+0, -0x1.6c00p-48, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
544 |
0x1.45c2042a7d201p+0, -0x1.bc00p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
545 |
0x1.46a41ed1d0016p+0, -0x1.2800p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
546 |
0x1.4786d668b3326p+0, 0x1.0e00p-44, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
547 |
0x1.486a2b5c13c00p+0, -0x1.d400p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
548 |
0x1.494e1e192af04p+0, 0x1.c200p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
549 |
0x1.4a32af0d7d372p+0, -0x1.e500p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
550 |
0x1.4b17dea6db801p+0, 0x1.7800p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
551 |
0x1.4bfdad53629e1p+0, -0x1.3800p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
552 |
0x1.4ce41b817c132p+0, 0x1.0800p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
553 |
0x1.4dcb299fddddbp+0, 0x1.c700p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
554 |
0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
555 |
0x1.4f9b2769d2d02p+0, 0x1.9200p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
556 |
0x1.508417f4531c1p+0, -0x1.8c00p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
557 |
0x1.516daa2cf662ap+0, -0x1.a000p-48, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
558 |
0x1.5257de83f51eap+0, 0x1.a080p-43, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
559 |
0x1.5342b569d4edap+0, -0x1.6d80p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
560 |
0x1.542e2f4f6ac1ap+0, -0x1.2440p-44, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
561 |
0x1.551a4ca5d94dbp+0, 0x1.83c0p-43, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
562 |
0x1.56070dde9116bp+0, 0x1.4b00p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
563 |
0x1.56f4736b529dep+0, 0x1.15a0p-43, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
564 |
0x1.57e27dbe2c40ep+0, -0x1.9e00p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
565 |
0x1.58d12d497c76fp+0, -0x1.3080p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
566 |
0x1.59c0827ff0b4cp+0, 0x1.dec0p-43, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
567 |
0x1.5ab07dd485427p+0, -0x1.4000p-51, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
568 |
0x1.5ba11fba87af4p+0, 0x1.0080p-44, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
569 |
0x1.5c9268a59460bp+0, -0x1.6c80p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
570 |
0x1.5d84590998e3fp+0, 0x1.69a0p-43, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
571 |
0x1.5e76f15ad20e1p+0, -0x1.b400p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
572 |
0x1.5f6a320dcebcap+0, 0x1.7700p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
573 |
0x1.605e1b976dcb8p+0, 0x1.6f80p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
574 |
0x1.6152ae6cdf715p+0, 0x1.1000p-47, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
575 |
0x1.6247eb03a5531p+0, -0x1.5d00p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
576 |
0x1.633dd1d1929b5p+0, -0x1.2d00p-46, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
577 |
0x1.6434634ccc313p+0, -0x1.a800p-49, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
578 |
0x1.652b9febc8efap+0, -0x1.8600p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
579 |
0x1.6623882553397p+0, 0x1.1fe0p-40, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
580 |
0x1.671c1c708328ep+0, -0x1.7200p-44, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
581 |
0x1.68155d44ca97ep+0, 0x1.6800p-49, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
582 |
0x1.690f4b19e9471p+0, -0x1.9780p-45, |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
583 |
}; |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
584 |
#endif //__CW32__ |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
585 |
|
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
586 |
|
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
587 |
/* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
588 |
* exp2(x): compute the base 2 exponential of x |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
589 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
590 |
* Accuracy: Peak error < 0.503 ulp for normalized results. |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
591 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
592 |
* Method: (accurate tables) |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
593 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
594 |
* Reduce x: |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
595 |
* x = 2**k + y, for integer k and |y| <= 1/2. |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
596 |
* Thus we have exp2(x) = 2**k * exp2(y). |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
597 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
598 |
* Reduce y: |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
599 |
* y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
600 |
* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
601 |
* with |z - eps[i]| <= 2**-9 + 2**-39 for the table used. |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
602 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
603 |
* We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
604 |
* a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61. |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
605 |
* The values in exp2t[] and eps[] are chosen such that |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
606 |
* exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
607 |
* that exp2t[i] is accurate to 2**-64. |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
608 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
609 |
* Note that the range of i is +-TBLSIZE/2, so we actually index the tables |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
610 |
* by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
611 |
* virtual tables, interleaved in the real table tbl[]. |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
612 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
613 |
* This method is due to Gal, with many details due to Gal and Bachelis: |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
614 |
* |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
615 |
* Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
616 |
* for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
617 |
*/ |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
618 |
EXPORT_C double |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
619 |
exp2(double x) |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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620 |
{ |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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621 |
double r, t, z; |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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622 |
uint32_t hx, hr, ix, lx, i0; |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
623 |
int k; |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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624 |
|
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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625 |
/* Filter out exceptional cases. */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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626 |
GET_HIGH_WORD(hx,x); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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627 |
ix = hx & 0x7fffffff; /* high word of |x| */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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628 |
if(ix >= 0x40900000) { /* |x| >= 1024 */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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|
629 |
if(ix >= 0x7ff00000) { |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
630 |
GET_LOW_WORD(lx,x); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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631 |
if(((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0) |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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632 |
return (x); /* x is NaN or +Inf */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
633 |
else |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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634 |
return (0.0); /* x is -Inf */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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635 |
} |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
636 |
#ifdef __SYMBIAN32__ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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637 |
if(x >= 1024) |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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638 |
#else |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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639 |
if(x >= 0x1.0p10) |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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640 |
#endif //__SYMBIAN32__ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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641 |
return (huge * huge); /* overflow */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
642 |
#ifdef __SYMBIAN32__ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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643 |
if(x <= -1075) |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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644 |
#else |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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645 |
if(x <= -0x1.0ccp10) |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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|
646 |
#endif //__SYMBIAN32__ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
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647 |
return (twom1000 * twom1000); /* underflow */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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|
648 |
} else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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|
649 |
return (1.0 + x); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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|
650 |
} |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
651 |
|
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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652 |
/* Reduce x, computing z, i0, and k. */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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653 |
t = x + redux; |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
654 |
GET_LOW_WORD(i0, t); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
655 |
i0 += TBLSIZE / 2; |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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656 |
k = (i0 >> TBLBITS) << 20; |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
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657 |
i0 = (i0 & (TBLSIZE - 1)) << 1; |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
658 |
t -= redux; |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
659 |
z = x - t; |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
660 |
|
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
661 |
/* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
662 |
t = tbl[i0]; /* exp2t[i0] */ |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
663 |
z -= tbl[i0 + 1]; /* eps[i0] */ |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
664 |
r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
665 |
|
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
666 |
/* Scale by 2**(k>>20). */ |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
667 |
if(k >= -1021 << 20) { |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
668 |
if (k != 0) { |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
669 |
GET_HIGH_WORD(hr, r); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
670 |
SET_HIGH_WORD(r, hr + k); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
671 |
} |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
672 |
return (r); |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
673 |
} else { |
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Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
674 |
GET_HIGH_WORD(hr, r); |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
675 |
SET_HIGH_WORD(r, hr + (k + (1000 << 20))); |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
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|
676 |
return (r * twom1000); |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
677 |
} |
e4d67989cc36
Revision: 201002
Dremov Kirill (Nokia-D-MSW/Tampere) <kirill.dremov@nokia.com>
parents:
diff
changeset
|
678 |
} |