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Diffstat (limited to 'sysdeps/ia64/fpu/s_tanhl.S')
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diff --git a/sysdeps/ia64/fpu/s_tanhl.S b/sysdeps/ia64/fpu/s_tanhl.S new file mode 100644 index 0000000..3435f43 --- /dev/null +++ b/sysdeps/ia64/fpu/s_tanhl.S @@ -0,0 +1,1348 @@ +.file "tanhl.s" + + +// Copyright (c) 2001 - 2003, Intel Corporation +// All rights reserved. +// +// Contributed 2001 by the Intel Numerics Group, Intel Corporation +// +// Redistribution and use in source and binary forms, with or without +// modification, are permitted provided that the following conditions are +// met: +// +// * Redistributions of source code must retain the above copyright +// notice, this list of conditions and the following disclaimer. +// +// * Redistributions in binary form must reproduce the above copyright +// notice, this list of conditions and the following disclaimer in the +// documentation and/or other materials provided with the distribution. +// +// * The name of Intel Corporation may not be used to endorse or promote +// products derived from this software without specific prior written +// permission. + +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS +// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY +// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING +// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +// +// Intel Corporation is the author of this code, and requests that all +// problem reports or change requests be submitted to it directly at +// http://www.intel.com/software/products/opensource/libraries/num.htm. +// +// History +//============================================================== +// 11/29/01 Initial version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 08/14/02 Changed mli templates to mlx +// 02/10/03 Reordered header: .section, .global, .proc, .align +// +// API +//============================================================== +// long double tanhl(long double) +// +// Overview of operation +//============================================================== +// +// Algorithm description +// --------------------- +// +// There are 4 paths: +// +// 1. Special path: x = 0, Inf, NaNs, denormal +// Return tanhl(x) = +/-0.0 for zeros +// Return tanhl(x) = QNaN for NaNs +// Return tanhl(x) = sign(x)*1.0 for Inf +// Return tanhl(x) = x + x^2 for - denormals +// Return tanhl(x) = x - x^2 for + denormals +// +// 2. [0;1/8] path: 0.0 < |x| < 1/8 +// Return tanhl(x) = x + x^3*A3 + ... + x^15*A15 +// +// 3. Main path: 1/8 <= |x| < 22.8 +// For several ranges of 1/8 <= |x| < 22.8 +// Return tanhl(x) = sign(x)*((A0H+A0L) + y*(A1H+A1L) + y^2*(A2H+A2L) + +// + y^3*A3 + y^4*A4 + ... + y^25*A25 ) +// where y = (|x|/a) - b +// +// For each range there is particular set of coefficients. +// Below is the list of ranges: +// 1/8 <= |x| < 1/4 a = 0.125, b = 1.5 +// 1/4 <= |x| < 1/2 a = 0.25, b = 1.5 +// 1/2 <= |x| < 1.0 a = 0.5, b = 1.5 +// 1.0 <= |x| < 2.0 a = 1.0, b = 1.5 +// 2.0 <= |x| < 3.25 a = 2.0, b = 1.5 +// 3.25 <= |x| < 4.0 a = 2.0, b = 2.0 +// 4.0 <= |x| < 6.5 a = 4.0, b = 1.5 +// 6.5 <= |x| < 8.0 a = 4.0, b = 2.0 +// 8.0 <= |x| < 13.0 a = 8.0, b = 1.5 +// 13.0 <= |x| < 16.0 a = 8.0, b = 2.0 +// 16.0 <= |x| < 22.8 a = 16.0, b = 1.5 +// ( [3.25;4.0], [6.5;8.0], [13.9;16.0] subranges separated +// for monotonicity issues resolve ) +// +// 4. Saturation path: 22.8 <= |x| < +INF +// Return tanhl(x) = sign(x)*(1.0 - tiny_value) +// (tiny_value ~ 1e-1233) +// +// Implementation notes +// -------------------- +// +// 1. Special path: x = 0, INF, NaNa, denormals +// +// This branch is cut off by one fclass operation. +// Then zeros+nans, infinities and denormals processed separately. +// For denormals we use simple fma operaton x+x*x (- for +denorms) +// +// 2. [0;1/8] path: 0.0 < |x| < 1/8 +// +// Here we use simple polynimial computations, where last step +// is performed as x + x^3*A3+... +// The rest of polynomial is factorized using binary tree technique. +// +// 3. Main path: 1/8 <= |x| < 22.8 +// +// Multiprecision have to be performed only for first few +// polynomial iterations (up to 3-rd x degree) +// Here we use the same parallelisation way as above: +// Split whole polynomial to first, "multiprecision" part, and second, +// so called "tail", native precision part. +// +// 1) Multiprecision part: +// [v1=(A0H+A0L)+y*(A1H+A1L)] + [v2=y^2*((A2H+A2L)+y*A3)] +// v1 and v2 terms calculated in parallel +// +// 2) Tail part: +// v3 = x^4 * ( A4 + x*A5 + ... + x^21*A25 ) +// v3 is splitted to 2 even parts (10 coefficient in each one). +// These 2 parts are also factorized using binary tree technique. +// +// So Multiprecision and Tail parts cost is almost the same +// and we have both results ready before final summation. +// +// Some tricks were applied to maintain symmetry at direct +// rounding modes (to +/-inf). We had to set result sign +// not at the last operation but much more earlier and at +// several places. +// +// 4. Saturation path: 22.8 <= |x| < +INF +// +// We use formula sign(x)*(1.0 - tiny_value) instead of simple sign(x)*1.0 +// just to meet IEEE requirements for different rounding modes in this case. +// +// Registers used +//============================================================== +// Floating Point registers used: +// f8 - input & output +// f32 -> f92 + +// General registers used: +// r2, r3, r32 -> r52 + +// Predicate registers used: +// p0, p6 -> p11, p14, p15 + +// p6 - arg is zero, denormal or special IEEE +// p7 - arg is in [16;32] binary interval +// p8 - arg is in one of subranges +// [3.25;4.0], [6.5;8.0], [13.9;16.0] +// p9 - arg < 1/8 +// p10 - arg is NOT in one of subranges +// [3.25;4.0], [6.5;8.0], [13.9;16.0] +// p11 - arg in saturation domain +// p14 - arg is positive +// p15 - arg is negative + +// Assembly macros +//============================================================== +rDataPtr = r2 +rTailDataPtr = r3 + +rBias = r33 +rSignBit = r34 +rInterval = r35 + +rArgExp = r36 +rArgSig = r37 +r3p25Offset = r38 +r2to4 = r39 +r1p25 = r40 +rOffset = r41 +r1p5 = r42 +rSaturation = r43 +r1625Sign = r44 +rTiny = r45 +rAddr1 = r46 +rAddr2 = r47 +rTailAddr1 = r48 +rTailAddr2 = r49 +rTailOffset = r50 +rTailAddOffset = r51 +rShiftedDataPtr = r52 + +//============================================================== +fA0H = f32 +fA0L = f33 +fA1H = f34 +fA1L = f35 +fA2H = f36 +fA2L = f37 +fA3 = f38 +fA4 = f39 +fA5 = f40 +fA6 = f41 +fA7 = f42 +fA8 = f43 +fA9 = f44 +fA10 = f45 +fA11 = f46 +fA12 = f47 +fA13 = f48 +fA14 = f49 +fA15 = f50 +fA16 = f51 +fA17 = f52 +fA18 = f53 +fA19 = f54 +fA20 = f55 +fA21 = f56 +fA22 = f57 +fA23 = f58 +fA24 = f59 +fA25 = f60 + +fArgSqr = f61 +fArgCube = f62 +fArgFour = f63 +fArgEight = f64 + +fArgAbsNorm = f65 +fArgAbsNorm2 = f66 +fArgAbsNorm2L = f67 +fArgAbsNorm3 = f68 +fArgAbsNorm4 = f69 +fArgAbsNorm11 = f70 + +fRes = f71 +fResH = f72 +fResL = f73 +fRes1H = f74 +fRes1L = f75 +fRes1Hd = f76 +fRes2H = f77 +fRes2L = f78 +fRes3H = f79 +fRes3L = f80 +fRes4 = f81 + +fTT = f82 +fTH = f83 +fTL = f84 +fTT2 = f85 +fTH2 = f86 +fTL2 = f87 + +f1p5 = f88 +f2p0 = f89 +fTiny = f90 +fSignumX = f91 +fArgAbsNorm4X = f92 + +// Data tables +//============================================================== +RODATA + +.align 16 +LOCAL_OBJECT_START(tanhl_data) + +////////// Main tables /////////// +_0p125_to_0p25_data: // exp = 2^-3 +// Polynomial coefficients for the tanh(x), 1/8 <= |x| < 1/4 +data8 0x93D27D6AE7E835F8, 0x0000BFF4 //A3 = -5.6389704216278164626050408239e-04 +data8 0xBF66E8668A78A8BC //A2H = -2.7963640930198357253955165902e-03 +data8 0xBBD5384EFD0E7A54 //A2L = -1.7974001252014762983581666453e-20 +data8 0x3FBEE69E31DB6156 //A1H = 1.2070645062647619716322822114e-01 +data8 0x3C43A0B4E24A3DCA //A1L = 2.1280460108882061756490131241e-18 +data8 0x3FC7B8FF903BF776 //A0H = 1.8533319990813951205765874874e-01 +data8 0x3C593F1A61986FD4 //A0L = 5.4744612262799573374268254539e-18 +data8 0xDB9E6735560AAE5A, 0x0000BFA3 //A25 = -3.4649731131719154051239475238e-28 +data8 0xF0DDE953E4327704, 0x00003FA4 //A24 = 7.6004173864565644629900702857e-28 +data8 0x8532AED11DEC5612, 0x00003FAB //A23 = 5.3798235684551098715428515761e-26 +data8 0xAEF72A34D88B0038, 0x0000BFAD //A22 = -2.8267199091484508912273222600e-25 +data8 0x9645EF1DCB759DDD, 0x0000BFB2 //A21 = -7.7689413112830095709522203109e-24 +data8 0xA5D12364E121F70F, 0x00003FB5 //A20 = 6.8580281614531622113161030550e-23 +data8 0x9CF166EA815AC705, 0x00003FB9 //A19 = 1.0385615003184753213024737634e-21 +data8 0x852B1D0252498752, 0x0000BFBD //A18 = -1.4099753997949827217635356478e-20 +data8 0x9270F5716D25EC9F, 0x0000BFC0 //A17 = -1.2404055949090177751123473821e-19 +data8 0xC216A9C4EEBDDDCA, 0x00003FC4 //A16 = 2.6303900460415782677749729120e-18 +data8 0xDCE944D89FF592F2, 0x00003FC6 //A15 = 1.1975620514752377092265425941e-17 +data8 0x83C8DDF213711381, 0x0000BFCC //A14 = -4.5721980583985311263109531319e-16 +LOCAL_OBJECT_END(tanhl_data) + +LOCAL_OBJECT_START(_0p25_to_0p5_data) +// Polynomial coefficients for the tanh(x), 1/4 <= |x| < 1/2 +data8 0xB6E27B747C47C8AD, 0x0000BFF6 //A3 = -2.7905990032063258105302045572e-03 +data8 0xBF93FD54E226F8F7 //A2H = -1.9521070769536099515084615064e-02 +data8 0xBC491BC884F6F18A //A2L = -2.7222721075104525371410300625e-18 +data8 0x3FCBE3FBB015A591 //A1H = 2.1789499376181400980279079249e-01 +data8 0x3C76AFC2D1AE35F7 //A1L = 1.9677459707672596091076696742e-17 +data8 0x3FD6EF53DE8C8FAF //A0H = 3.5835739835078589399230963863e-01 +data8 0x3C8E2A1C14355F9D //A0L = 5.2327050592919416045278607775e-17 +data8 0xF56D363AAE3BAD53, 0x00003FBB //A25 = 6.4963882412697389947564301120e-21 +data8 0xAD6348526CEEB897, 0x0000BFBD //A24 = -1.8358149767147407353343152624e-20 +data8 0x85D96A988565FD65, 0x0000BFC1 //A23 = -2.2674950494950919052759556703e-19 +data8 0xD52CAF6B1E4D9717, 0x00003FC3 //A22 = 1.4445269502644677106995571101e-18 +data8 0xBD7E1BE5CBEF7A01, 0x00003FC5 //A21 = 5.1362075721080004718090799595e-18 +data8 0xAE84A9B12ADD6948, 0x0000BFC9 //A20 = -7.5685210830925426342786733068e-17 +data8 0xEAC2D5FCF80E250C, 0x00003FC6 //A19 = 1.2726423522879522181100392135e-17 +data8 0xE0D2A8AC8C2EDB95, 0x00003FCE //A18 = 3.1200443098733419749016380203e-15 +data8 0xB22F0AB7B417F78E, 0x0000BFD0 //A17 = -9.8911854977385933809488291835e-15 +data8 0xE25A627BAEFFA7A4, 0x0000BFD3 //A16 = -1.0052095388666003876301743498e-13 +data8 0xC90F32EC4A17F908, 0x00003FD6 //A15 = 7.1430637679768183097897337145e-13 +data8 0x905F6F124AF956B1, 0x00003FD8 //A14 = 2.0516607231389483452611375485e-12 +LOCAL_OBJECT_END(_0p25_to_0p5_data) + +LOCAL_OBJECT_START(_0p5_to_1_data) +// Polynomial coefficients for the tanh(x), 1/2 <= |x| < 1 +data8 0xAB402BE491EE72A7, 0x00003FF7 //A3 = 5.2261556931080934657023772945e-03 +data8 0xBFB8403D3DDA87BE //A2H = -9.4730212784752659826992271519e-02 +data8 0xBC6FF7BC2AB71A8B //A2L = -1.3863786398568460929625760740e-17 +data8 0x3FD3173B1EFA6EF4 //A1H = 2.9829290414066567116435635398e-01 +data8 0x3C881E4DCABDE840 //A1L = 4.1838710466827119847963316219e-17 +data8 0x3FE45323E552F228 //A0H = 6.3514895238728730220145735075e-01 +data8 0x3C739D5832BF7BCF //A0L = 1.7012977006567066423682445459e-17 +data8 0xF153980BECD8AE12, 0x00003FD0 //A25 = 1.3396313991261493342597057700e-14 +data8 0xEC9ACCD245368129, 0x0000BFD3 //A24 = -1.0507358886349528807350792383e-13 +data8 0x8AE6498CA36D2D1A, 0x00003FD4 //A23 = 1.2336759149738309660361813001e-13 +data8 0x8DF02FBF5AC70E64, 0x00003FD7 //A22 = 1.0085317723615282268326194551e-12 +data8 0x9E15C7125DA204EE, 0x0000BFD9 //A21 = -4.4930478919612724261941857560e-12 +data8 0xA62C6F39BDDCEC1C, 0x00003FD7 //A20 = 1.1807342457875095150035780314e-12 +data8 0xDFD8D65D30F80F52, 0x00003FDC //A19 = 5.0896919887121116317817665996e-11 +data8 0xB795AFFD458F743E, 0x0000BFDE //A18 = -1.6696932710534097241291327756e-10 +data8 0xFEF30234CB01EC89, 0x0000BFDD //A17 = -1.1593749714588103589483091370e-10 +data8 0xA2F638356E13761E, 0x00003FE2 //A16 = 2.3714062288761887457674853605e-09 +data8 0xC429CC0D031E4FD5, 0x0000BFE3 //A15 = -5.7091025466377379046489586383e-09 +data8 0xC78363FF929EFF62, 0x0000BFE4 //A14 = -1.1613199289622686725595739572e-08 +LOCAL_OBJECT_END(_0p5_to_1_data) + +LOCAL_OBJECT_START(_1_to_2_data) +// Polynomial coefficients for the tanh(x), 1 <= |x| < 2.0 +data8 0xB3D8FB48A548D99A, 0x00003FFB //A3 = 8.7816203264683800892441646129e-02 +data8 0xBFC4EFBD8FB38E3B //A2H = -1.6356629864377389416141284073e-01 +data8 0xBC77687FD8087B23 //A2L = -2.0303377679446772162287121190e-17 +data8 0x3FC72165282C6F72 //A1H = 1.8070663892364852154415189034e-01 +data8 0x3C64E01F7A76D777 //A1L = 9.0532964466719018524360408402e-18 +data8 0x3FECF6F9786DF577 //A0H = 9.0514825364486639625027919465e-01 +data8 0x3C8834EDCE71A65B //A0L = 4.1992023813070331863928976191e-17 +data8 0xC3EEEB3EFA688094, 0x00003FE2 //A25 = 2.8512044383274095705865793485e-09 +data8 0x88461973672AEB12, 0x0000BFE1 //A24 = -9.9152258079470849685057375343e-10 +data8 0xFC2AF9950DC5027E, 0x0000BFE4 //A23 = -1.4678101918123116001692289670e-08 +data8 0x9C80CA742F89B7B5, 0x00003FE6 //A22 = 3.6438714992394138274843759814e-08 +data8 0xA0B3D7FAA606260A, 0x0000BFE6 //A21 = -3.7416469848124568887944709492e-08 +data8 0xDA5858432FBD9D9D, 0x0000BFE6 //A20 = -5.0837429421503142141842414978e-08 +data8 0xB0244D1E1AE9C1B0, 0x00003FE9 //A19 = 3.2808967255272595749004827841e-07 +data8 0xC8D3109ACF740738, 0x0000BFEA //A18 = -7.4812945767507614821609020680e-07 +data8 0xBB0F3440EEA55BBF, 0x00003FEA //A17 = 6.9685053481643125932497676583e-07 +data8 0xC13A8B08D8576C19, 0x00003FEB //A16 = 1.4396658837712390333960587173e-06 +data8 0xFF3A1163CC5522A1, 0x0000BFED //A15 = -7.6063522055104010298762276148e-06 +data8 0x8672AF27EB0823B7, 0x00003FEF //A14 = 1.6027448793338500004496520337e-05 +LOCAL_OBJECT_END(_1_to_2_data) + +LOCAL_OBJECT_START(_2_to_3p25_data) +// Polynomial coefficients for the tanh(x), 2 <= |x| < 3.25 +data8 0xD45657BEC559E366, 0x00003FFA //A3 = 5.1840155367548909799883161889e-02 +data8 0xBFA41B109CA6AB81 //A2H = -3.9268988726084870510835145296e-02 +data8 0xBC2C3D708A4E56C5 //A2L = -7.6544669252238280132415018518e-19 +data8 0x3F9434A517BBC5F4 //A1H = 1.9732074330880380874653212686e-02 +data8 0x3C3ED62DD9585229 //A1L = 1.6716574468135097509707871438e-18 +data8 0x3FEFD77D111A0AFF //A0H = 9.9505475368673035330147058630e-01 +data8 0x3C9C415E151C6CA5 //A0L = 9.8030409604070051319822874013e-17 +data8 0xB1596391D4534D52, 0x00003FEC //A25 = 2.6427086526487251988631279067e-06 +data8 0xC4DC44E243D1AF5F, 0x00003FEF //A24 = 2.3467591534149209236830008333e-05 +data8 0xAED5786023982BB8, 0x00003FF0 //A23 = 4.1683642395739762658623742687e-05 +data8 0xCF39926C9FBC6A10, 0x00003FF0 //A22 = 4.9406263949321793291856681624e-05 +data8 0xA255A72359928142, 0x00003FF0 //A21 = 3.8703580278108400672236161973e-05 +data8 0xA2E573B9FC332C0D, 0x00003FED //A20 = 4.8546879618263642155709302480e-06 +data8 0x82C7BD01830ACA93, 0x00003FF0 //A19 = 3.1180436075031301077175550468e-05 +data8 0xB38AF4C76E96444B, 0x0000BFF0 //A18 = -4.2806338675404452784440167120e-05 +data8 0xEC08FF0FB194464C, 0x00003FF0 //A17 = 5.6275163156181928637744511210e-05 +data8 0xB850825D9E235135, 0x0000BFF0 //A16 = -4.3943998628289568813056822585e-05 +data8 0xF98436E838763687, 0x0000BFEF //A15 = -2.9744680263523220185672219686e-05 +data8 0xE1851A2D00737A5D, 0x00003FF2 //A14 = 2.1507256570895163202182573369e-04 +LOCAL_OBJECT_END(_2_to_3p25_data) + +LOCAL_OBJECT_START(_4_to_6p5_data) +// Polynomial coefficients for the tanh(x), 4 <= |x| < 6.5 +data8 0x896FDBD321A0BE58, 0x00003FF5 //A3 = 1.0485606995331904734870550114e-03 +data8 0xBF39C522B95A37D6 //A2H = -3.9321992640217512306882730044e-04 +data8 0xBBA9B3EC39A45338 //A2L = -2.7213922673282819034134988241e-21 +data8 0x3F19C5377A48B5AD //A1H = 9.8306189621330793766869338146e-05 +data8 0x3BCAFCB1D08A891C //A1L = 1.1429476443042275163117526657e-20 +data8 0x3FEFFFE63ABE253B //A0H = 9.9998771165079547440512897083e-01 +data8 0x3C9BB74C4EE0D16F //A0L = 9.6159219890436197391279544561e-17 +data8 0x8D86121D469AFA7E, 0x0000BFEF //A25 = -1.6870941388985743600323604423e-05 +data8 0x9D3656A36593C5C4, 0x00003FEF //A24 = 1.8741161763079973068909254398e-05 +data8 0xDCD772D5BF9ADB96, 0x00003FF0 //A23 = 5.2652739523018349983563695656e-05 +data8 0xFF79ADCF0DCBCC2D, 0x00003FF1 //A22 = 1.2182012003034659966028035977e-04 +data8 0x84D24E394DEFD0D2, 0x00003FF1 //A21 = 6.3334229517535065590380468696e-05 +data8 0xA66B56BFD2782544, 0x00003FF1 //A20 = 7.9354902476954571736114945842e-05 +data8 0xFB15771FBF3155FE, 0x0000BFEE //A19 = -1.4965763624796745134798717707e-05 +data8 0xC774790126BE54C3, 0x00003FEF //A18 = 2.3776885435831770523136610539e-05 +data8 0x825A13DACB8C68CD, 0x00003FEF //A17 = 1.5539153272890695426189818556e-05 +data8 0xCFF96E6810AACE27, 0x0000BFF1 //A16 = -9.9169893703251156059893890295e-05 +data8 0x8A85D2061B865024, 0x00003FF3 //A15 = 2.6421115104625621420758344535e-04 +data8 0x922EC6F3CFE0496E, 0x0000BFF4 //A14 = -5.5764283474946207558456581668e-04 +LOCAL_OBJECT_END(_4_to_6p5_data) + +LOCAL_OBJECT_START(_8_to_13_data) +// Polynomial coefficients for the tanh(x), 8 <= |x| < 13 +data8 0xDD6050A898303460, 0x00003FE6 //A3 = 5.1543170295688189081352133793e-08 +data8 0xBE44C1078FDBADC0 //A2H = -9.6643444318955652627581125180e-09 +data8 0xBAF95FCAA6DBBA6F //A2L = -1.3118146684038113473094275420e-24 +data8 0x3E14C1078FE26748 //A1H = 1.2080430540780827633746315479e-09 +data8 0x3A88168082F37D95 //A1L = 9.7290246966246404028418245094e-27 +data8 0x3FEFFFFFFFF59F7C //A0H = 9.9999999992449728480892190419e-01 +data8 0x3C7C068EBC5C2EEB //A0L = 2.4308346546749583521003998922e-17 +data8 0x9DC155C77A6C46E5, 0x00003FF2 //A25 = 1.5044709695520252096006763473e-04 +data8 0xF2F9E09CA47F46E9, 0x00003FF3 //A24 = 4.6344010077547944693833282056e-04 +data8 0xCBFD67E704734BC8, 0x00003FF4 //A23 = 7.7815958662026429864083620142e-04 +data8 0xC18DC821CD67E621, 0x00003FF4 //A22 = 7.3834928521190855055818897104e-04 +data8 0x8AF72BCAB05A296E, 0x00003FF4 //A21 = 5.3011135848666430331904214879e-04 +data8 0xC2E73BE9B9AB4007, 0x00003FF2 //A20 = 1.8587423129049905806822275188e-04 +data8 0xE7E8C2058E2FF9F7, 0x00003FF1 //A19 = 1.1058292891321512917337425414e-04 +data8 0xC46309F52E429F97, 0x0000BFF0 //A18 = -4.6822278664829811025251866877e-05 +data8 0x81966C1E007E9BEB, 0x00003FF1 //A17 = 6.1792176836716291200611553354e-05 +data8 0x8CEDC4BEFCAB9A7E, 0x0000BFF1 //A16 = -6.7200080564674449915571760779e-05 +data8 0x8B64E9FA53210018, 0x00003FF1 //A15 = 6.6468331917938095774361868182e-05 +data8 0x82DEDAA539A3A3F1, 0x0000BFF1 //A14 = -6.2403928644276709411156885292e-05 +LOCAL_OBJECT_END(_8_to_13_data) + +LOCAL_OBJECT_START(_16_to_22p8_data) +// Polynomial coefficients for the tanh(x), 16 <= |x| < 22.88 +data8 0x992C00F33DDE804D, 0x00003FCE //A3 = 2.1256869805798788337547274131e-15 +data8 0x3C8D42EA28102760 //A2H = 5.0760412270332007485198379096e-17 +data8 0x391A747B43B072DD //A2L = 1.2737621993898125881520341053e-33 +data8 0x3C309BC5C3CB4D5F //A1H = 9.0034785192019775952205276560e-19 +data8 0x38A8EF3B5C9DCE71 //A1L = 9.3793162715476168397242934494e-36 +data8 0x3FF0000000000000 //A0H = 1.0000000000000000000000000000e+00 +data8 0x3BACC66AFD5CA22A //A0L = 3.0466790472070565954180861749e-21 +data8 0xF020FB351C2F37CB, 0x00003FF1 //A25 = 1.1450235038836625246604146870e-04 +data8 0xBE80596C51302A7B, 0x00003FF4 //A24 = 7.2670503421185030764546828414e-04 +data8 0x91343CF8577E0131, 0x00003FF6 //A23 = 2.2156380512949603402001207105e-03 +data8 0x8D029A8679641286, 0x00003FF7 //A22 = 4.3032888906494613055765544559e-03 +data8 0xC3713F64D8DC4BAB, 0x00003FF7 //A21 = 5.9644279041951657632420721490e-03 +data8 0xCD678C455A5D06C2, 0x00003FF7 //A20 = 6.2684473911812928601693994403e-03 +data8 0xA9E1C825BDCEEBCC, 0x00003FF7 //A19 = 5.1843859941826642445235686826e-03 +data8 0xE29C919AD93F6EB9, 0x00003FF6 //A18 = 3.4578185539872939928152204329e-03 +data8 0xF7E615A75994A607, 0x00003FF5 //A17 = 1.8913175041916131006881986311e-03 +data8 0xE102EFE0F7F2B2AD, 0x00003FF4 //A16 = 8.5835064987089641065525269712e-04 +data8 0xAAD62946DEE96996, 0x00003FF3 //A15 = 3.2584489313998677644253007210e-04 +data8 0xDA2470DE110B293E, 0x00003FF1 //A14 = 1.0401837693241806604296821650e-04 +LOCAL_OBJECT_END(_16_to_22p8_data) + +LOCAL_OBJECT_START(_3p25_to_4_data) +// Polynomial coefficients for the tanh(x), 3.25 <= |x| < 4 +data8 0xE9E07240432926E6, 0x00003FF7 //A3 = 7.1373517862636557382403555215e-03 +data8 0xBF75F495227AF306 //A2H = -5.3602052282115727338540622782e-03 +data8 0xBBBE92D355A6B716 //A2L = -6.4741983326810209847018826624e-21 +data8 0x3F65F85AD510B690 //A1H = 2.6819013660517934671823070403e-03 +data8 0x3C159A0B73E6EC01 //A1L = 2.9275813076637328121849573333e-19 +data8 0x3FEFFA81708A0B42 //A0H = 9.9932929973906703402519724477e-01 +data8 0x3C66857246C19DC6 //A0L = 9.7670460995685717424398031188e-18 +data8 0xE6B6B8365B1E4D6C, 0x00003FE3 //A25 = 6.7146538162212081470554423396e-09 +data8 0xE0453CEEF483A510, 0x00003FE2 //A24 = 3.2635647369924061614015292015e-09 +data8 0x9C7D83B56E92CF1A, 0x00003FE5 //A23 = 1.8217867585545497089756353348e-08 +data8 0xA94635C48ABA9EB4, 0x0000BFE4 //A22 = -9.8530586070049930796756799547e-09 +data8 0xB1B0C14443067646, 0x00003FE5 //A21 = 2.0685890807654992387562340307e-08 +data8 0x9C6E549781E293C3, 0x00003FDE //A20 = 1.4227314592865135171341122138e-10 +data8 0xB0CBFCE7C80F57A7, 0x0000BFE7 //A19 = -8.2327438416004542109809245219e-08 +data8 0xB151AB3876E896E1, 0x00003FE9 //A18 = 3.3028241036175815328309577940e-07 +data8 0xFCF3A5C1A5CB7EEE, 0x0000BFEA //A17 = -9.4231869277542043001280640966e-07 +data8 0x96A9016C7C95BEDA, 0x00003FEC //A16 = 2.2450115975007100522962781833e-06 +data8 0x9B9B0A3901DEC05B, 0x0000BFED //A15 = -4.6374089937147736266514566049e-06 +data8 0x8987DF26A6789CCF, 0x00003FEE //A14 = 8.1974714257536543772040700977e-06 +LOCAL_OBJECT_END(_3p25_to_4_data) + +LOCAL_OBJECT_START(_6p5_to_8_data) +// Polynomial coefficients for the tanh(x), 6.5 <= |x| < 8.0 +data8 0xA11C8A63815E5657, 0x00003FEF //A3 = 1.9205985861286093001394561449e-05 +data8 0xBEDE355AD6CB61D8 //A2H = -7.2022479400070228499307345427e-06 +data8 0xBB8E6B50B8468A63 //A2L = -8.0518953122203408718779840543e-22 +data8 0x3EBE355B48DCF330 //A1H = 1.8005623902549165889479948488e-06 +data8 0x3B5837550FFA98DA //A1L = 8.0124491698609178046195694087e-23 +data8 0x3FEFFFFF872A91F8 //A0H = 9.9999977492967584424832239165e-01 +data8 0x3C8A43B839B4EB63 //A0L = 4.5561696441306660142461355317e-17 +data8 0xB5BC1948966B8826, 0x0000BFE6 //A25 = -4.2313421330480692560677276010e-08 +data8 0x91D0BE367389BDFC, 0x0000BFE8 //A24 = -1.3580117599617083801153887619e-07 +data8 0xFFD950AF282AB36C, 0x0000BFE8 //A23 = -2.3827784451962439125197203287e-07 +data8 0x959B1770EBB8903A, 0x0000BFE9 //A22 = -2.7866256690165347051403663794e-07 +data8 0xCC78060D1C0CFF3C, 0x0000BFE8 //A21 = -1.9042644867126442102188429523e-07 +data8 0xF8919BAF2E87F31D, 0x0000BFE8 //A20 = -2.3149771783868910586746973299e-07 +data8 0xC5B6AC942A3F2440, 0x00003FE8 //A19 = 1.8413511183396213757149263639e-07 +data8 0xABF1A4703056450A, 0x0000BFEA //A18 = -6.4054099983863829656292958643e-07 +data8 0xBB543D8BDB670453, 0x00003FEB //A17 = 1.3957102903892251890348444989e-06 +data8 0xC9D6F37700C1D092, 0x0000BFEC //A16 = -3.0076451968978522605262647414e-06 +data8 0xCA6EF4BB64E49EC8, 0x00003FED //A15 = 6.0329860989478473738709576062e-06 +data8 0xBE25D0FD069D0A93, 0x0000BFEE //A14 = -1.1333687314965721384777951065e-05 +LOCAL_OBJECT_END(_6p5_to_8_data) + +LOCAL_OBJECT_START(_13_to_16_data) +// Polynomial coefficients for the tanh(x), 13 <= |x| < 16 +data8 0x98176FD2075BDBD5, 0x00003FDB //A3 = 1.7290807363028159200235264756e-11 +data8 0xBD8C8464F76162D1 //A2H = -3.2420263805679445515400340441e-12 +data8 0xBA2D56B508E0F1FD //A2L = -1.8515322669984580704502445180e-28 +data8 0x3D5C8464F761639C //A1H = 4.0525329757100331782338488690e-13 +data8 0x3A0A09D9E328E620 //A1L = 4.1081479300866418212862258651e-29 +data8 0x3FEFFFFFFFFFFF1B //A0H = 9.9999999999997457589273608392e-01 +data8 0x3C9B9B089E9BFD89 //A0L = 9.5776165728054091471814161399e-17 +data8 0xC5395B9EC765BDB7, 0x00003FE6 //A25 = 4.5919803498257974411526879804e-08 +data8 0x9A0F1FCB1DC24C3A, 0x00003FE8 //A24 = 1.4347869798460288751020493795e-07 +data8 0x8AA5C3459FAD0B28, 0x00003FE9 //A23 = 2.5825111356333853968900510087e-07 +data8 0x9578B747988CFF9D, 0x00003FE9 //A22 = 2.7841245127068220034870119246e-07 +data8 0x810DF1A589D9CAF1, 0x00003FE9 //A21 = 2.4038267971021370956311255310e-07 +data8 0x8A00D77B9416EB75, 0x00003FE8 //A20 = 1.2852557749068320312899366352e-07 +data8 0xB2436C4A1849C498, 0x00003FE7 //A19 = 8.3010350873515703893886683374e-08 +data8 0xEA6405B18356600B, 0x00003FE3 //A18 = 6.8216675390299296071261114202e-09 +data8 0xF7606C022194B7E8, 0x00003FE5 //A17 = 2.8798432098264655723769995993e-08 +data8 0xAF4B0C453FCAF34E, 0x0000BFE5 //A16 = -2.0406809167824936143455638336e-08 +data8 0xC324C1F10D5FA7CC, 0x00003FE5 //A15 = 2.2717703170390130238356558599e-08 +data8 0xB34A2E3A4D3B9C31, 0x0000BFE5 //A14 = -2.0872076027950789618606920471e-08 +LOCAL_OBJECT_END(_13_to_16_data) + + +//////// "Tail" tables ////////// +LOCAL_OBJECT_START(_0p125_to_0p25_data_tail) +// Polynomial coefficients for the erf(x), 1/8 <= |x| < 1/4 +data8 0x9D7D206E97ADC83A, 0x0000BFCC //A13 = -5.4639895428711257047470806445e-16 +data8 0xA8972B666A845810, 0x00003FD3 //A12 = 7.4869224589947988668562043110e-14 +data8 0x9A5B31511C9F4698, 0x0000BFD4 //A11 = -1.3709586467430093373657009487e-13 +data8 0xCBB8047BCB274982, 0x0000BFDA //A10 = -1.1580074124926108509393610532e-11 +data8 0xF95EB849E5F9247C, 0x00003FDC //A9 = 5.6700173336564916962945623180e-11 +data8 0xE7893404C6A53386, 0x00003FE1 //A8 = 1.6846457582993065168777704528e-09 +data8 0xF2E5C7E2B5F55ECC, 0x0000BFE4 //A7 = -1.4138500046802141367543484859e-08 +data8 0xF43906FF53A002C0, 0x0000BFE8 //A6 = -2.2745017243678613107034288816e-07 +data8 0xC6175D5E47D1D259, 0x00003FEC //A5 = 2.9517899220726077077586632607e-06 +data8 0xE7C2AE92CB36769B, 0x00003FEF //A4 = 2.7628001723157068127646694830e-05 +LOCAL_OBJECT_END(_0p125_to_0p25_data_tail) + +LOCAL_OBJECT_START(_0p25_to_0p5_data_tail) +// Polynomial coefficients for the tanh(x), 1/4 <= |x| < 1/2 +data8 0x9E2972C008B9965E, 0x0000BFDC //A13 = -3.5961854154738002253192260213e-11 +data8 0xC3EABA3D219BEA8A, 0x00003FDB //A12 = 2.2273173303628274478819473067e-11 +data8 0xC50FB68D960D5CD9, 0x00003FE1 //A11 = 1.4338102430978399800743148719e-09 +data8 0xB3BB92499EF2D583, 0x0000BFE3 //A10 = -5.2309100551458044083112632491e-09 +data8 0xBD915BE632F1D04E, 0x0000BFE6 //A9 = -4.4137194873936112573773943707e-08 +data8 0xBC48C813FA819141, 0x00003FE9 //A8 = 3.5070684356359066908197915734e-07 +data8 0xD3E34EA031AC611B, 0x00003FEA //A7 = 7.8934400708919584259192272835e-07 +data8 0x8EAC489D859541CD, 0x0000BFEF //A6 = -1.7007944944124693133572815137e-05 +data8 0x98D4D7E5D1508B8A, 0x00003FEF //A5 = 1.8218924920302265989878708948e-05 +data8 0xAC262F3F8CF49C02, 0x00003FF4 //A4 = 6.5669692402266433496312492412e-04 +LOCAL_OBJECT_END(_0p25_to_0p5_data_tail) + +LOCAL_OBJECT_START(_0p5_to_1_data_tail) +// Polynomial coefficients for the tanh(x), 1/2 <= |x| < 1 +data8 0xDF67FB36FFA2A538, 0x00003FE7 //A13 = 1.0403160796697495720021114635e-07 +data8 0xB7FB80FB5AFA63A4, 0x0000BFE8 //A12 = -1.7134699677764282023124981753e-07 +data8 0xC87625A0BA7D6C5F, 0x0000BFEA //A11 = -7.4677732458471897291461679095e-07 +data8 0x90DA375DD9AF6D79, 0x00003FED //A10 = 4.3169381418023765618186668159e-06 +data8 0x82DFB03317B17316, 0x0000BFED //A9 = -3.9003426534601562552753368105e-06 +data8 0xAA582FD4F3438BB4, 0x0000BFF0 //A8 = -4.0613288845040776435400454867e-05 +data8 0xB1532D8CF763B21C, 0x00003FF2 //A7 = 1.6911021594787399557528570601e-04 +data8 0x82E12AEF7CAB76C6, 0x0000BFEF //A6 = -1.5602059530458172761585925044e-05 +data8 0x83256E3D0FBA5C93, 0x0000BFF6 //A5 = -2.0011324059500451791903108104e-03 +data8 0xCC4AB2EC0965499B, 0x00003FF7 //A4 = 6.2344907419841579664122448353e-03 +LOCAL_OBJECT_END(_0p5_to_1_data_tail) + +LOCAL_OBJECT_START(_1_to_2_data_tail) +// Polynomial coefficients for the tanh(x), 1 <= |x| < 2.0 +data8 0xCCAEE174EAC17F78, 0x0000BFEE //A13 = -1.2200065117856038355953618829e-05 +data8 0xA39DD0981D1A2776, 0x0000BFF0 //A12 = -3.9009204899026604074167603200e-05 +data8 0xB7104FA27FAF80D0, 0x00003FF2 //A11 = 1.7458316338540792661905876072e-04 +data8 0xB219A7274436A734, 0x0000BFF3 //A10 = -3.3969918595931391572998415468e-04 +data8 0xCCD9D03C0C73CECF, 0x00003FF2 //A9 = 1.9536097875337884986025498958e-04 +data8 0x85321EA40CFEEBEE, 0x00003FF5 //A8 = 1.0162031558369402750607778300e-03 +data8 0x81F272C08C308220, 0x0000BFF7 //A7 = -3.9656696618251138315464862909e-03 +data8 0xE8761C6BDEA9ED87, 0x00003FF7 //A6 = 7.0941580558970243020090656343e-03 +data8 0xAE4E9F3691F66877, 0x0000BFF6 //A5 = -2.6597155288710984120834711909e-03 +data8 0xCC8286B331BD8AAA, 0x0000BFF9 //A4 = -2.4964583478826523250880337777e-02 +LOCAL_OBJECT_END(_1_to_2_data_tail) + +LOCAL_OBJECT_START(_2_to_3p25_data_tail) +// Polynomial coefficients for the tanh(x), 2 <= |x| < 3.25 +data8 0x92E1711A3BD6408B, 0x0000BFF4 //A13 = -5.6030514548041036913731470443e-04 +data8 0x8B9BD885FF3E98C5, 0x00003FF5 //A12 = 1.0651304064581604055612602669e-03 +data8 0xD041356C7FA26A22, 0x0000BFF5 //A11 = -1.5888574328066952147023520244e-03 +data8 0xDFA210BE9BE6B7FD, 0x00003FF5 //A10 = 1.7061849060196387827639060629e-03 +data8 0x8ECC3606808028E9, 0x0000BFF4 //A9 = -5.4472999329435778312080340471e-04 +data8 0xD5C053B8EEBD10C8, 0x0000BFF6 //A8 = -3.2615856552479930645151033322e-03 +data8 0xB7BFD63AC5051539, 0x00003FF8 //A7 = 1.1215171059191957498023766643e-02 +data8 0xC367C59D7FA3ADA2, 0x0000BFF9 //A6 = -2.3853193251842394834616848995e-02 +data8 0x9FC9FB890BB053CF, 0x00003FFA //A5 = 3.9010984954739386625695104667e-02 +data8 0xD01D077B42E7ED76, 0x0000BFFA //A4 = -5.0808934425896607486919526567e-02 +LOCAL_OBJECT_END(_2_to_3p25_data_tail) + +LOCAL_OBJECT_START(_4_to_6p5_data_tail) +// Polynomial coefficients for the tanh(x), 4 <= |x| < 6.5 +data8 0x870CCE8C76C52C7E, 0x00003FF5 //A13 = 1.0303499350193060915603525934e-03 +data8 0xE1431E54AD2A738B, 0x0000BFF5 //A12 = -1.7186140560972621669872002486e-03 +data8 0xAB20056533E28734, 0x00003FF6 //A11 = 2.6111615345168277554841545330e-03 +data8 0xECCB91D64718B9BD, 0x0000BFF6 //A10 = -3.6132079169671860943878776041e-03 +data8 0x94771DA3B8C2EB4F, 0x00003FF7 //A9 = 4.5308012699419563988381317896e-03 +data8 0xA7497377E4946F2C, 0x0000BFF7 //A8 = -5.1051915941441437592654444804e-03 +data8 0xA76B2D6FCA088AE9, 0x00003FF7 //A7 = 5.1092120989582196669504468168e-03 +data8 0x928C8961F33C9560, 0x0000BFF7 //A6 = -4.4723196805537430568162704711e-03 +data8 0xDBDDDF6CDE9AB9BE, 0x00003FF6 //A5 = 3.3548994514326736175581084349e-03 +data8 0x896E211733AD9D40, 0x0000BFF6 //A4 = -2.0970183170010094667442967500e-03 +LOCAL_OBJECT_END(_4_to_6p5_data_tail) + +LOCAL_OBJECT_START(_8_to_13_data_tail) +// Polynomial coefficients for the tanh(x), 8 <= |x| < 13 +data8 0xE50C3476BED020AA, 0x00003FF0 //A13 = 5.4609221347524272615754239857e-05 +data8 0xBA16F5F4EDC0EABC, 0x0000BFF0 //A12 = -4.4367239594986428539386662937e-05 +data8 0x8B916C2F002C3D91, 0x00003FF0 //A11 = 3.3275617838067362533536610680e-05 +data8 0xBFE8031097CB4442, 0x0000BFEF //A10 = -2.2877013297722792747267224605e-05 +data8 0xEFE1FFD106B2DA41, 0x00003FEE //A9 = 1.4298129659899553350478452989e-05 +data8 0x86EF1FF403A6622E, 0x0000BFEE //A8 = -8.0426979849841642112688693288e-06 +data8 0x86EF200FD047306B, 0x00003FED //A7 = 4.0213490418736097707257704218e-06 +data8 0xEC22782377882553, 0x0000BFEB //A6 = -1.7593402092805559754997565942e-06 +data8 0xB119DA1DB7C47773, 0x00003FEA //A5 = 6.5975257917246601211360847253e-07 +data8 0xDD6050A7761D67BB, 0x0000BFE8 //A4 = -2.0617268111985310661707082242e-07 +LOCAL_OBJECT_END(_8_to_13_data_tail) + +LOCAL_OBJECT_START(_16_to_22p8_data_tail) +// Polynomial coefficients for the tanh(x), 16 <= |x| < 22.88 +data8 0xEAF4AF87336E81B1, 0x00003FEF //A13 = 2.8008914392791730186582989654e-05 +data8 0xD5B309EA768E2711, 0x00003FED //A12 = 6.3687375204024238267961143128e-06 +data8 0xA4048CA537113538, 0x00003FEB //A11 = 1.2220276227448617951538196845e-06 +data8 0xD3EC78BB3425377D, 0x00003FE8 //A10 = 1.9736934193679794194181457250e-07 +data8 0xE5763CD37440266E, 0x00003FE5 //A9 = 2.6712876934440631473215182284e-08 +data8 0xCECA765EEB4A265F, 0x00003FE2 //A8 = 3.0092031912460315516888139627e-09 +data8 0x99ABF588DF81A52E, 0x00003FDF //A7 = 2.7952722177649984066847682907e-10 +data8 0xB9C78918294A4685, 0x00003FDB //A6 = 2.1120676552098603524020495036e-11 +data8 0xB3A3C42AD539D50F, 0x00003FD7 //A5 = 1.2764169243389521270291967366e-12 +data8 0x86BC347939478174, 0x00003FD3 //A4 = 5.9834437707863962671883176163e-14 +LOCAL_OBJECT_END(_16_to_22p8_data_tail) + +LOCAL_OBJECT_START(_3p25_to_4_data_tail) +// Polynomial coefficients for the tanh(x), 3.25 <= |x| < 4 +data8 0xBE9A2BE19F21BA1C, 0x0000BFEE //A13 = -1.1360778336288065244475976873e-05 +data8 0xF84910F515BDB014, 0x00003FED //A12 = 7.3994819819577018481862729782e-06 +data8 0xC4C84FB788AA4007, 0x00003FEF //A11 = 2.3458298013663976251972482656e-05 +data8 0x86CC6243C170E5ED, 0x0000BFF2 //A10 = -1.2855374755847770638424932233e-04 +data8 0xD3065AC539ABABFF, 0x00003FF3 //A9 = 4.0249790677367806832685138089e-04 +data8 0x82C4413795EC381B, 0x0000BFF5 //A8 = -9.9767013652382759950854031514e-04 +data8 0x88D588720888899A, 0x00003FF6 //A7 = 2.0879228705174076794011525274e-03 +data8 0xF4CA066137741469, 0x0000BFF6 //A6 = -3.7351861548964870836350490741e-03 +data8 0xB998746D56E81737, 0x00003FF7 //A5 = 5.6639259807333999973200378964e-03 +data8 0xE93FB2F48233275B, 0x0000BFF7 //A4 = -7.1181892208343798194003322900e-03 +LOCAL_OBJECT_END(_3p25_to_4_data_tail) + +LOCAL_OBJECT_START(_6p5_to_8_data_tail) +// Polynomial coefficients for the tanh(x), 6.5 <= |x| < 8.0 +data8 0xA6881D7D21774BFD, 0x00003FEF //A13 = 1.9852125640303530752913966680e-05 +data8 0x875E983AA042E605, 0x0000BFF0 //A12 = -3.2274606306629334402383651599e-05 +data8 0xCB19E01E94FC133C, 0x00003FF0 //A11 = 4.8423069963831314927026982707e-05 +data8 0x8BA5E8D9E72D56B2, 0x0000BFF1 //A10 = -6.6589395655200734237190902534e-05 +data8 0xAE91F647ED4E46B2, 0x00003FF1 //A9 = 8.3241541003842930001632190258e-05 +data8 0xC465A7E0B22F884E, 0x0000BFF1 //A8 = -9.3649431639051891449916386619e-05 +data8 0xC4666148AA01A4D7, 0x00003FF1 //A7 = 9.3650780646160216748407869111e-05 +data8 0xABD9E63D181B0C6C, 0x0000BFF1 //A6 = -8.1945023256769295802996591839e-05 +data8 0x80E38B18E509387A, 0x00003FF1 //A5 = 6.1458988764532931141264026311e-05 +data8 0xA11C80E20ADA5A64, 0x0000BFF0 //A4 = -3.8411937140983728563216440713e-05 +LOCAL_OBJECT_END(_6p5_to_8_data_tail) + +LOCAL_OBJECT_START(_13_to_16_data_tail) +// Polynomial coefficients for the tanh(x), 13 <= |x| < 16 +data8 0x9D6CCDA4767CA6D9, 0x00003FE5 //A13 = 1.8326683535066775712253572575e-08 +data8 0xFFAF154F334BF403, 0x0000BFE4 //A12 = -1.4882762852665077172347508377e-08 +data8 0xBFC68FA7C61B6C17, 0x00003FE4 //A11 = 1.1162810813806544919835662888e-08 +data8 0x83D8439A6B19A015, 0x0000BFE4 //A10 = -7.6743763372603959795701788561e-09 +data8 0xA4CE5BE9DC6A2962, 0x00003FE3 //A9 = 4.7964885012772346158732715382e-09 +data8 0xB96826C0697253CA, 0x0000BFE2 //A8 = -2.6980246373950994097953903952e-09 +data8 0xB96826CADDC00E35, 0x00003FE1 //A7 = 1.3490123232313844006540534789e-09 +data8 0xA23B21F1155DF322, 0x0000BFE0 //A6 = -5.9019289132168830718664922372e-10 +data8 0xF358B2E9A50C349C, 0x00003FDE //A5 = 2.2132233424669131155945897524e-10 +data8 0x98176FD2074C1D77, 0x0000BFDD //A4 = -6.9163229452106125388824134881e-11 +LOCAL_OBJECT_END(_13_to_16_data_tail) + +LOCAL_OBJECT_START(_0_to_1o8_data) +// Polynomial coefficients for the tanh(x), 0.0 <= |x| < 0.125 +data8 0xBA0EC1879495150B, 0x0000BFF5 // A15 = -1.4195071451378679802688367813e-03 +data8 0xEB5A82898D1BCBA4, 0x00003FF6 // A13 = 3.5912102408030526706365632879e-03 +data8 0x91370DAFE0B64438, 0x0000BFF8 // A11 = -8.8632234251336964576640807982e-03 +data8 0xB327A435358F1200, 0x00003FF9 // A9 = 2.1869488447622383899199238857e-02 +data8 0xDD0DD0DD07A0775F, 0x0000BFFA // A7 = -5.3968253967902161405327069187e-02 +data8 0x888888888887C299, 0x00003FFC // A5 = 1.3333333333333264660338062012e-01 +data8 0xAAAAAAAAAAAAAA98, 0x0000BFFD // A3 = -3.3333333333333333282255458755e-01 +LOCAL_OBJECT_END(_0_to_1o8_data) + + +.section .text +GLOBAL_LIBM_ENTRY(tanhl) + +{ .mfi + alloc r32 = ar.pfs, 0, 21, 0, 0 + fmerge.se fArgAbsNorm = f1, f8 // normalized x (1.0 <= x < 2.0) + addl rSignBit = 0x20000, r0 // Set sign bit for exponent +} +{ .mlx + addl rDataPtr = @ltoff(tanhl_data), gp // Get common data ptr + movl r1p5 = 0x3FF8000000000000 // 1.5 in dbl repres. +};; + +{ .mfi + getf.exp rArgExp = f8 // Get arg exponent + fclass.m p6,p0 = f8, 0xEF // Filter 0, denormals and specials + // 0xEF = @qnan|@snan|@pos|@neg|@zero|@unorm|@inf + addl rBias = 0xfffc, r0 // Value to subtract from exp + // to get actual interval number +} +{ .mfi + ld8 rDataPtr = [rDataPtr] // Get real common data pointer + fma.s1 fArgSqr = f8, f8, f0 // x^2 (for [0;1/8] path) + addl r2to4 = 0x10000, r0 // unbiased exponent + // for [2;4] binary interval +};; + +{ .mfi + getf.sig rArgSig = f8 // Get arg significand + fcmp.lt.s1 p15, p14 = f8, f0 // Is arg negative/positive? + addl rSaturation = 0xb70, r0 // First 12 bits of + // saturation value signif. +} +{ .mfi + setf.d f1p5 = r1p5 // 1.5 construction + fma.s1 f2p0 = f1,f1,f1 // 2.0 construction + addl r1625Sign = 0xd01, r0 // First 12 bits of + // 1.625 value signif. + // 1.625 significand used to filter values greater than 3.25, 6.5, 13.0 +};; + +{ .mfi + addl rTailDataPtr = 0xB00, rDataPtr // Pointer to "tail" data + fmerge.s fSignumX = f8, f1 // signum(x) + andcm rArgExp = rArgExp, rSignBit // Remove sign of exp +} +{ .mfb + addl rTiny = 0xf000, r0 // Tiny value for saturation path + nop.f 0 +(p6) br.cond.spnt tanhl_spec // Branch to zero, denorm & specs +};; + +{ .mfi + sub rInterval = rArgExp, rBias // Get actual interval number + nop.f 0 + shr.u rArgSig = rArgSig, 52 // Leave only 12 bits of sign. +} +{ .mfi + adds rShiftedDataPtr = 0x10, rDataPtr // Second ptr to data + nop.f 0 + cmp.ge p8, p10 = rArgExp, r2to4 // If exp >= 2to4 interval? +};; + +{ .mfi +(p8) cmp.le p8, p10 = r1625Sign, rArgSig // If signd is greater + // than 1.625? (arg is at one of binary subranges) + nop.f 0 + shl rOffset = rInterval, 8 // Make offset from + // interval number +} +{ .mfi + cmp.gt p9, p0 = 0x0, rInterval // If interval is less than 0 + // (means arg is in [0; 1/8]) + nop.f 0 + cmp.eq p7, p0 = 0x7, rInterval // If arg is in [16;] interv.? +};; + +{ .mfi +(p8) adds rOffset = 0x400, rOffset // Add additional offset + // (arg is at one of binary subranges) + fma.s1 fArgCube = fArgSqr, f8, f0 // x^3 (for [0;1/8] path) + shl rTailOffset = rInterval, 7 // Make offset to "tail" data + // from interval number +} +{ .mib + setf.exp fTiny = rTiny // Construct "tiny" value + // for saturation path + cmp.ltu p11, p0 = 0x7, rInterval // if arg > 32 +(p9) br.cond.spnt _0_to_1o8 +};; + +{ .mfi + add rAddr1 = rDataPtr, rOffset // Get address for + // interval data + nop.f 0 + shl rTailAddOffset = rInterval, 5 // Offset to interval + // "tail" data +} +{ .mib + add rAddr2 = rShiftedDataPtr, rOffset // Get second + // address for interval data +(p7) cmp.leu p11, p0 = rSaturation, rArgSig // if arg is + // in [22.8;32] interval +(p11) br.cond.spnt _saturation // Branch to Saturation path +};; + +{ .mmi + ldfe fA3 = [rAddr1], 0x90 // Load A3 + ldfpd fA2H, fA2L = [rAddr2], 16 // Load A2High, A2Low + add rTailOffset = rTailOffset, rTailAddOffset // "Tail" offset +};; + +{ .mmi + ldfe fA20 = [rAddr1], 16 // Load A20 + ldfpd fA1H, fA1L = [rAddr2], 16 // Load A1High, A1Low +(p8) adds rTailOffset = 0x280, rTailOffset // Additional offset + // (arg is at one of binary subranges) +};; + +{ .mmi + ldfe fA19 = [rAddr1], 16 // Load A19 + ldfpd fA0H, fA0L = [rAddr2], 16 // Load A0High, A0Low + add rTailAddr1 = rTailDataPtr, rTailOffset // First tail + // data address +};; + +.pred.rel "mutex",p8,p10 +{ .mfi + ldfe fA18 = [rAddr1], 16 // Load A18 +(p8) fms.s1 fArgAbsNorm = fArgAbsNorm, f1, f2p0 // Add 2.0 + // (arg is at one of binary subranges) + adds rTailAddr2 = 0x10, rTailAddr1 // First tail + // data address +} +{ .mfi + ldfe fA25 = [rAddr2], 16 // Load A25 +(p10) fms.s1 fArgAbsNorm = fArgAbsNorm, f1, f1p5 // Add 1.5 + // to normalized arg + nop.i 0 +};; + +{ .mmi + ldfe fA17 = [rAddr1], 16 // Load A17 + ldfe fA24 = [rAddr2], 16 // Load A24 + nop.i 0 +};; + +{ .mmi + ldfe fA16 = [rAddr1], 16 // Load A16 + ldfe fA23 = [rAddr2], 16 // Load A23 + nop.i 0 +};; + +{ .mmi + ldfe fA15 = [rAddr1], 16 // Load A15 + ldfe fA22 = [rAddr2], 16 // Load A22 + nop.i 0 +};; + +{ .mmi + ldfe fA14 = [rAddr1], 16 // Load A14 + ldfe fA21 = [rAddr2], 16 // Load A21 + nop.i 0 +};; + +{ .mfi + ldfe fA13 = [rTailAddr1], 32 // Load A13 + fms.s1 fArgAbsNorm2 = fArgAbsNorm, fArgAbsNorm, f0 // x^2 + nop.i 0 +} +{ .mfi + ldfe fA12 = [rTailAddr2], 32 // Load A12 + nop.f 0 + nop.i 0 +};; + +{ .mfi + ldfe fA11 = [rTailAddr1], 32 // Load A11 + fma.s1 fRes3H = fA3, fArgAbsNorm, fA2H // (A3*x+A2)*x^2 + nop.i 0 +} +{ .mfi + ldfe fA10 = [rTailAddr2], 32 // Load A10 + fma.s1 fTH = fA3, fArgAbsNorm, f0 // (A3*x+A2)*x^2 + nop.i 0 +};; + +{ .mfi + ldfe fA9 = [rTailAddr1], 32 // Load A9 + fma.s1 fTT2 = fA1L, fArgAbsNorm, f0 // A1*x+A0 + nop.i 0 +} +{ .mfi + ldfe fA8 = [rTailAddr2], 32 // Load A8 + nop.f 0 + nop.i 0 +};; + +{ .mmi + ldfe fA7 = [rTailAddr1], 32 // Load A7 + ldfe fA6 = [rTailAddr2], 32 // Load A6 + nop.i 0 +};; + +{ .mmi + ldfe fA5 = [rTailAddr1], 32 // Load A5 + ldfe fA4 = [rTailAddr2], 32 // Load A4 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 fArgAbsNorm2L = fArgAbsNorm, fArgAbsNorm, fArgAbsNorm2 + // Low part of x^2 (delta) + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fArgAbsNorm4 = fArgAbsNorm2, fArgAbsNorm2, f0 // x^4 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 fRes3L = fA2H, f1, fRes3H // // (A3*x+A2)*x^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 fArgAbsNorm3 = fArgAbsNorm2, fArgAbsNorm, f0 // x^3 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fTH2 = fA1H, fArgAbsNorm, fTT2 // A1*x+A0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA23 = fA24, fArgAbsNorm, fA23 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA21 = fA22, fArgAbsNorm, fA21 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA12 = fA13, fArgAbsNorm, fA12 // Polynomial tail + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fRes3L = fRes3L, f1, fTH // (A3*x+A2)*x^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA19 = fA20, fArgAbsNorm, fA19 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes1H = fTH2, f1, fA0H // A1*x+A0 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fTL2 = fA1H, fArgAbsNorm, fTH2 // A1*x+A0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA8 = fA9, fArgAbsNorm, fA8 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA10 = fA11, fArgAbsNorm, fA10 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA15 = fA16, fArgAbsNorm, fA15 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA17 = fA18, fArgAbsNorm, fA17 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 fArgAbsNorm11 = fArgAbsNorm4, fArgAbsNorm4, f0 // x^8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA4 = fA5, fArgAbsNorm, fA4 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes3L = fRes3L, f1, fA2L // (A3*x+A2)*x^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA6 = fA7, fArgAbsNorm, fA6 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fTL2 = fTL2, f1, fTT2 // A1*x+A0 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fRes1L = fA0H, f1, fRes1H // A1*x+A0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA23 = fA25, fArgAbsNorm2, fA23 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA12 = fA14, fArgAbsNorm2, fA12 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA19 = fA21, fArgAbsNorm2, fA19 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA8 = fA10, fArgAbsNorm2, fA8 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA15 = fA17, fArgAbsNorm2, fA15 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fArgAbsNorm11 = fArgAbsNorm11, fArgAbsNorm3, f0 // x^11 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fTT = fRes3L, fArgAbsNorm2, f0 // (A3*x+A2)*x^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA4 = fA6, fArgAbsNorm2, fA4 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes1L = fRes1L, f1, fTH2 // A1*x+A0 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fArgAbsNorm4X = fArgAbsNorm4, fSignumX, f0 // x^4 * signum + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA19 = fA23, fArgAbsNorm4, fA19 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA8 = fA12, fArgAbsNorm4, fA8 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fTT = fRes3H, fArgAbsNorm2L, fTT // (A3*x+A2)*x^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes1L = fRes1L, f1, fTL2 // A1*x+A0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA15 = fA19, fArgAbsNorm4, fA15 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA4 = fA8, fArgAbsNorm4, fA4 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes2H = fRes3H, fArgAbsNorm2, fTT // (A3*x+A2)*x^2 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes1L = fRes1L, f1, fA0L // A1*x+A0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes4 = fA15, fArgAbsNorm11, fA4 // Result of + // polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fms.s1 fRes2L = fRes3H, fArgAbsNorm2, fRes2H // (A3*x+A2)*x^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fResH = fRes2H, f1, fRes1H // High result + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p14) fma.s1 fRes1L = fRes4, fArgAbsNorm4X, fRes1L // A1*x+A0 + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fms.s1 fRes1L = fRes4, fArgAbsNorm4X, fRes1L // A1*x+A0 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes2L = fRes2L, f1, fTT // (A3*x+A2)*x^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fResL = fRes1H, f1, fResH // Low result + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s0 fRes1L = fRes2L, fSignumX, fRes1L // Low result + // .s0 - for symmetry issue resolving at +/-inf rounding mode + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fResL = fResL, f1, fRes2H // Low result + nop.i 0 +};; + +{ .mfi + nop.m 0 +(p14) fma.s0 fResL = fRes1L, f1, fResL // Low result + // .s0 - for symmetry issue resolving at +/-inf rounding mode + nop.i 0 +} +{ .mfi + nop.m 0 +(p15) fms.s0 fResL = fRes1L, f1, fResL // Low result + // .s0 - for symmetry issue resolving at +/-inf rounding mode + nop.i 0 +};; + +.pred.rel "mutex",p14,p15 +{ .mfi + nop.m 0 +(p14) fma.s0 f8 = fResL, f1, fResH// Add high and low results + nop.i 0 +} +{ .mfb + nop.m 0 +(p15) fms.s0 f8 = fResL, f1, fResH // Add high and low results + br.ret.sptk b0 // Main path return +};; + +// satiration path //////////////////////////////////////////////////////////// +_saturation: + +.pred.rel "mutex",p14,p15 +{ .mfi + nop.m 0 +(p14) fms.s0 f8 = f1, f1, fTiny // Saturation result r = 1-tiny + nop.i 0 +};; +{ .mfb + nop.m 0 +(p15) fnma.s0 f8 = f1, f1, fTiny // Saturation result r = tiny-1 + br.ret.sptk b0 // Saturation path return +};; + + +// 0, denormals and special IEEE numbers path ///////////////////////////////// +tanhl_spec: + +{ .mfi + nop.m 0 + fclass.m p6,p0 = f8, 0x23 // To filter infinities + // 0x23 = @pos|@neg|@inf + nop.i 0 +};; + +{ .mfi + nop.m 0 + fclass.m p7,p0 = f8, 0xC7 // To filter NaNs & Zeros + // 0xC7 = @pos|@neg|@zero|@qnan|@snan + nop.i 0 +};; + +{ .mfb + nop.m 0 +(p6) fmerge.s f8 = f8, f1 // +/-1 for INF args +(p6) br.ret.spnt b0 // exit for x = INF +};; + +{ .mfb + nop.m 0 +(p7) fma.s0 f8 = f8, f1, f8 // +/-0 for 0 args + // and NaNs for NaNs +(p7) br.ret.spnt b0 // exit for x = NaN or +/-0 +};; + +{ .mfi + nop.m 0 + fnorm.s0 f8 = f8 // Normalize arg + nop.i 0 +};; + +.pred.rel "mutex",p14,p15 +{ .mfi + nop.m 0 +(p14) fnma.s0 f8 = f8, f8, f8 // res = r-r^2 + nop.i 0 +} +{ .mfb + nop.m 0 +(p15) fma.s0 f8 = f8, f8, f8 // res = r+r^2 + br.ret.sptk b0 // 0, denormals, IEEE specials return +};; + + +// 0 < |x| < 1/8 path ///////////////////////////////////////////////////////// +_0_to_1o8: + +{ .mmi + adds rAddr1 = 0x11e0, rDataPtr // Ptr 1 to coeffs + adds rAddr2 = 0x11f0, rDataPtr // Ptr 2 to coeffs + nop.i 0 +};; + +{ .mmi + ldfe fA15 = [rAddr1], 32 // Load A15 + ldfe fA13 = [rAddr2], 32 // Load A13 + nop.i 0 +};; + +{ .mmi + ldfe fA11 = [rAddr1], 32 // Load A11 + ldfe fA9 = [rAddr2], 32 // Load A9 + nop.i 0 +};; + +{ .mmi + ldfe fA7 = [rAddr1], 32 // Load A7 + ldfe fA5 = [rAddr2] // Load A5 + nop.i 0 +};; + +{ .mfi + ldfe fA3 = [rAddr1] // Load A3 + fma.s1 fA11 = fA13, fArgSqr, fA11 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fArgFour = fArgSqr, fArgSqr, f0 // a^4 + nop.i 0 +};; + + +{ .mfi + nop.m 0 + fma.s1 fA3 = fA5, fArgSqr, fA3 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA7 = fA9, fArgSqr, fA7 // Polynomial tail + nop.i 0 +};; + + +{ .mfi + nop.m 0 + fma.s1 fA11 = fA15, fArgFour, fA11 // Polynomial tail + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fA3 = fA7, fArgFour, fA3 // Polynomial tail + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fArgEight = fArgFour, fArgFour, f0 // a^8 + nop.i 0 +};; + +{ .mfi + nop.m 0 + fma.s1 fRes = fA11, fArgEight, fA3 //Polynomial tail result + nop.i 0 +};; + +{ .mfb + nop.m 0 + fma.s0 f8 = fRes, fArgCube, f8 // (Polynomial tail)*x^3 + br.ret.sptk b0 // [0;1/8] interval return +};; + +GLOBAL_LIBM_END(tanhl) + + + + |