/* EXP function tables - for use in computing double precision exponential
   Copyright (C) 2017 Free Software Foundation, Inc.
   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <http://www.gnu.org/licenses/>.  */


/*
   TBL[2*j] is 2**(j/64), rounded to nearest.
   TBL[2*j+1] is 2**(j/64) - TBL[2*j], rounded to nearest.
   These values are used to approximate exp(x) using the formula
   given in the comments for e_exp.c.  */

static const double TBL[128] = {
    0x1.0000000000000p+0,  0x0.0000000000000p+0,
    0x1.02c9a3e778061p+0, -0x1.19083535b085dp-56,
    0x1.059b0d3158574p+0,  0x1.d73e2a475b465p-55,
    0x1.0874518759bc8p+0,  0x1.186be4bb284ffp-57,
    0x1.0b5586cf9890fp+0,  0x1.8a62e4adc610bp-54,
    0x1.0e3ec32d3d1a2p+0,  0x1.03a1727c57b52p-59,
    0x1.11301d0125b51p+0, -0x1.6c51039449b3ap-54,
    0x1.1429aaea92de0p+0, -0x1.32fbf9af1369ep-54,
    0x1.172b83c7d517bp+0, -0x1.19041b9d78a76p-55,
    0x1.1a35beb6fcb75p+0,  0x1.e5b4c7b4968e4p-55,
    0x1.1d4873168b9aap+0,  0x1.e016e00a2643cp-54,
    0x1.2063b88628cd6p+0,  0x1.dc775814a8495p-55,
    0x1.2387a6e756238p+0,  0x1.9b07eb6c70573p-54,
    0x1.26b4565e27cddp+0,  0x1.2bd339940e9d9p-55,
    0x1.29e9df51fdee1p+0,  0x1.612e8afad1255p-55,
    0x1.2d285a6e4030bp+0,  0x1.0024754db41d5p-54,
    0x1.306fe0a31b715p+0,  0x1.6f46ad23182e4p-55,
    0x1.33c08b26416ffp+0,  0x1.32721843659a6p-54,
    0x1.371a7373aa9cbp+0, -0x1.63aeabf42eae2p-54,
    0x1.3a7db34e59ff7p+0, -0x1.5e436d661f5e3p-56,
    0x1.3dea64c123422p+0,  0x1.ada0911f09ebcp-55,
    0x1.4160a21f72e2ap+0, -0x1.ef3691c309278p-58,
    0x1.44e086061892dp+0,  0x1.89b7a04ef80d0p-59,
    0x1.486a2b5c13cd0p+0,  0x1.3c1a3b69062f0p-56,
    0x1.4bfdad5362a27p+0,  0x1.d4397afec42e2p-56,
    0x1.4f9b2769d2ca7p+0, -0x1.4b309d25957e3p-54,
    0x1.5342b569d4f82p+0, -0x1.07abe1db13cadp-55,
    0x1.56f4736b527dap+0,  0x1.9bb2c011d93adp-54,
    0x1.5ab07dd485429p+0,  0x1.6324c054647adp-54,
    0x1.5e76f15ad2148p+0,  0x1.ba6f93080e65ep-54,
    0x1.6247eb03a5585p+0, -0x1.383c17e40b497p-54,
    0x1.6623882552225p+0, -0x1.bb60987591c34p-54,
    0x1.6a09e667f3bcdp+0, -0x1.bdd3413b26456p-54,
    0x1.6dfb23c651a2fp+0, -0x1.bbe3a683c88abp-57,
    0x1.71f75e8ec5f74p+0, -0x1.16e4786887a99p-55,
    0x1.75feb564267c9p+0, -0x1.0245957316dd3p-54,
    0x1.7a11473eb0187p+0, -0x1.41577ee04992fp-55,
    0x1.7e2f336cf4e62p+0,  0x1.05d02ba15797ep-56,
    0x1.82589994cce13p+0, -0x1.d4c1dd41532d8p-54,
    0x1.868d99b4492edp+0, -0x1.fc6f89bd4f6bap-54,
    0x1.8ace5422aa0dbp+0,  0x1.6e9f156864b27p-54,
    0x1.8f1ae99157736p+0,  0x1.5cc13a2e3976cp-55,
    0x1.93737b0cdc5e5p+0, -0x1.75fc781b57ebcp-57,
    0x1.97d829fde4e50p+0, -0x1.d185b7c1b85d1p-54,
    0x1.9c49182a3f090p+0,  0x1.c7c46b071f2bep-56,
    0x1.a0c667b5de565p+0, -0x1.359495d1cd533p-54,
    0x1.a5503b23e255dp+0, -0x1.d2f6edb8d41e1p-54,
    0x1.a9e6b5579fdbfp+0,  0x1.0fac90ef7fd31p-54,
    0x1.ae89f995ad3adp+0,  0x1.7a1cd345dcc81p-54,
    0x1.b33a2b84f15fbp+0, -0x1.2805e3084d708p-57,
    0x1.b7f76f2fb5e47p+0, -0x1.5584f7e54ac3bp-56,
    0x1.bcc1e904bc1d2p+0,  0x1.23dd07a2d9e84p-55,
    0x1.c199bdd85529cp+0,  0x1.11065895048ddp-55,
    0x1.c67f12e57d14bp+0,  0x1.2884dff483cadp-54,
    0x1.cb720dcef9069p+0,  0x1.503cbd1e949dbp-56,
    0x1.d072d4a07897cp+0, -0x1.cbc3743797a9cp-54,
    0x1.d5818dcfba487p+0,  0x1.2ed02d75b3707p-55,
    0x1.da9e603db3285p+0,  0x1.c2300696db532p-54,
    0x1.dfc97337b9b5fp+0, -0x1.1a5cd4f184b5cp-54,
    0x1.e502ee78b3ff6p+0,  0x1.39e8980a9cc8fp-55,
    0x1.ea4afa2a490dap+0, -0x1.e9c23179c2893p-54,
    0x1.efa1bee615a27p+0,  0x1.dc7f486a4b6b0p-54,
    0x1.f50765b6e4540p+0,  0x1.9d3e12dd8a18bp-54,
    0x1.fa7c1819e90d8p+0,  0x1.74853f3a5931ep-55};

/* For i = 0, ..., 66,
     TBL2[2*i] is a double precision number near (i+1)*2^-6, and
     TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
     than 2^-60.

   For i = 67, ..., 133,
     TBL2[2*i] is a double precision number near -(i+1)*2^-6, and
     TBL2[2*i+1] = exp(TBL2[2*i]) to within a relative error less
     than 2^-60.  */

static const double TBL2[268] = {
    0x1.ffffffffffc82p-7,   0x1.04080ab55de32p+0,
    0x1.fffffffffffdbp-6,   0x1.08205601127ecp+0,
    0x1.80000000000a0p-5,   0x1.0c49236829e91p+0,
    0x1.fffffffffff79p-5,   0x1.1082b577d34e9p+0,
    0x1.3fffffffffffcp-4,   0x1.14cd4fc989cd6p+0,
    0x1.8000000000060p-4,   0x1.192937074e0d4p+0,
    0x1.c000000000061p-4,   0x1.1d96b0eff0e80p+0,
    0x1.fffffffffffd6p-4,   0x1.2216045b6f5cap+0,
    0x1.1ffffffffff58p-3,   0x1.26a7793f6014cp+0,
    0x1.3ffffffffff75p-3,   0x1.2b4b58b372c65p+0,
    0x1.5ffffffffff00p-3,   0x1.3001ecf601ad1p+0,
    0x1.8000000000020p-3,   0x1.34cb8170b583ap+0,
    0x1.9ffffffffa629p-3,   0x1.39a862bd3b344p+0,
    0x1.c00000000000fp-3,   0x1.3e98deaa11dcep+0,
    0x1.e00000000007fp-3,   0x1.439d443f5f16dp+0,
    0x1.0000000000072p-2,   0x1.48b5e3c3e81abp+0,
    0x1.0fffffffffecap-2,   0x1.4de30ec211dfbp+0,
    0x1.1ffffffffff8fp-2,   0x1.5325180cfacd2p+0,
    0x1.300000000003bp-2,   0x1.587c53c5a7b04p+0,
    0x1.4000000000034p-2,   0x1.5de9176046007p+0,
    0x1.4ffffffffff89p-2,   0x1.636bb9a98322fp+0,
    0x1.5ffffffffffe7p-2,   0x1.690492cbf942ap+0,
    0x1.6ffffffffff78p-2,   0x1.6eb3fc55b1e45p+0,
    0x1.7ffffffffff65p-2,   0x1.747a513dbef32p+0,
    0x1.8ffffffffffd5p-2,   0x1.7a57ede9ea22ep+0,
    0x1.9ffffffffff6ep-2,   0x1.804d30347b50fp+0,
    0x1.affffffffffc3p-2,   0x1.865a7772164aep+0,
    0x1.c000000000053p-2,   0x1.8c802477b0030p+0,
    0x1.d00000000004dp-2,   0x1.92be99a09bf1ep+0,
    0x1.e000000000096p-2,   0x1.99163ad4b1e08p+0,
    0x1.efffffffffefap-2,   0x1.9f876d8e8c4fcp+0,
    0x1.fffffffffffd0p-2,   0x1.a61298e1e0688p+0,
    0x1.0800000000002p-1,   0x1.acb82581eee56p+0,
    0x1.100000000001fp-1,   0x1.b3787dc80f979p+0,
    0x1.17ffffffffff8p-1,   0x1.ba540dba56e4fp+0,
    0x1.1fffffffffffap-1,   0x1.c14b431256441p+0,
    0x1.27fffffffffc4p-1,   0x1.c85e8d43f7c9bp+0,
    0x1.2fffffffffffdp-1,   0x1.cf8e5d84758a6p+0,
    0x1.380000000001fp-1,   0x1.d6db26d16cd84p+0,
    0x1.3ffffffffffd8p-1,   0x1.de455df80e39bp+0,
    0x1.4800000000052p-1,   0x1.e5cd799c6a59cp+0,
    0x1.4ffffffffffc8p-1,   0x1.ed73f240dc10cp+0,
    0x1.5800000000013p-1,   0x1.f539424d90f71p+0,
    0x1.5ffffffffffbcp-1,   0x1.fd1de6182f885p+0,
    0x1.680000000002dp-1,   0x1.02912df5ce741p+1,
    0x1.7000000000040p-1,   0x1.06a39207f0a2ap+1,
    0x1.780000000004fp-1,   0x1.0ac660691652ap+1,
    0x1.7ffffffffff6fp-1,   0x1.0ef9db467dcabp+1,
    0x1.87fffffffffe5p-1,   0x1.133e45d82e943p+1,
    0x1.9000000000035p-1,   0x1.1793e4652cc6dp+1,
    0x1.97fffffffffb3p-1,   0x1.1bfafc47bda48p+1,
    0x1.a000000000000p-1,   0x1.2073d3f1bd518p+1,
    0x1.a80000000004ap-1,   0x1.24feb2f105ce2p+1,
    0x1.affffffffffedp-1,   0x1.299be1f3e7f11p+1,
    0x1.b7ffffffffffbp-1,   0x1.2e4baacdb6611p+1,
    0x1.c00000000001dp-1,   0x1.330e587b62b39p+1,
    0x1.c800000000079p-1,   0x1.37e437282d538p+1,
    0x1.cffffffffff51p-1,   0x1.3ccd943268248p+1,
    0x1.d7fffffffff74p-1,   0x1.41cabe304cadcp+1,
    0x1.e000000000011p-1,   0x1.46dc04f4e5343p+1,
    0x1.e80000000001ep-1,   0x1.4c01b9950a124p+1,
    0x1.effffffffff9ep-1,   0x1.513c2e6c73196p+1,
    0x1.f7fffffffffedp-1,   0x1.568bb722dd586p+1,
    0x1.0000000000034p+0,   0x1.5bf0a8b1457b0p+1,
    0x1.03fffffffffe2p+0,   0x1.616b5967376dfp+1,
    0x1.07fffffffff4bp+0,   0x1.66fc20f0337a9p+1,
    0x1.0bffffffffffdp+0,   0x1.6ca35859290f5p+1,
   -0x1.fffffffffffe4p-7,   0x1.f80feabfeefa5p-1,
   -0x1.ffffffffffb0bp-6,   0x1.f03f56a88b5fep-1,
   -0x1.7ffffffffffa7p-5,   0x1.e88dc6afecfc5p-1,
   -0x1.ffffffffffea8p-5,   0x1.e0fabfbc702b8p-1,
   -0x1.3ffffffffffb3p-4,   0x1.d985c89d041acp-1,
   -0x1.7ffffffffffe3p-4,   0x1.d22e6a0197c06p-1,
   -0x1.bffffffffff9ap-4,   0x1.caf42e73a4c89p-1,
   -0x1.fffffffffff98p-4,   0x1.c3d6a24ed822dp-1,
   -0x1.1ffffffffffe9p-3,   0x1.bcd553b9d7b67p-1,
   -0x1.3ffffffffffe0p-3,   0x1.b5efd29f24c2dp-1,
   -0x1.5fffffffff553p-3,   0x1.af25b0a61a9f4p-1,
   -0x1.7ffffffffff8bp-3,   0x1.a876812c08794p-1,
   -0x1.9fffffffffe51p-3,   0x1.a1e1d93d68828p-1,
   -0x1.bffffffffff6ep-3,   0x1.9b674f8f2f3f5p-1,
   -0x1.dffffffffff7fp-3,   0x1.95067c7837a0cp-1,
   -0x1.fffffffffff7ap-3,   0x1.8ebef9eac8225p-1,
   -0x1.0fffffffffffep-2,   0x1.8890636e31f55p-1,
   -0x1.1ffffffffff41p-2,   0x1.827a56188975ep-1,
   -0x1.2ffffffffffbap-2,   0x1.7c7c708877656p-1,
   -0x1.3fffffffffff8p-2,   0x1.769652df22f81p-1,
   -0x1.4ffffffffff90p-2,   0x1.70c79eba33c2fp-1,
   -0x1.5ffffffffffdbp-2,   0x1.6b0ff72deb8aap-1,
   -0x1.6ffffffffff9ap-2,   0x1.656f00bf5798ep-1,
   -0x1.7ffffffffff9fp-2,   0x1.5fe4615e98eb0p-1,
   -0x1.8ffffffffffeep-2,   0x1.5a6fc061433cep-1,
   -0x1.9fffffffffc4ap-2,   0x1.5510c67cd26cdp-1,
   -0x1.affffffffff30p-2,   0x1.4fc71dc13566bp-1,
   -0x1.bfffffffffff0p-2,   0x1.4a9271936fd0ep-1,
   -0x1.cfffffffffff3p-2,   0x1.45726ea84fb8cp-1,
   -0x1.dfffffffffff3p-2,   0x1.4066c2ff3912bp-1,
   -0x1.effffffffff80p-2,   0x1.3b6f1ddd05ab9p-1,
   -0x1.fffffffffffdfp-2,   0x1.368b2fc6f9614p-1,
   -0x1.0800000000000p-1,   0x1.31baaa7dca843p-1,
   -0x1.0ffffffffffa4p-1,   0x1.2cfd40f8bdce4p-1,
   -0x1.17fffffffff0ap-1,   0x1.2852a760d5ce7p-1,
   -0x1.2000000000000p-1,   0x1.23ba930c1568bp-1,
   -0x1.27fffffffffbbp-1,   0x1.1f34ba78d568dp-1,
   -0x1.2fffffffffe32p-1,   0x1.1ac0d5492c1dbp-1,
   -0x1.37ffffffff042p-1,   0x1.165e9c3e67ef2p-1,
   -0x1.3ffffffffff77p-1,   0x1.120dc93499431p-1,
   -0x1.47fffffffff6bp-1,   0x1.0dce171e34ecep-1,
   -0x1.4fffffffffff1p-1,   0x1.099f41ffbe588p-1,
   -0x1.57ffffffffe02p-1,   0x1.058106eb8a7aep-1,
   -0x1.5ffffffffffe5p-1,   0x1.017323fd9002ep-1,
   -0x1.67fffffffffb0p-1,   0x1.faeab0ae9386cp-2,
   -0x1.6ffffffffffb2p-1,   0x1.f30ec837503d7p-2,
   -0x1.77fffffffff7fp-1,   0x1.eb5210d627133p-2,
   -0x1.7ffffffffffe8p-1,   0x1.e3b40ebefcd95p-2,
   -0x1.87fffffffffc8p-1,   0x1.dc3448110dae2p-2,
   -0x1.8fffffffffb30p-1,   0x1.d4d244cf4ef06p-2,
   -0x1.97fffffffffefp-1,   0x1.cd8d8ed8ee395p-2,
   -0x1.9ffffffffffa7p-1,   0x1.c665b1e1f1e5cp-2,
   -0x1.a7fffffffffdcp-1,   0x1.bf5a3b6bf18d6p-2,
   -0x1.affffffffff95p-1,   0x1.b86ababeef93bp-2,
   -0x1.b7fffffffffcbp-1,   0x1.b196c0e24d256p-2,
   -0x1.bffffffffff32p-1,   0x1.aadde095dadf7p-2,
   -0x1.c7fffffffff6ap-1,   0x1.a43fae4b047c9p-2,
   -0x1.cffffffffffb6p-1,   0x1.9dbbc01e182a4p-2,
   -0x1.d7fffffffffcap-1,   0x1.9751adcfa81ecp-2,
   -0x1.dffffffffffcdp-1,   0x1.910110be0699ep-2,
   -0x1.e7ffffffffffbp-1,   0x1.8ac983dedbc69p-2,
   -0x1.effffffffff88p-1,   0x1.84aaa3b8d51a9p-2,
   -0x1.f7fffffffffbbp-1,   0x1.7ea40e5d6d92ep-2,
   -0x1.fffffffffffdbp-1,   0x1.78b56362cef53p-2,
   -0x1.03fffffffff00p+0,   0x1.72de43ddcb1f2p-2,
   -0x1.07ffffffffe6fp+0,   0x1.6d1e525bed085p-2,
   -0x1.0bfffffffffd6p+0,   0x1.677532dda1c57p-2};

static const double
/* invln2_64 = 64/ln2 - used to scale x to primary range. */
  invln2_64 = 0x1.71547652b82fep+6,
/* ln2_64hi = high 32 bits of log(2.)/64. */
  ln2_64hi = 0x1.62e42fee00000p-7,
/* ln2_64lo = remainder bits for log(2.)/64 - ln2_64hi. */
  ln2_64lo = 0x1.a39ef35793c76p-39,
/* t2-t5 terms used for polynomial computation.  */
  t2 = 0x1.5555555555555p-3, /* 1.6666666666666665741e-1 */
  t3 = 0x1.5555555555555p-5, /* 4.1666666666666664354e-2 */
  t4 = 0x1.1111111111111p-7, /* 8.3333333333333332177e-3 */
  t5 = 0x1.6c16c16c16c17p-10, /* 1.3888888888888719040e-3 */
/* Maximum value for x to not overflow.  */
  threshold1 = 0x1.62e42fefa39efp+9, /* 7.09782712893383973096e+02 */
/* Maximum value for -x to not underflow to zero in FE_TONEAREST mode.  */
  threshold2 = 0x1.74910d52d3051p+9, /* 7.45133219101941108420e+02 */
/* Scaling factor used when result near zero.  */
  twom54 = 0x1.0000000000000p-54; /* 5.55111512312578270212e-17 */