sysdeps/ieee754/ldbl-96/e_rem_pio2l.c

   1 /* Extended-precision floating point argument reduction.
   2    Copyright (C) 1999-2016 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Based on quad-precision code by Jakub Jelinek <jj@ultra.linux.cz>
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Lesser General Public
   8    License as published by the Free Software Foundation; either
   9    version 2.1 of the License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Lesser General Public License for more details.
  15
  16    You should have received a copy of the GNU Lesser General Public
  17    License along with the GNU C Library; if not, see
  18    <http://www.gnu.org/licenses/>.  */
  19
  20 #include <math.h>
  21 #include <math_private.h>
  22
  23 /*  Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi.  */
  24 static const int32_t two_over_pi[] = {
  25 0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62,
  26 0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a,
  27 0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129,
  28 0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41,
  29 0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8,
  30 0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf,
  31 0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5,
  32 0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08,
  33 0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3,
  34 0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880,
  35 0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b,
  36 0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6,
  37 0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2,
  38 0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35,
  39 0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30,
  40 0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c,
  41 0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4,
  42 0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770,
  43 0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7,
  44 0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19,
  45 0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522,
  46 0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16,
  47 0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6,
  48 0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e,
  49 0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48,
  50 0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3,
  51 0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf,
  52 0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55,
  53 0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612,
  54 0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929,
  55 0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec,
  56 0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b,
  57 0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c,
  58 0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4,
  59 0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb,
  60 0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc,
  61 0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c,
  62 0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f,
  63 0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5,
  64 0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437,
  65 0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b,
  66 0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea,
  67 0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad,
  68 0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3,
  69 0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3,
  70 0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717,
  71 0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f,
  72 0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61,
  73 0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db,
  74 0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51,
  75 0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0,
  76 0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c,
  77 0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6,
  78 0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc,
  79 0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed,
  80 0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328,
  81 0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d,
  82 0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0,
  83 0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b,
  84 0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4,
  85 0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3,
  86 0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f,
  87 0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad,
  88 0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b,
  89 0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4,
  90 0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761,
  91 0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31,
  92 0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30,
  93 0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262,
  94 0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e,
  95 0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1,
  96 0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c,
  97 0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4,
  98 0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08,
  99 0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196,
 100 0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9,
 101 0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4,
 102 0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc,
 103 0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c,
 104 0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0,
 105 0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c,
 106 0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0,
 107 0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac,
 108 0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22,
 109 0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893,
 110 0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7,
 111 0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5,
 112 0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f,
 113 0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4,
 114 0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf,
 115 0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b,
 116 0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2,
 117 0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138,
 118 0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e,
 119 0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569,
 120 0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34,
 121 0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9,
 122 0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d,
 123 0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f,
 124 0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855,
 125 0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569,
 126 0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b,
 127 0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe,
 128 0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41,
 129 0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49,
 130 0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f,
 131 0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110,
 132 0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8,
 133 0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365,
 134 0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a,
 135 0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270,
 136 0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5,
 137 0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616,
 138 0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b,
 139 0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0,
 140 0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb,
 141 0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a,
 142 0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e,
 143 0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa,
 144 0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5,
 145 0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0,
 146 0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2,
 147 0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886,
 148 0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142,
 149 0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba,
 150 0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4,
 151 0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708,
 152 0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555,
 153 0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3,
 154 0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55,
 155 0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58,
 156 0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5,
 157 0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c,
 158 0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe,
 159 0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b,
 160 0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8,
 161 0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005,
 162 0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7,
 163 0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50,
 164 0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604,
 165 0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643,
 166 0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485,
 167 0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d,
 168 0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6,
 169 0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2,
 170 0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02,
 171 0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3,
 172 0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412,
 173 0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274,
 174 0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755,
 175 0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849,
 176 0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce,
 177 0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5,
 178 0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba,
 179 0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6,
 180 0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d,
 181 0x7b7b89, 0x483d38,
 182 };
 183
 184 int32_t
 185 __ieee754_rem_pio2l (long double x, long double *y)
 186 {
 187   double tx[3], ty[3];
 188   int32_t se, j0;
 189   u_int32_t i0, i1;
 190   int sx;
 191   int n, exp;
 192
 193   GET_LDOUBLE_WORDS (se, i0, i1, x);
 194   sx = (se >> 15) & 1;
 195   j0 = (se & 0x7fff) - 0x3fff;
 196
 197   if (j0 < -1)
 198     {
 199       /* |x| < pi/4.  */
 200       y[0] = x;
 201       y[1] = 0;
 202       return 0;
 203     }
 204
 205   if (j0 >= 0x8000)
 206     {
 207       /* x is infinite or NaN.  */
 208       y[0] = x - x;
 209       y[1] = y[0];
 210       return 0;
 211     }
 212
 213   /* Split the 64 bits of the mantissa into three 24-bit integers
 214      stored in a double array.  */
 215   exp = j0 - 23;
 216   tx[0] = (double) (i0 >> 8);
 217   tx[1] = (double) (((i0 << 16) | (i1 >> 16)) & 0xffffff);
 218   tx[2] = (double) ((i1 << 8) & 0xffffff);
 219
 220   n = __kernel_rem_pio2 (tx, ty, exp, 3, 2, two_over_pi);
 221
 222   /* The result is now stored in two double values, we need to convert
 223      it into two long double values.  */
 224   if (sx == 0)
 225     {
 226       y[0] = (long double) ty[0] + (long double) ty[1];
 227       y[1] = ty[1] - (y[0] - ty[0]);
 228       return n;
 229     }
 230   else
 231     {
 232       y[0] = -((long double) ty[0] + (long double) ty[1]);
 233       y[1] = -ty[1] - (y[0] + ty[0]);
 234       return -n;
 235     }
 236 }