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annotate lib/trigl.c @ 17907:0a1c2535cad9

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euidaccess: Fix Android build * modules/euidaccess (Depends-on): Add fcntl-h to ensure that AT_EACCESS gets declared.
author Kevin Cernekee <cernekee@google.com>
date Wed, 11 Feb 2015 15:22:54 -0800
parents ab58d4870664
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 /* Quad-precision floating point argument reduction.
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2 Copyright (C) 1999, 2007, 2009-2015 Free Software Foundation, Inc.
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3 This file is part of the GNU C Library.
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4 Contributed by Jakub Jelinek <jj@ultra.linux.cz>
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5
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6 This program is free software: you can redistribute it and/or modify
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7 it under the terms of the GNU General Public License as published by
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8 the Free Software Foundation; either version 3 of the License, or
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9 (at your option) any later version.
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10
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11 This program is distributed in the hope that it will be useful,
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12 but WITHOUT ANY WARRANTY; without even the implied warranty of
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13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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14 GNU General Public License for more details.
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15
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16 You should have received a copy of the GNU General Public License
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17 along with this program. If not, see <http://www.gnu.org/licenses/>. */
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18
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c115624bf99a New module 'math'. <math.h> replaces mathl.h.
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19 #include <config.h>
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20
c115624bf99a New module 'math'. <math.h> replaces mathl.h.
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21 /* Specification. */
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22 #include "trigl.h"
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23
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24 #include <float.h>
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25 #include <math.h>
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26
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27 /* Code based on glibc/sysdeps/ieee754/ldbl-128/e_rem_pio2l.c
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28 and glibc/sysdeps/ieee754/dbl-64/k_rem_pio2.c. */
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29
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30 /* Table of constants for 2/pi, 5628 hexadecimal digits of 2/pi */
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31 static const int two_over_pi[] = {
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32 0xa2f983, 0x6e4e44, 0x1529fc, 0x2757d1, 0xf534dd, 0xc0db62,
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33 0x95993c, 0x439041, 0xfe5163, 0xabdebb, 0xc561b7, 0x246e3a,
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34 0x424dd2, 0xe00649, 0x2eea09, 0xd1921c, 0xfe1deb, 0x1cb129,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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35 0xa73ee8, 0x8235f5, 0x2ebb44, 0x84e99c, 0x7026b4, 0x5f7e41,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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36 0x3991d6, 0x398353, 0x39f49c, 0x845f8b, 0xbdf928, 0x3b1ff8,
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37 0x97ffde, 0x05980f, 0xef2f11, 0x8b5a0a, 0x6d1f6d, 0x367ecf,
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38 0x27cb09, 0xb74f46, 0x3f669e, 0x5fea2d, 0x7527ba, 0xc7ebe5,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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39 0xf17b3d, 0x0739f7, 0x8a5292, 0xea6bfb, 0x5fb11f, 0x8d5d08,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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40 0x560330, 0x46fc7b, 0x6babf0, 0xcfbc20, 0x9af436, 0x1da9e3,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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41 0x91615e, 0xe61b08, 0x659985, 0x5f14a0, 0x68408d, 0xffd880,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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42 0x4d7327, 0x310606, 0x1556ca, 0x73a8c9, 0x60e27b, 0xc08c6b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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43 0x47c419, 0xc367cd, 0xdce809, 0x2a8359, 0xc4768b, 0x961ca6,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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44 0xddaf44, 0xd15719, 0x053ea5, 0xff0705, 0x3f7e33, 0xe832c2,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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45 0xde4f98, 0x327dbb, 0xc33d26, 0xef6b1e, 0x5ef89f, 0x3a1f35,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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46 0xcaf27f, 0x1d87f1, 0x21907c, 0x7c246a, 0xfa6ed5, 0x772d30,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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47 0x433b15, 0xc614b5, 0x9d19c3, 0xc2c4ad, 0x414d2c, 0x5d000c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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48 0x467d86, 0x2d71e3, 0x9ac69b, 0x006233, 0x7cd2b4, 0x97a7b4,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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49 0xd55537, 0xf63ed7, 0x1810a3, 0xfc764d, 0x2a9d64, 0xabd770,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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50 0xf87c63, 0x57b07a, 0xe71517, 0x5649c0, 0xd9d63b, 0x3884a7,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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51 0xcb2324, 0x778ad6, 0x23545a, 0xb91f00, 0x1b0af1, 0xdfce19,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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52 0xff319f, 0x6a1e66, 0x615799, 0x47fbac, 0xd87f7e, 0xb76522,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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53 0x89e832, 0x60bfe6, 0xcdc4ef, 0x09366c, 0xd43f5d, 0xd7de16,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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54 0xde3b58, 0x929bde, 0x2822d2, 0xe88628, 0x4d58e2, 0x32cac6,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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55 0x16e308, 0xcb7de0, 0x50c017, 0xa71df3, 0x5be018, 0x34132e,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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56 0x621283, 0x014883, 0x5b8ef5, 0x7fb0ad, 0xf2e91e, 0x434a48,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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57 0xd36710, 0xd8ddaa, 0x425fae, 0xce616a, 0xa4280a, 0xb499d3,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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58 0xf2a606, 0x7f775c, 0x83c2a3, 0x883c61, 0x78738a, 0x5a8caf,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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59 0xbdd76f, 0x63a62d, 0xcbbff4, 0xef818d, 0x67c126, 0x45ca55,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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60 0x36d9ca, 0xd2a828, 0x8d61c2, 0x77c912, 0x142604, 0x9b4612,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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61 0xc459c4, 0x44c5c8, 0x91b24d, 0xf31700, 0xad43d4, 0xe54929,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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62 0x10d5fd, 0xfcbe00, 0xcc941e, 0xeece70, 0xf53e13, 0x80f1ec,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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63 0xc3e7b3, 0x28f8c7, 0x940593, 0x3e71c1, 0xb3092e, 0xf3450b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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64 0x9c1288, 0x7b20ab, 0x9fb52e, 0xc29247, 0x2f327b, 0x6d550c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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65 0x90a772, 0x1fe76b, 0x96cb31, 0x4a1679, 0xe27941, 0x89dff4,
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66 0x9794e8, 0x84e6e2, 0x973199, 0x6bed88, 0x365f5f, 0x0efdbb,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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67 0xb49a48, 0x6ca467, 0x427271, 0x325d8d, 0xb8159f, 0x09e5bc,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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68 0x25318d, 0x3974f7, 0x1c0530, 0x010c0d, 0x68084b, 0x58ee2c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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69 0x90aa47, 0x02e774, 0x24d6bd, 0xa67df7, 0x72486e, 0xef169f,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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70 0xa6948e, 0xf691b4, 0x5153d1, 0xf20acf, 0x339820, 0x7e4bf5,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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71 0x6863b2, 0x5f3edd, 0x035d40, 0x7f8985, 0x295255, 0xc06437,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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72 0x10d86d, 0x324832, 0x754c5b, 0xd4714e, 0x6e5445, 0xc1090b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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73 0x69f52a, 0xd56614, 0x9d0727, 0x50045d, 0xdb3bb4, 0xc576ea,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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74 0x17f987, 0x7d6b49, 0xba271d, 0x296996, 0xacccc6, 0x5414ad,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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75 0x6ae290, 0x89d988, 0x50722c, 0xbea404, 0x940777, 0x7030f3,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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76 0x27fc00, 0xa871ea, 0x49c266, 0x3de064, 0x83dd97, 0x973fa3,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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77 0xfd9443, 0x8c860d, 0xde4131, 0x9d3992, 0x8c70dd, 0xe7b717,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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78 0x3bdf08, 0x2b3715, 0xa0805c, 0x93805a, 0x921110, 0xd8e80f,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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79 0xaf806c, 0x4bffdb, 0x0f9038, 0x761859, 0x15a562, 0xbbcb61,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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80 0xb989c7, 0xbd4010, 0x04f2d2, 0x277549, 0xf6b6eb, 0xbb22db,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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81 0xaa140a, 0x2f2689, 0x768364, 0x333b09, 0x1a940e, 0xaa3a51,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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82 0xc2a31d, 0xaeedaf, 0x12265c, 0x4dc26d, 0x9c7a2d, 0x9756c0,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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83 0x833f03, 0xf6f009, 0x8c402b, 0x99316d, 0x07b439, 0x15200c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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84 0x5bc3d8, 0xc492f5, 0x4badc6, 0xa5ca4e, 0xcd37a7, 0x36a9e6,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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85 0x9492ab, 0x6842dd, 0xde6319, 0xef8c76, 0x528b68, 0x37dbfc,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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86 0xaba1ae, 0x3115df, 0xa1ae00, 0xdafb0c, 0x664d64, 0xb705ed,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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87 0x306529, 0xbf5657, 0x3aff47, 0xb9f96a, 0xf3be75, 0xdf9328,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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88 0x3080ab, 0xf68c66, 0x15cb04, 0x0622fa, 0x1de4d9, 0xa4b33d,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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89 0x8f1b57, 0x09cd36, 0xe9424e, 0xa4be13, 0xb52333, 0x1aaaf0,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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90 0xa8654f, 0xa5c1d2, 0x0f3f0b, 0xcd785b, 0x76f923, 0x048b7b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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91 0x721789, 0x53a6c6, 0xe26e6f, 0x00ebef, 0x584a9b, 0xb7dac4,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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92 0xba66aa, 0xcfcf76, 0x1d02d1, 0x2df1b1, 0xc1998c, 0x77adc3,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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93 0xda4886, 0xa05df7, 0xf480c6, 0x2ff0ac, 0x9aecdd, 0xbc5c3f,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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94 0x6dded0, 0x1fc790, 0xb6db2a, 0x3a25a3, 0x9aaf00, 0x9353ad,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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95 0x0457b6, 0xb42d29, 0x7e804b, 0xa707da, 0x0eaa76, 0xa1597b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
96 0x2a1216, 0x2db7dc, 0xfde5fa, 0xfedb89, 0xfdbe89, 0x6c76e4,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
97 0xfca906, 0x70803e, 0x156e85, 0xff87fd, 0x073e28, 0x336761,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
98 0x86182a, 0xeabd4d, 0xafe7b3, 0x6e6d8f, 0x396795, 0x5bbf31,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
99 0x48d784, 0x16df30, 0x432dc7, 0x356125, 0xce70c9, 0xb8cb30,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
100 0xfd6cbf, 0xa200a4, 0xe46c05, 0xa0dd5a, 0x476f21, 0xd21262,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
101 0x845cb9, 0x496170, 0xe0566b, 0x015299, 0x375550, 0xb7d51e,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
102 0xc4f133, 0x5f6e13, 0xe4305d, 0xa92e85, 0xc3b21d, 0x3632a1,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
103 0xa4b708, 0xd4b1ea, 0x21f716, 0xe4698f, 0x77ff27, 0x80030c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
104 0x2d408d, 0xa0cd4f, 0x99a520, 0xd3a2b3, 0x0a5d2f, 0x42f9b4,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
105 0xcbda11, 0xd0be7d, 0xc1db9b, 0xbd17ab, 0x81a2ca, 0x5c6a08,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
106 0x17552e, 0x550027, 0xf0147f, 0x8607e1, 0x640b14, 0x8d4196,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
107 0xdebe87, 0x2afdda, 0xb6256b, 0x34897b, 0xfef305, 0x9ebfb9,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
108 0x4f6a68, 0xa82a4a, 0x5ac44f, 0xbcf82d, 0x985ad7, 0x95c7f4,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
109 0x8d4d0d, 0xa63a20, 0x5f57a4, 0xb13f14, 0x953880, 0x0120cc,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
110 0x86dd71, 0xb6dec9, 0xf560bf, 0x11654d, 0x6b0701, 0xacb08c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
111 0xd0c0b2, 0x485551, 0x0efb1e, 0xc37295, 0x3b06a3, 0x3540c0,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
112 0x7bdc06, 0xcc45e0, 0xfa294e, 0xc8cad6, 0x41f3e8, 0xde647c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
113 0xd8649b, 0x31bed9, 0xc397a4, 0xd45877, 0xc5e369, 0x13daf0,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
114 0x3c3aba, 0x461846, 0x5f7555, 0xf5bdd2, 0xc6926e, 0x5d2eac,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
115 0xed440e, 0x423e1c, 0x87c461, 0xe9fd29, 0xf3d6e7, 0xca7c22,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
116 0x35916f, 0xc5e008, 0x8dd7ff, 0xe26a6e, 0xc6fdb0, 0xc10893,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
117 0x745d7c, 0xb2ad6b, 0x9d6ecd, 0x7b723e, 0x6a11c6, 0xa9cff7,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
118 0xdf7329, 0xbac9b5, 0x5100b7, 0x0db2e2, 0x24ba74, 0x607de5,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
119 0x8ad874, 0x2c150d, 0x0c1881, 0x94667e, 0x162901, 0x767a9f,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
120 0xbefdfd, 0xef4556, 0x367ed9, 0x13d9ec, 0xb9ba8b, 0xfc97c4,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
121 0x27a831, 0xc36ef1, 0x36c594, 0x56a8d8, 0xb5a8b4, 0x0ecccf,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
122 0x2d8912, 0x34576f, 0x89562c, 0xe3ce99, 0xb920d6, 0xaa5e6b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
123 0x9c2a3e, 0xcc5f11, 0x4a0bfd, 0xfbf4e1, 0x6d3b8e, 0x2c86e2,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
124 0x84d4e9, 0xa9b4fc, 0xd1eeef, 0xc9352e, 0x61392f, 0x442138,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
125 0xc8d91b, 0x0afc81, 0x6a4afb, 0xd81c2f, 0x84b453, 0x8c994e,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
126 0xcc2254, 0xdc552a, 0xd6c6c0, 0x96190b, 0xb8701a, 0x649569,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
127 0x605a26, 0xee523f, 0x0f117f, 0x11b5f4, 0xf5cbfc, 0x2dbc34,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
128 0xeebc34, 0xcc5de8, 0x605edd, 0x9b8e67, 0xef3392, 0xb817c9,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
129 0x9b5861, 0xbc57e1, 0xc68351, 0x103ed8, 0x4871dd, 0xdd1c2d,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
130 0xa118af, 0x462c21, 0xd7f359, 0x987ad9, 0xc0549e, 0xfa864f,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
131 0xfc0656, 0xae79e5, 0x362289, 0x22ad38, 0xdc9367, 0xaae855,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
132 0x382682, 0x9be7ca, 0xa40d51, 0xb13399, 0x0ed7a9, 0x480569,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
133 0xf0b265, 0xa7887f, 0x974c88, 0x36d1f9, 0xb39221, 0x4a827b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
134 0x21cf98, 0xdc9f40, 0x5547dc, 0x3a74e1, 0x42eb67, 0xdf9dfe,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
135 0x5fd45e, 0xa4677b, 0x7aacba, 0xa2f655, 0x23882b, 0x55ba41,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
136 0x086e59, 0x862a21, 0x834739, 0xe6e389, 0xd49ee5, 0x40fb49,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
137 0xe956ff, 0xca0f1c, 0x8a59c5, 0x2bfa94, 0xc5c1d3, 0xcfc50f,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
138 0xae5adb, 0x86c547, 0x624385, 0x3b8621, 0x94792c, 0x876110,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
139 0x7b4c2a, 0x1a2c80, 0x12bf43, 0x902688, 0x893c78, 0xe4c4a8,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
140 0x7bdbe5, 0xc23ac4, 0xeaf426, 0x8a67f7, 0xbf920d, 0x2ba365,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
141 0xb1933d, 0x0b7cbd, 0xdc51a4, 0x63dd27, 0xdde169, 0x19949a,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
142 0x9529a8, 0x28ce68, 0xb4ed09, 0x209f44, 0xca984e, 0x638270,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
143 0x237c7e, 0x32b90f, 0x8ef5a7, 0xe75614, 0x08f121, 0x2a9db5,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
144 0x4d7e6f, 0x5119a5, 0xabf9b5, 0xd6df82, 0x61dd96, 0x023616,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
145 0x9f3ac4, 0xa1a283, 0x6ded72, 0x7a8d39, 0xa9b882, 0x5c326b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
146 0x5b2746, 0xed3400, 0x7700d2, 0x55f4fc, 0x4d5901, 0x8071e0,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
147 0xe13f89, 0xb295f3, 0x64a8f1, 0xaea74b, 0x38fc4c, 0xeab2bb,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
148 0x47270b, 0xabc3a7, 0x34ba60, 0x52dd34, 0xf8563a, 0xeb7e8a,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
149 0x31bb36, 0x5895b7, 0x47f7a9, 0x94c3aa, 0xd39225, 0x1e7f3e,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
150 0xd8974e, 0xbba94f, 0xd8ae01, 0xe661b4, 0x393d8e, 0xa523aa,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
151 0x33068e, 0x1633b5, 0x3bb188, 0x1d3a9d, 0x4013d0, 0xcc1be5,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
152 0xf862e7, 0x3bf28f, 0x39b5bf, 0x0bc235, 0x22747e, 0xa247c0,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
153 0xd52d1f, 0x19add3, 0x9094df, 0x9311d0, 0xb42b25, 0x496db2,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
154 0xe264b2, 0x5ef135, 0x3bc6a4, 0x1a4ad0, 0xaac92e, 0x64e886,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
155 0x573091, 0x982cfb, 0x311b1a, 0x08728b, 0xbdcee1, 0x60e142,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
156 0xeb641d, 0xd0bba3, 0xe559d4, 0x597b8c, 0x2a4483, 0xf332ba,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
157 0xf84867, 0x2c8d1b, 0x2fa9b0, 0x50f3dd, 0xf9f573, 0xdb61b4,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
158 0xfe233e, 0x6c41a6, 0xeea318, 0x775a26, 0xbc5e5c, 0xcea708,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
159 0x94dc57, 0xe20196, 0xf1e839, 0xbe4851, 0x5d2d2f, 0x4e9555,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
160 0xd96ec2, 0xe7d755, 0x6304e0, 0xc02e0e, 0xfc40a0, 0xbbf9b3,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
161 0x7125a7, 0x222dfb, 0xf619d8, 0x838c1c, 0x6619e6, 0xb20d55,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
162 0xbb5137, 0x79e809, 0xaf9149, 0x0d73de, 0x0b0da5, 0xce7f58,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
163 0xac1934, 0x724667, 0x7a1a13, 0x9e26bc, 0x4555e7, 0x585cb5,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
164 0x711d14, 0x486991, 0x480d60, 0x56adab, 0xd62f64, 0x96ee0c,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
165 0x212ff3, 0x5d6d88, 0xa67684, 0x95651e, 0xab9e0a, 0x4ddefe,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
166 0x571010, 0x836a39, 0xf8ea31, 0x9e381d, 0xeac8b1, 0xcac96b,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
167 0x37f21e, 0xd505e9, 0x984743, 0x9fc56c, 0x0331b7, 0x3b8bf8,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
168 0x86e56a, 0x8dc343, 0x6230e7, 0x93cfd5, 0x6a8f2d, 0x733005,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
169 0x1af021, 0xa09fcb, 0x7415a1, 0xd56b23, 0x6ff725, 0x2f4bc7,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
170 0xb8a591, 0x7fac59, 0x5c55de, 0x212c38, 0xb13296, 0x5cff50,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
171 0x366262, 0xfa7b16, 0xf4d9a6, 0x2acfe7, 0xf07403, 0xd4d604,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
172 0x6fd916, 0x31b1bf, 0xcbb450, 0x5bd7c8, 0x0ce194, 0x6bd643,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
173 0x4fd91c, 0xdf4543, 0x5f3453, 0xe2b5aa, 0xc9aec8, 0x131485,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
174 0xf9d2bf, 0xbadb9e, 0x76f5b9, 0xaf15cf, 0xca3182, 0x14b56d,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
175 0xe9fe4d, 0x50fc35, 0xf5aed5, 0xa2d0c1, 0xc96057, 0x192eb6,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
176 0xe91d92, 0x07d144, 0xaea3c6, 0x343566, 0x26d5b4, 0x3161e2,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
177 0x37f1a2, 0x209eff, 0x958e23, 0x493798, 0x35f4a6, 0x4bdc02,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
178 0xc2be13, 0xbe80a0, 0x0b72a3, 0x115c5f, 0x1e1bd1, 0x0db4d3,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
179 0x869e85, 0x96976b, 0x2ac91f, 0x8a26c2, 0x3070f0, 0x041412,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
180 0xfc9fa5, 0xf72a38, 0x9c6878, 0xe2aa76, 0x50cfe1, 0x559274,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
181 0x934e38, 0x0a92f7, 0x5533f0, 0xa63db4, 0x399971, 0xe2b755,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
182 0xa98a7c, 0x008f19, 0xac54d2, 0x2ea0b4, 0xf5f3e0, 0x60c849,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
183 0xffd269, 0xae52ce, 0x7a5fdd, 0xe9ce06, 0xfb0ae8, 0xa50cce,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
184 0xea9d3e, 0x3766dd, 0xb834f5, 0x0da090, 0x846f88, 0x4ae3d5,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
185 0x099a03, 0x2eae2d, 0xfcb40a, 0xfb9b33, 0xe281dd, 0x1b16ba,
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
186 0xd8c0af, 0xd96b97, 0xb52dc9, 0x9c277f, 0x5951d5, 0x21ccd6,
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parents:
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187 0xb6496b, 0x584562, 0xb3baf2, 0xa1a5c4, 0x7ca2cf, 0xa9b93d,
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parents:
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188 0x7b7b89, 0x483d38,
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parents:
diff changeset
189 };
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diff changeset
190
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Bruno Haible <bruno@clisp.org>
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191 static const long double c[] = {
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parents:
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192 /* 93 bits of pi/2 */
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193 #define PI_2_1 c[0]
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194 1.57079632679489661923132169155131424e+00L, /* 3fff921fb54442d18469898cc5100000 */
4239
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195
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196 /* pi/2 - PI_2_1 */
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197 #define PI_2_1t c[1]
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198 8.84372056613570112025531863263659260e-29L, /* 3fa1c06e0e68948127044533e63a0106 */
4239
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199 };
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200
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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201 static int kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec,
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202 const int *ipio2);
4239
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203
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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204 int
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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205 ieee754_rem_pio2l (long double x, long double *y)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
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206 {
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207 long double z, w, t;
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208 double tx[8];
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Bruno Haible <bruno@clisp.org>
parents:
diff changeset
209 int exp, n;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
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210
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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211 if (x >= -0.78539816339744830961566084581987572104929234984377
9923
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212 && x <= 0.78539816339744830961566084581987572104929234984377)
4239
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213 /* x in <-pi/4, pi/4> */
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214 {
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215 y[0] = x;
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216 y[1] = 0;
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217 return 0;
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218 }
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219
9923
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220 if (x > 0 && x < 2.35619449019234492884698253745962716314787704953131)
4239
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diff changeset
221 {
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222 /* 113 + 93 bit PI is ok */
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223 z = x - PI_2_1;
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224 y[0] = z - PI_2_1t;
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225 y[1] = (z - y[0]) - PI_2_1t;
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226 return 1;
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227 }
9923
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Paolo Bonzini <bonzini@gnu.org>
parents: 9309
diff changeset
228
810b08d769f8 fix typos in mathl
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diff changeset
229 if (x < 0 && x > -2.35619449019234492884698253745962716314787704953131)
4239
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230 {
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231 /* 113 + 93 bit PI is ok */
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232 z = x + PI_2_1;
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233 y[0] = z + PI_2_1t;
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234 y[1] = (z - y[0]) + PI_2_1t;
e8d2c6fc33ad Use spaces for indentation, not tabs.
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235 return -1;
4239
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236 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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237
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238 if (x + x == x) /* x is ±oo */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
239 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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240 y[0] = x - x;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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241 y[1] = y[0];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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242 return 0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
243 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
244
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
245 /* Handle large arguments.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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246 We split the 113 bits of the mantissa into 5 24bit integers
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
247 stored in a double array. */
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Bruno Haible <bruno@clisp.org>
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diff changeset
248 z = frexp (x, &exp);
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diff changeset
249 tx[0] = floorl (z *= 16777216.0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
250 z -= tx[0];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
251 tx[1] = floorl (z *= 16777216.0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
252 z -= tx[1];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
253 tx[2] = floorl (z *= 16777216.0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
254 z -= tx[2];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
255 tx[3] = floorl (z *= 16777216.0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
256 z -= tx[3];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
257 tx[4] = floorl (z *= 16777216.0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
258
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
259 n = kernel_rem_pio2 (tx, tx + 5, exp - 24, tx[4] ? 5 : 4, 3, two_over_pi);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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260
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
261 /* The result is now stored in 3 double values, we need to convert it into
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
262 two long double values. */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
263 t = (long double) tx[6] + (long double) tx[7];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
264 w = (long double) tx[5];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
265
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
266 if (x > 0)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
267 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
268 y[0] = w + t;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
269 y[1] = t - (y[0] - w);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
270 return n;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
271 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
272 else
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
273 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
274 y[0] = -(w + t);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
275 y[1] = -t - (y[0] + w);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
276 return -n;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
277 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
278 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
279
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
280 /* @(#)k_rem_pio2.c 5.1 93/09/24 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
281 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
282 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
283 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
284 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
285 * Developed at SunPro, a Sun Microsystems, Inc. business.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
286 * Permission to use, copy, modify, and distribute this
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
287 * software is freely granted, provided that this notice
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
288 * is preserved.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
289 * ====================================================
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
290 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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diff changeset
291
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
292 #if defined(LIBM_SCCS) && !defined(lint)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
293 static char rcsid[] =
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Bruno Haible <bruno@clisp.org>
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diff changeset
294 "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $";
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
295 #endif
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
296
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
297 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
298 * kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
299 * double x[],y[]; int e0,nx,prec; int ipio2[];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
300 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
301 * kernel_rem_pio2 return the last three digits of N with
12421
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diff changeset
302 * y = x - N*pi/2
4239
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Bruno Haible <bruno@clisp.org>
parents:
diff changeset
303 * so that |y| < pi/2.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
304 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
305 * The method is to compute the integer (mod 8) and fraction parts of
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
306 * (2/pi)*x without doing the full multiplication. In general we
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
307 * skip the part of the product that are known to be a huge integer (
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
308 * more accurately, = 0 mod 8 ). Thus the number of operations are
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
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parents:
diff changeset
309 * independent of the exponent of the input.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
310 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
311 * (2/pi) is represented by an array of 24-bit integers in ipio2[].
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
312 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
313 * Input parameters:
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diff changeset
314 * x[] The input value (must be positive) is broken into nx
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parents: 9923
diff changeset
315 * pieces of 24-bit integers in double precision format.
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parents: 9923
diff changeset
316 * x[i] will be the i-th 24 bit of x. The scaled exponent
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parents: 9923
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317 * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0
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parents: 9923
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318 * match x's up to 24 bits.
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parents:
diff changeset
319 *
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320 * Example of breaking a double positive z into x[0]+x[1]+x[2]:
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parents: 9923
diff changeset
321 * e0 = ilogb(z)-23
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Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
322 * z = scalbn(z,-e0)
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parents: 9923
diff changeset
323 * for i = 0,1,2
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parents: 9923
diff changeset
324 * x[i] = floor(z)
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parents: 9923
diff changeset
325 * z = (z-x[i])*2**24
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Bruno Haible <bruno@clisp.org>
parents:
diff changeset
326 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
327 *
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328 * y[] ouput result in an array of double precision numbers.
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diff changeset
329 * The dimension of y[] is:
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parents: 9923
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330 * 24-bit precision 1
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parents: 9923
diff changeset
331 * 53-bit precision 2
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parents: 9923
diff changeset
332 * 64-bit precision 2
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Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
333 * 113-bit precision 3
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parents: 9923
diff changeset
334 * The actual value is the sum of them. Thus for 113-bit
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Bruno Haible <bruno@clisp.org>
parents: 9923
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335 * precision, one may have to do something like:
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
336 *
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337 * long double t,w,r_head, r_tail;
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parents: 9923
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338 * t = (long double)y[2] + (long double)y[1];
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339 * w = (long double)y[0];
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parents: 9923
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340 * r_head = t+w;
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341 * r_tail = w - (r_head - t);
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parents:
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342 *
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parents: 9923
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343 * e0 The exponent of x[0]
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Bruno Haible <bruno@clisp.org>
parents:
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344 *
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345 * nx dimension of x[]
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Bruno Haible <bruno@clisp.org>
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346 *
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347 * prec an integer indicating the precision:
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348 * 0 24 bits (single)
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349 * 1 53 bits (double)
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350 * 2 64 bits (extended)
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351 * 3 113 bits (quad)
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352 *
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353 * ipio2[]
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parents: 9923
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354 * integer array, contains the (24*i)-th to (24*i+23)-th
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parents: 9923
diff changeset
355 * bit of 2/pi after binary point. The corresponding
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parents: 9923
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356 * floating value is
4239
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parents:
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357 *
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358 * ipio2[i] * 2^(-24(i+1)).
4239
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Bruno Haible <bruno@clisp.org>
parents:
diff changeset
359 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
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360 * External function:
12421
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361 * double scalbn(), floor();
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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362 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
363 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
364 * Here is the description of some local variables:
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
365 *
12421
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366 * jk jk+1 is the initial number of terms of ipio2[] needed
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parents: 9923
diff changeset
367 * in the computation. The recommended value is 2,3,4,
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parents: 9923
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368 * 6 for single, double, extended,and quad.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
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diff changeset
369 *
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370 * jz local integer variable indicating the number of
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parents: 9923
diff changeset
371 * terms of ipio2[] used.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
372 *
12421
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373 * jx nx - 1
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
374 *
12421
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375 * jv index for pointing to the suitable ipio2[] for the
e8d2c6fc33ad Use spaces for indentation, not tabs.
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parents: 9923
diff changeset
376 * computation. In general, we want
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Bruno Haible <bruno@clisp.org>
parents: 9923
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377 * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8
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Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
378 * is an integer. Thus
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parents: 9923
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379 * e0-3-24*jv >= 0 or (e0-3)/24 >= jv
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parents: 9923
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380 * Hence jv = max(0,(e0-3)/24).
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
381 *
12421
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382 * jp jp+1 is the number of terms in PIo2[] needed, jp = jk.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
383 *
12421
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Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
384 * q[] double array with integral value, representing the
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
385 * 24-bits chunk of the product of x and 2/pi.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
386 *
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
387 * q0 the corresponding exponent of q[0]. Note that the
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
388 * exponent for q[i] would be q0-24*i.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
389 *
12421
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parents: 9923
diff changeset
390 * PIo2[] double precision array, obtained by cutting pi/2
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
391 * into 24 bits chunks.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
392 *
12421
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parents: 9923
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393 * f[] ipio2[] in floating point
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
394 *
12421
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parents: 9923
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395 * iq[] integer array by breaking up q[] in 24-bits chunk.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
396 *
12421
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Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
397 * fq[] final product of x*(2/pi) in fq[0],..,fq[jk]
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
398 *
12421
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parents: 9923
diff changeset
399 * ih integer. If >0 it indicates q[] is >= 0.5, hence
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
400 * it also indicates the *sign* of the result.
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
401 *
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
402 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
403
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
404
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
405 /*
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
406 * Constants:
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
407 * The hexadecimal values are the intended ones for the following
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
408 * constants. The decimal values may be used, provided that the
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
409 * compiler will convert from decimal to binary accurately enough
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
410 * to produce the hexadecimal values shown.
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
411 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
412
12421
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Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
413 static const int init_jk[] = { 2, 3, 4, 6 }; /* initial value for jk */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
414 static const double PIo2[] = {
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
415 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
416 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
417 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
418 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
419 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
420 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
421 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
422 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
423 };
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
424
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
425 static const double zero = 0.0, one = 1.0, two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
426 twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
427
8539
51b7bf6751cf Avoid HP-UX cc compiler warning.
Bruno Haible <bruno@clisp.org>
parents: 8186
diff changeset
428 static int
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
429 kernel_rem_pio2 (double *x, double *y, int e0, int nx, int prec,
12421
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Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
430 const int *ipio2)
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
431 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
432 int jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
433 double z, fw, f[20], fq[20], q[20];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
434
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
435 /* initialize jk */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
436 jk = init_jk[prec];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
437 jp = jk;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
438
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
439 /* determine jx,jv,q0, note that 3>q0 */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
440 jx = nx - 1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
441 jv = (e0 - 3) / 24;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
442 if (jv < 0)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
443 jv = 0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
444 q0 = e0 - 24 * (jv + 1);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
445
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
446 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
447 j = jv - jx;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
448 m = jx + jk;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
449 for (i = 0; i <= m; i++, j++)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
450 f[i] = (j < 0) ? zero : (double) ipio2[j];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
451
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
452 /* compute q[0],q[1],...q[jk] */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
453 for (i = 0; i <= jk; i++)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
454 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
455 for (j = 0, fw = 0.0; j <= jx; j++)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
456 fw += x[j] * f[jx + i - j];
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
457 q[i] = fw;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
458 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
459
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
460 jz = jk;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
461 recompute:
16358
a712776b11ce maint: spelling fixes
Paul Eggert <eggert@cs.ucla.edu>
parents: 16201
diff changeset
462 /* distill q[] into iq[] in reverse order */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
463 for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
464 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
465 fw = (double) ((int) (twon24 * z));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
466 iq[i] = (int) (z - two24 * fw);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
467 z = q[j - 1] + fw;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
468 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
469
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
470 /* compute n */
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
471 z = ldexp (z, q0); /* actual value of z */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
472 z -= 8.0 * floor (z * 0.125); /* trim off integer >= 8 */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
473 n = (int) z;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
474 z -= (double) n;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
475 ih = 0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
476 if (q0 > 0)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
477 { /* need iq[jz-1] to determine n */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
478 i = (iq[jz - 1] >> (24 - q0));
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
479 n += i;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
480 iq[jz - 1] -= i << (24 - q0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
481 ih = iq[jz - 1] >> (23 - q0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
482 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
483 else if (q0 == 0)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
484 ih = iq[jz - 1] >> 23;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
485 else if (z >= 0.5)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
486 ih = 2;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
487
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
488 if (ih > 0)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
489 { /* q > 0.5 */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
490 n += 1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
491 carry = 0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
492 for (i = 0; i < jz; i++)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
493 { /* compute 1-q */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
494 j = iq[i];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
495 if (carry == 0)
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
496 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
497 if (j != 0)
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
498 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
499 carry = 1;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
500 iq[i] = 0x1000000 - j;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
501 }
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
502 }
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
503 else
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
504 iq[i] = 0xffffff - j;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
505 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
506 if (q0 > 0)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
507 { /* rare case: chance is 1 in 12 */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
508 switch (q0)
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
509 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
510 case 1:
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
511 iq[jz - 1] &= 0x7fffff;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
512 break;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
513 case 2:
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
514 iq[jz - 1] &= 0x3fffff;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
515 break;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
516 }
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
517 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
518 if (ih == 2)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
519 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
520 z = one - z;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
521 if (carry != 0)
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
522 z -= ldexp (one, q0);
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
523 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
524 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
525
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
526 /* check if recomputation is needed */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
527 if (z == zero)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
528 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
529 j = 0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
530 for (i = jz - 1; i >= jk; i--)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
531 j |= iq[i];
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
532 if (j == 0)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
533 { /* need recomputation */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
534 for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
535
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
536 for (i = jz + 1; i <= jz + k; i++)
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
537 { /* add q[jz+1] to q[jz+k] */
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
538 f[jx + i] = (double) ipio2[jv + i];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
539 for (j = 0, fw = 0.0; j <= jx; j++)
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
540 fw += x[j] * f[jx + i - j];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
541 q[i] = fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
542 }
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
543 jz += k;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
544 goto recompute;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
545 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
546 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
547
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
548 /* chop off zero terms */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
549 if (z == 0.0)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
550 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
551 jz -= 1;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
552 q0 -= 24;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
553 while (iq[jz] == 0)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
554 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
555 jz--;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
556 q0 -= 24;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
557 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
558 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
559 else
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
560 { /* break z into 24-bit if necessary */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
561 z = ldexp (z, -q0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
562 if (z >= two24)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
563 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
564 fw = (double) ((int) (twon24 * z));
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
565 iq[jz] = (int) (z - two24 * fw);
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
566 jz += 1;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
567 q0 += 24;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
568 iq[jz] = (int) fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
569 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
570 else
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
571 iq[jz] = (int) z;
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
572 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
573
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
574 /* convert integer "bit" chunk to floating-point value */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
575 fw = ldexp (one, q0);
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
576 for (i = jz; i >= 0; i--)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
577 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
578 q[i] = fw * (double) iq[i];
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
579 fw *= twon24;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
580 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
581
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
582 /* compute PIo2[0,...,jp]*q[jz,...,0] */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
583 for (i = jz; i >= 0; i--)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
584 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
585 for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
586 fw += PIo2[k] * q[i + k];
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
587 fq[jz - i] = fw;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
588 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
589
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
590 /* compress fq[] into y[] */
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
591 switch (prec)
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
592 {
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
593 case 0:
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
594 fw = 0.0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
595 for (i = jz; i >= 0; i--)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
596 fw += fq[i];
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
597 y[0] = (ih == 0) ? fw : -fw;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
598 break;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
599 case 1:
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
600 case 2:
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
601 fw = 0.0;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
602 for (i = jz; i >= 0; i--)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
603 fw += fq[i];
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
604 y[0] = (ih == 0) ? fw : -fw;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
605 fw = fq[0] - fw;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
606 for (i = 1; i <= jz; i++)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
607 fw += fq[i];
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
608 y[1] = (ih == 0) ? fw : -fw;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
609 break;
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
610 case 3: /* painful */
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
611 for (i = jz; i > 0; i--)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
612 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
613 fw = fq[i - 1] + fq[i];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
614 fq[i] += fq[i - 1] - fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
615 fq[i - 1] = fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
616 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
617 for (i = jz; i > 1; i--)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
618 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
619 fw = fq[i - 1] + fq[i];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
620 fq[i] += fq[i - 1] - fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
621 fq[i - 1] = fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
622 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
623 for (fw = 0.0, i = jz; i >= 2; i--)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
624 fw += fq[i];
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
625 if (ih == 0)
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
626 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
627 y[0] = fq[0];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
628 y[1] = fq[1];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
629 y[2] = fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
630 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
631 else
12421
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
632 {
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
633 y[0] = -fq[0];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
634 y[1] = -fq[1];
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
635 y[2] = -fw;
e8d2c6fc33ad Use spaces for indentation, not tabs.
Bruno Haible <bruno@clisp.org>
parents: 9923
diff changeset
636 }
4239
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
637 }
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
638 return n & 7;
b33b8603715c Transcendental functions for 'long double', from Paolo Bonzini.
Bruno Haible <bruno@clisp.org>
parents:
diff changeset
639 }