| 1 | #include "erfa.h"
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| 2 |
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| 3 | void eraNut00b(double date1, double date2, double *dpsi, double *deps)
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| 4 | /*
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| 5 | ** - - - - - - - - - -
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| 6 | ** e r a N u t 0 0 b
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| 7 | ** - - - - - - - - - -
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| 8 | **
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| 9 | ** Nutation, IAU 2000B model.
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| 10 | **
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| 11 | ** Given:
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| 12 | ** date1,date2 double TT as a 2-part Julian Date (Note 1)
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| 13 | **
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| 14 | ** Returned:
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| 15 | ** dpsi,deps double nutation, luni-solar + planetary (Note 2)
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| 16 | **
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| 17 | ** Notes:
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| 18 | **
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| 19 | ** 1) The TT date date1+date2 is a Julian Date, apportioned in any
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| 20 | ** convenient way between the two arguments. For example,
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| 21 | ** JD(TT)=2450123.7 could be expressed in any of these ways,
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| 22 | ** among others:
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| 23 | **
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| 24 | ** date1 date2
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| 25 | **
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| 26 | ** 2450123.7 0.0 (JD method)
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| 27 | ** 2451545.0 -1421.3 (J2000 method)
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| 28 | ** 2400000.5 50123.2 (MJD method)
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| 29 | ** 2450123.5 0.2 (date & time method)
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| 30 | **
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| 31 | ** The JD method is the most natural and convenient to use in
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| 32 | ** cases where the loss of several decimal digits of resolution
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| 33 | ** is acceptable. The J2000 method is best matched to the way
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| 34 | ** the argument is handled internally and will deliver the
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| 35 | ** optimum resolution. The MJD method and the date & time methods
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| 36 | ** are both good compromises between resolution and convenience.
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| 37 | **
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| 38 | ** 2) The nutation components in longitude and obliquity are in radians
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| 39 | ** and with respect to the equinox and ecliptic of date. The
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| 40 | ** obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
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| 41 | ** value of 84381.448 arcsec. (The errors that result from using
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| 42 | ** this function with the IAU 2006 value of 84381.406 arcsec can be
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| 43 | ** neglected.)
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| 44 | **
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| 45 | ** The nutation model consists only of luni-solar terms, but
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| 46 | ** includes also a fixed offset which compensates for certain long-
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| 47 | ** period planetary terms (Note 7).
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| 48 | **
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| 49 | ** 3) This function is an implementation of the IAU 2000B abridged
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| 50 | ** nutation model formally adopted by the IAU General Assembly in
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| 51 | ** 2000. The function computes the MHB_2000_SHORT luni-solar
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| 52 | ** nutation series (Luzum 2001), but without the associated
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| 53 | ** corrections for the precession rate adjustments and the offset
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| 54 | ** between the GCRS and J2000.0 mean poles.
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| 55 | **
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| 56 | ** 4) The full IAU 2000A (MHB2000) nutation model contains nearly 1400
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| 57 | ** terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only
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| 58 | ** 77 terms, plus additional simplifications, yet still delivers
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| 59 | ** results of 1 mas accuracy at present epochs. This combination of
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| 60 | ** accuracy and size makes the IAU 2000B abridged nutation model
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| 61 | ** suitable for most practical applications.
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| 62 | **
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| 63 | ** The function delivers a pole accurate to 1 mas from 1900 to 2100
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| 64 | ** (usually better than 1 mas, very occasionally just outside
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| 65 | ** 1 mas). The full IAU 2000A model, which is implemented in the
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| 66 | ** function eraNut00a (q.v.), delivers considerably greater accuracy
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| 67 | ** at current dates; however, to realize this improved accuracy,
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| 68 | ** corrections for the essentially unpredictable free-core-nutation
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| 69 | ** (FCN) must also be included.
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| 70 | **
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| 71 | ** 5) The present function provides classical nutation. The
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| 72 | ** MHB_2000_SHORT algorithm, from which it is adapted, deals also
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| 73 | ** with (i) the offsets between the GCRS and mean poles and (ii) the
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| 74 | ** adjustments in longitude and obliquity due to the changed
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| 75 | ** precession rates. These additional functions, namely frame bias
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| 76 | ** and precession adjustments, are supported by the ERFA functions
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| 77 | ** eraBi00 and eraPr00.
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| 78 | **
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| 79 | ** 6) The MHB_2000_SHORT algorithm also provides "total" nutations,
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| 80 | ** comprising the arithmetic sum of the frame bias, precession
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| 81 | ** adjustments, and nutation (luni-solar + planetary). These total
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| 82 | ** nutations can be used in combination with an existing IAU 1976
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| 83 | ** precession implementation, such as eraPmat76, to deliver GCRS-
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| 84 | ** to-true predictions of mas accuracy at current epochs. However,
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| 85 | ** for symmetry with the eraNut00a function (q.v. for the reasons),
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| 86 | ** the ERFA functions do not generate the "total nutations"
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| 87 | ** directly. Should they be required, they could of course easily
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| 88 | ** be generated by calling eraBi00, eraPr00 and the present function
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| 89 | ** and adding the results.
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| 90 | **
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| 91 | ** 7) The IAU 2000B model includes "planetary bias" terms that are
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| 92 | ** fixed in size but compensate for long-period nutations. The
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| 93 | ** amplitudes quoted in McCarthy & Luzum (2003), namely
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| 94 | ** Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
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| 95 | ** the "total nutations" method described in Note 6. The Luzum
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| 96 | ** (2001) values used in this ERFA implementation, namely -0.135 mas
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| 97 | ** and +0.388 mas, are optimized for the "rigorous" method, where
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| 98 | ** frame bias, precession and nutation are applied separately and in
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| 99 | ** that order. During the interval 1995-2050, the ERFA
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| 100 | ** implementation delivers a maximum error of 1.001 mas (not
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| 101 | ** including FCN).
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| 102 | **
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| 103 | ** References:
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| 104 | **
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| 105 | ** Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
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| 106 | ** for the precession quantities based upon the IAU /1976/ system of
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| 107 | ** astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)
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| 108 | **
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| 109 | ** Luzum, B., private communication, 2001 (Fortran code
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| 110 | ** MHB_2000_SHORT)
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| 111 | **
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| 112 | ** McCarthy, D.D. & Luzum, B.J., "An abridged model of the
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| 113 | ** precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
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| 114 | ** 85, 37-49 (2003)
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| 115 | **
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| 116 | ** Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
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| 117 | ** Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)
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| 118 | **
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| 119 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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| 120 | ** Derived, with permission, from the SOFA library. See notes at end of file.
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| 121 | */
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| 122 | {
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| 123 | double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
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| 124 | dpsils, depsls, dpsipl, depspl;
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| 125 | int i;
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| 126 |
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| 127 | /* Units of 0.1 microarcsecond to radians */
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| 128 | static const double U2R = ERFA_DAS2R / 1e7;
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| 129 |
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| 130 | /* ---------------------------------------- */
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| 131 | /* Fixed offsets in lieu of planetary terms */
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| 132 | /* ---------------------------------------- */
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| 133 |
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| 134 | static const double DPPLAN = -0.135 * ERFA_DMAS2R;
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| 135 | static const double DEPLAN = 0.388 * ERFA_DMAS2R;
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| 136 |
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| 137 | /* --------------------------------------------------- */
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| 138 | /* Luni-solar nutation: argument and term coefficients */
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| 139 | /* --------------------------------------------------- */
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| 140 |
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| 141 | /* The units for the sine and cosine coefficients are */
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| 142 | /* 0.1 microarcsec and the same per Julian century */
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| 143 |
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| 144 | static const struct {
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| 145 | int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
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| 146 | double ps,pst,pc; /* longitude sin, t*sin, cos coefficients */
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| 147 | double ec,ect,es; /* obliquity cos, t*cos, sin coefficients */
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| 148 |
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| 149 | } x[] = {
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| 150 |
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| 151 | /* 1-10 */
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| 152 | { 0, 0, 0, 0,1,
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| 153 | -172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0},
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| 154 | { 0, 0, 2,-2,2,
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| 155 | -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0},
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| 156 | { 0, 0, 2, 0,2,-2276413.0,-234.0, 2796.0, 978459.0,-485.0,1374.0},
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| 157 | { 0, 0, 0, 0,2,2074554.0, 207.0, -698.0,-897492.0, 470.0,-291.0},
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| 158 | { 0, 1, 0, 0,0,1475877.0,-3633.0,11817.0, 73871.0,-184.0,-1924.0},
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| 159 | { 0, 1, 2,-2,2,-516821.0, 1226.0, -524.0, 224386.0,-677.0,-174.0},
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| 160 | { 1, 0, 0, 0,0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0},
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| 161 | { 0, 0, 2, 0,1,-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0},
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| 162 | { 1, 0, 2, 0,2,-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0},
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| 163 | { 0,-1, 2,-2,2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0},
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| 164 |
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| 165 | /* 11-20 */
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| 166 | { 0, 0, 2,-2,1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0},
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| 167 | {-1, 0, 2, 0,2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0},
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| 168 | {-1, 0, 0, 2,0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0},
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| 169 | { 1, 0, 0, 0,1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0},
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| 170 | {-1, 0, 0, 0,1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0},
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| 171 | {-1, 0, 2, 2,2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0},
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| 172 | { 1, 0, 2, 0,1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0},
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| 173 | {-2, 0, 2, 0,1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0},
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| 174 | { 0, 0, 0, 2,0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0},
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| 175 | { 0, 0, 2, 2,2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0},
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| 176 |
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| 177 | /* 21-30 */
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| 178 | { 0,-2, 2,-2,2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0},
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| 179 | {-2, 0, 0, 2,0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0},
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| 180 | { 2, 0, 2, 0,2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0},
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| 181 | { 1, 0, 2,-2,2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0},
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| 182 | {-1, 0, 2, 0,1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0},
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| 183 | { 2, 0, 0, 0,0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0},
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| 184 | { 0, 0, 2, 0,0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0},
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| 185 | { 0, 1, 0, 0,1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0},
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| 186 | {-1, 0, 0, 2,1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0},
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| 187 | { 0, 2, 2,-2,2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0},
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| 188 |
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| 189 | /* 31-40 */
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| 190 | { 0, 0,-2, 2,0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0},
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| 191 | { 1, 0, 0,-2,1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0},
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| 192 | { 0,-1, 0, 0,1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0},
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| 193 | {-1, 0, 2, 2,1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0},
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| 194 | { 0, 2, 0, 0,0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0},
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| 195 | { 1, 0, 2, 2,2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0},
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| 196 | {-2, 0, 2, 0,0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0},
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| 197 | { 0, 1, 2, 0,2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0},
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| 198 | { 0, 0, 2, 2,1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0},
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| 199 | { 0,-1, 2, 0,2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0},
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| 200 |
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| 201 | /* 41-50 */
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| 202 | { 0, 0, 0, 2,1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0},
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| 203 | { 1, 0, 2,-2,1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0},
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| 204 | { 2, 0, 2,-2,2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0},
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| 205 | {-2, 0, 0, 2,1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0},
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| 206 | { 2, 0, 2, 0,1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0},
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| 207 | { 0,-1, 2,-2,1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0},
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| 208 | { 0, 0, 0,-2,1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0},
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| 209 | {-1,-1, 0, 2,0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0},
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| 210 | { 2, 0, 0,-2,1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0},
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| 211 | { 1, 0, 0, 2,0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0},
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| 212 |
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| 213 | /* 51-60 */
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| 214 | { 0, 1, 2,-2,1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0},
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| 215 | { 1,-1, 0, 0,0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0},
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| 216 | {-2, 0, 2, 0,2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0},
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| 217 | { 3, 0, 2, 0,2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0},
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| 218 | { 0,-1, 0, 2,0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0},
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| 219 | { 1,-1, 2, 0,2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0},
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| 220 | { 0, 0, 0, 1,0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0},
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| 221 | {-1,-1, 2, 2,2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0},
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| 222 | {-1, 0, 2, 0,0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0},
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| 223 | { 0,-1, 2, 2,2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0},
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| 224 |
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| 225 | /* 61-70 */
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| 226 | {-2, 0, 0, 0,1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0},
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| 227 | { 1, 1, 2, 0,2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0},
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| 228 | { 2, 0, 0, 0,1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0},
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| 229 | {-1, 1, 0, 1,0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0},
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| 230 | { 1, 1, 0, 0,0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0},
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| 231 | { 1, 0, 2, 0,0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0},
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| 232 | {-1, 0, 2,-2,1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0},
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| 233 | { 1, 0, 0, 0,2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0},
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| 234 | {-1, 0, 0, 1,0, 4026.0, 0.0, -353.0, -553.0, 0.0,-139.0},
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| 235 | { 0, 0, 2, 1,2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0},
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| 236 |
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| 237 | /* 71-77 */
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| 238 | {-1, 0, 2, 4,2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0},
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| 239 | {-1, 1, 0, 1,1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0},
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| 240 | { 0,-2, 2,-2,1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0},
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| 241 | { 1, 0, 2, 2,1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0},
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| 242 | {-2, 0, 2, 2,2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0},
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| 243 | {-1, 0, 0, 0,2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0},
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| 244 | { 1, 1, 2,-2,2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0}
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| 245 | };
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| 246 |
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| 247 | /* Number of terms in the series */
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| 248 | const int NLS = (int) (sizeof x / sizeof x[0]);
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| 249 |
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| 250 | /*--------------------------------------------------------------------*/
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| 251 |
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| 252 | /* Interval between fundamental epoch J2000.0 and given date (JC). */
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| 253 | t = ((date1 - ERFA_DJ00) + date2) / ERFA_DJC;
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| 254 |
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| 255 | /* --------------------*/
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| 256 | /* LUNI-SOLAR NUTATION */
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| 257 | /* --------------------*/
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| 258 |
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| 259 | /* Fundamental (Delaunay) arguments from Simon et al. (1994) */
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| 260 |
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| 261 | /* Mean anomaly of the Moon. */
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| 262 | el = fmod(485868.249036 + (1717915923.2178) * t, ERFA_TURNAS) * ERFA_DAS2R;
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| 263 |
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| 264 | /* Mean anomaly of the Sun. */
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| 265 | elp = fmod(1287104.79305 + (129596581.0481) * t, ERFA_TURNAS) * ERFA_DAS2R;
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| 266 |
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| 267 | /* Mean argument of the latitude of the Moon. */
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| 268 | f = fmod(335779.526232 + (1739527262.8478) * t, ERFA_TURNAS) * ERFA_DAS2R;
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| 269 |
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| 270 | /* Mean elongation of the Moon from the Sun. */
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| 271 | d = fmod(1072260.70369 + (1602961601.2090) * t, ERFA_TURNAS) * ERFA_DAS2R;
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| 272 |
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| 273 | /* Mean longitude of the ascending node of the Moon. */
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| 274 | om = fmod(450160.398036 + (-6962890.5431) * t, ERFA_TURNAS) * ERFA_DAS2R;
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| 275 |
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| 276 | /* Initialize the nutation values. */
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| 277 | dp = 0.0;
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| 278 | de = 0.0;
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| 279 |
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| 280 | /* Summation of luni-solar nutation series (smallest terms first). */
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| 281 | for (i = NLS-1; i >= 0; i--) {
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| 282 |
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| 283 | /* Argument and functions. */
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| 284 | arg = fmod( (double)x[i].nl * el +
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| 285 | (double)x[i].nlp * elp +
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| 286 | (double)x[i].nf * f +
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| 287 | (double)x[i].nd * d +
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| 288 | (double)x[i].nom * om, ERFA_D2PI );
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| 289 | sarg = sin(arg);
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| 290 | carg = cos(arg);
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| 291 |
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| 292 | /* Term. */
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| 293 | dp += (x[i].ps + x[i].pst * t) * sarg + x[i].pc * carg;
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| 294 | de += (x[i].ec + x[i].ect * t) * carg + x[i].es * sarg;
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| 295 | }
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| 296 |
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| 297 | /* Convert from 0.1 microarcsec units to radians. */
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| 298 | dpsils = dp * U2R;
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| 299 | depsls = de * U2R;
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| 300 |
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| 301 | /* ------------------------------*/
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| 302 | /* IN LIEU OF PLANETARY NUTATION */
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| 303 | /* ------------------------------*/
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| 304 |
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| 305 | /* Fixed offset to correct for missing terms in truncated series. */
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| 306 | dpsipl = DPPLAN;
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| 307 | depspl = DEPLAN;
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| 308 |
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| 309 | /* --------*/
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| 310 | /* RESULTS */
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| 311 | /* --------*/
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| 312 |
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| 313 | /* Add luni-solar and planetary components. */
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| 314 | *dpsi = dpsils + dpsipl;
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| 315 | *deps = depsls + depspl;
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| 316 |
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| 317 | return;
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| 318 |
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| 319 | }
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| 320 | /*----------------------------------------------------------------------
|
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| 321 | **
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| 322 | **
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| 323 | ** Copyright (C) 2013-2017, NumFOCUS Foundation.
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| 324 | ** All rights reserved.
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|---|
| 325 | **
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| 326 | ** This library is derived, with permission, from the International
|
|---|
| 327 | ** Astronomical Union's "Standards of Fundamental Astronomy" library,
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| 328 | ** available from http://www.iausofa.org.
|
|---|
| 329 | **
|
|---|
| 330 | ** The ERFA version is intended to retain identical functionality to
|
|---|
| 331 | ** the SOFA library, but made distinct through different function and
|
|---|
| 332 | ** file names, as set out in the SOFA license conditions. The SOFA
|
|---|
| 333 | ** original has a role as a reference standard for the IAU and IERS,
|
|---|
| 334 | ** and consequently redistribution is permitted only in its unaltered
|
|---|
| 335 | ** state. The ERFA version is not subject to this restriction and
|
|---|
| 336 | ** therefore can be included in distributions which do not support the
|
|---|
| 337 | ** concept of "read only" software.
|
|---|
| 338 | **
|
|---|
| 339 | ** Although the intent is to replicate the SOFA API (other than
|
|---|
| 340 | ** replacement of prefix names) and results (with the exception of
|
|---|
| 341 | ** bugs; any that are discovered will be fixed), SOFA is not
|
|---|
| 342 | ** responsible for any errors found in this version of the library.
|
|---|
| 343 | **
|
|---|
| 344 | ** If you wish to acknowledge the SOFA heritage, please acknowledge
|
|---|
| 345 | ** that you are using a library derived from SOFA, rather than SOFA
|
|---|
| 346 | ** itself.
|
|---|
| 347 | **
|
|---|
| 348 | **
|
|---|
| 349 | ** TERMS AND CONDITIONS
|
|---|
| 350 | **
|
|---|
| 351 | ** Redistribution and use in source and binary forms, with or without
|
|---|
| 352 | ** modification, are permitted provided that the following conditions
|
|---|
| 353 | ** are met:
|
|---|
| 354 | **
|
|---|
| 355 | ** 1 Redistributions of source code must retain the above copyright
|
|---|
| 356 | ** notice, this list of conditions and the following disclaimer.
|
|---|
| 357 | **
|
|---|
| 358 | ** 2 Redistributions in binary form must reproduce the above copyright
|
|---|
| 359 | ** notice, this list of conditions and the following disclaimer in
|
|---|
| 360 | ** the documentation and/or other materials provided with the
|
|---|
| 361 | ** distribution.
|
|---|
| 362 | **
|
|---|
| 363 | ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
|
|---|
| 364 | ** the International Astronomical Union nor the names of its
|
|---|
| 365 | ** contributors may be used to endorse or promote products derived
|
|---|
| 366 | ** from this software without specific prior written permission.
|
|---|
| 367 | **
|
|---|
| 368 | ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|---|
| 369 | ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|---|
| 370 | ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
|---|
| 371 | ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
|---|
| 372 | ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|---|
| 373 | ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
|---|
| 374 | ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|---|
| 375 | ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
|---|
| 376 | ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|---|
| 377 | ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
|---|
| 378 | ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|---|
| 379 | ** POSSIBILITY OF SUCH DAMAGE.
|
|---|
| 380 | **
|
|---|
| 381 | */
|
|---|
