1 2 /******************************************************************************* 3 MIT License 4 ----------- 5 6 Copyright (c) 2002-2019 Advanced Micro Devices, Inc. 7 8 Permission is hereby granted, free of charge, to any person obtaining a copy 9 of this Software and associated documentaon files (the "Software"), to deal 10 in the Software without restriction, including without limitation the rights 11 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 12 copies of the Software, and to permit persons to whom the Software is 13 furnished to do so, subject to the following conditions: 14 15 The above copyright notice and this permission notice shall be included in 16 all copies or substantial portions of the Software. 17 18 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 19 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 20 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 21 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 22 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 23 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 24 THE SOFTWARE. 25 *******************************************************************************/ 26 27 #include "libm.h" 28 #include "libm_util.h" 29 30 #define USE_VALF_WITH_FLAGS 31 #define USE_NAN_WITH_FLAGS 32 #define USE_SCALEDOUBLE_1 33 #define USE_SCALEDOWNDOUBLE 34 #define USE_HANDLE_ERRORF 35 #include "libm_inlines.h" 36 #undef USE_VALF_WITH_FLAGS 37 #undef USE_NAN_WITH_FLAGS 38 #undef USE_SCALEDOUBLE_1 39 #undef USE_SCALEDOWNDOUBLE 40 #undef USE_HANDLE_ERRORF 41 42 #include "libm_errno.h" 43 44 #ifdef _MSC_VER 45 // Disable "C4163: not available as intrinsic function" warning that older 46 // compilers may issue here. 47 #pragma warning(disable:4163) 48 #pragma function(atan2f) 49 #endif 50 51 float FN_PROTOTYPE(atan2f)(float fy, float fx) 52 { 53 /* Array atan_jby256 contains precomputed values of atan(j/256), 54 for j = 16, 17, ..., 256. */ 55 56 static const double atan_jby256[ 241] = { 57 6.24188099959573430842e-02, /* 0x3faff55bb72cfde9 */ 58 6.63088949198234745008e-02, /* 0x3fb0f99ea71d52a6 */ 59 7.01969710718705064423e-02, /* 0x3fb1f86dbf082d58 */ 60 7.40829225490337306415e-02, /* 0x3fb2f719318a4a9a */ 61 7.79666338315423007588e-02, /* 0x3fb3f59f0e7c559d */ 62 8.18479898030765457007e-02, /* 0x3fb4f3fd677292fb */ 63 8.57268757707448092464e-02, /* 0x3fb5f2324fd2d7b2 */ 64 8.96031774848717321724e-02, /* 0x3fb6f03bdcea4b0c */ 65 9.34767811585894559112e-02, /* 0x3fb7ee182602f10e */ 66 9.73475734872236708739e-02, /* 0x3fb8ebc54478fb28 */ 67 1.01215441667466668485e-01, /* 0x3fb9e94153cfdcf1 */ 68 1.05080273416329528224e-01, /* 0x3fbae68a71c722b8 */ 69 1.08941956989865793015e-01, /* 0x3fbbe39ebe6f07c3 */ 70 1.12800381201659388752e-01, /* 0x3fbce07c5c3cca32 */ 71 1.16655435441069349478e-01, /* 0x3fbddd21701eba6e */ 72 1.20507009691224548087e-01, /* 0x3fbed98c2190043a */ 73 1.24354994546761424279e-01, /* 0x3fbfd5ba9aac2f6d */ 74 1.28199281231298117811e-01, /* 0x3fc068d584212b3d */ 75 1.32039761614638734288e-01, /* 0x3fc0e6adccf40881 */ 76 1.35876328229701304195e-01, /* 0x3fc1646541060850 */ 77 1.39708874289163620386e-01, /* 0x3fc1e1fafb043726 */ 78 1.43537293701821222491e-01, /* 0x3fc25f6e171a535c */ 79 1.47361481088651630200e-01, /* 0x3fc2dcbdb2fba1ff */ 80 1.51181331798580037562e-01, /* 0x3fc359e8edeb99a3 */ 81 1.54996741923940972718e-01, /* 0x3fc3d6eee8c6626c */ 82 1.58807608315631065832e-01, /* 0x3fc453cec6092a9e */ 83 1.62613828597948567589e-01, /* 0x3fc4d087a9da4f17 */ 84 1.66415301183114927586e-01, /* 0x3fc54d18ba11570a */ 85 1.70211925285474380276e-01, /* 0x3fc5c9811e3ec269 */ 86 1.74003600935367680469e-01, /* 0x3fc645bfffb3aa73 */ 87 1.77790228992676047071e-01, /* 0x3fc6c1d4898933d8 */ 88 1.81571711160032150945e-01, /* 0x3fc73dbde8a7d201 */ 89 1.85347949995694760705e-01, /* 0x3fc7b97b4bce5b02 */ 90 1.89118848926083965578e-01, /* 0x3fc8350be398ebc7 */ 91 1.92884312257974643856e-01, /* 0x3fc8b06ee2879c28 */ 92 1.96644245190344985064e-01, /* 0x3fc92ba37d050271 */ 93 2.00398553825878511514e-01, /* 0x3fc9a6a8e96c8626 */ 94 2.04147145182116990236e-01, /* 0x3fca217e601081a5 */ 95 2.07889927202262986272e-01, /* 0x3fca9c231b403279 */ 96 2.11626808765629753628e-01, /* 0x3fcb1696574d780b */ 97 2.15357699697738047551e-01, /* 0x3fcb90d7529260a2 */ 98 2.19082510780057748701e-01, /* 0x3fcc0ae54d768466 */ 99 2.22801153759394493514e-01, /* 0x3fcc84bf8a742e6d */ 100 2.26513541356919617664e-01, /* 0x3fccfe654e1d5395 */ 101 2.30219587276843717927e-01, /* 0x3fcd77d5df205736 */ 102 2.33919206214733416127e-01, /* 0x3fcdf110864c9d9d */ 103 2.37612313865471241892e-01, /* 0x3fce6a148e96ec4d */ 104 2.41298826930858800743e-01, /* 0x3fcee2e1451d980c */ 105 2.44978663126864143473e-01, /* 0x3fcf5b75f92c80dd */ 106 2.48651741190513253521e-01, /* 0x3fcfd3d1fc40dbe4 */ 107 2.52317980886427151166e-01, /* 0x3fd025fa510665b5 */ 108 2.55977303013005474952e-01, /* 0x3fd061eea03d6290 */ 109 2.59629629408257511791e-01, /* 0x3fd09dc597d86362 */ 110 2.63274882955282396590e-01, /* 0x3fd0d97ee509acb3 */ 111 2.66912987587400396539e-01, /* 0x3fd1151a362431c9 */ 112 2.70543868292936529052e-01, /* 0x3fd150973a9ce546 */ 113 2.74167451119658789338e-01, /* 0x3fd18bf5a30bf178 */ 114 2.77783663178873208022e-01, /* 0x3fd1c735212dd883 */ 115 2.81392432649178403370e-01, /* 0x3fd2025567e47c95 */ 116 2.84993688779881237938e-01, /* 0x3fd23d562b381041 */ 117 2.88587361894077354396e-01, /* 0x3fd278372057ef45 */ 118 2.92173383391398755471e-01, /* 0x3fd2b2f7fd9b5fe2 */ 119 2.95751685750431536626e-01, /* 0x3fd2ed987a823cfe */ 120 2.99322202530807379706e-01, /* 0x3fd328184fb58951 */ 121 3.02884868374971361060e-01, /* 0x3fd362773707ebcb */ 122 3.06439619009630070945e-01, /* 0x3fd39cb4eb76157b */ 123 3.09986391246883430384e-01, /* 0x3fd3d6d129271134 */ 124 3.13525122985043869228e-01, /* 0x3fd410cbad6c7d32 */ 125 3.17055753209146973237e-01, /* 0x3fd44aa436c2af09 */ 126 3.20578221991156986359e-01, /* 0x3fd4845a84d0c21b */ 127 3.24092470489871664618e-01, /* 0x3fd4bdee586890e6 */ 128 3.27598440950530811477e-01, /* 0x3fd4f75f73869978 */ 129 3.31096076704132047386e-01, /* 0x3fd530ad9951cd49 */ 130 3.34585322166458920545e-01, /* 0x3fd569d88e1b4cd7 */ 131 3.38066122836825466713e-01, /* 0x3fd5a2e0175e0f4e */ 132 3.41538425296541714449e-01, /* 0x3fd5dbc3fbbe768d */ 133 3.45002177207105076295e-01, /* 0x3fd614840309cfe1 */ 134 3.48457327308122011278e-01, /* 0x3fd64d1ff635c1c5 */ 135 3.51903825414964732676e-01, /* 0x3fd685979f5fa6fd */ 136 3.55341622416168290144e-01, /* 0x3fd6bdeac9cbd76c */ 137 3.58770670270572189509e-01, /* 0x3fd6f61941e4def0 */ 138 3.62190922004212156882e-01, /* 0x3fd72e22d53aa2a9 */ 139 3.65602331706966821034e-01, /* 0x3fd7660752817501 */ 140 3.69004854528964421068e-01, /* 0x3fd79dc6899118d1 */ 141 3.72398446676754202311e-01, /* 0x3fd7d5604b63b3f7 */ 142 3.75783065409248884237e-01, /* 0x3fd80cd46a14b1d0 */ 143 3.79158669033441808605e-01, /* 0x3fd84422b8df95d7 */ 144 3.82525216899905096124e-01, /* 0x3fd87b4b0c1ebedb */ 145 3.85882669398073752109e-01, /* 0x3fd8b24d394a1b25 */ 146 3.89230987951320717144e-01, /* 0x3fd8e92916f5cde8 */ 147 3.92570135011828580396e-01, /* 0x3fd91fde7cd0c662 */ 148 3.95900074055262896078e-01, /* 0x3fd9566d43a34907 */ 149 3.99220769575252543149e-01, /* 0x3fd98cd5454d6b18 */ 150 4.02532187077682512832e-01, /* 0x3fd9c3165cc58107 */ 151 4.05834293074804064450e-01, /* 0x3fd9f93066168001 */ 152 4.09127055079168300278e-01, /* 0x3fda2f233e5e530b */ 153 4.12410441597387267265e-01, /* 0x3fda64eec3cc23fc */ 154 4.15684422123729413467e-01, /* 0x3fda9a92d59e98cf */ 155 4.18948967133552840902e-01, /* 0x3fdad00f5422058b */ 156 4.22204048076583571270e-01, /* 0x3fdb056420ae9343 */ 157 4.25449637370042266227e-01, /* 0x3fdb3a911da65c6c */ 158 4.28685708391625730496e-01, /* 0x3fdb6f962e737efb */ 159 4.31912235472348193799e-01, /* 0x3fdba473378624a5 */ 160 4.35129193889246812521e-01, /* 0x3fdbd9281e528191 */ 161 4.38336559857957774877e-01, /* 0x3fdc0db4c94ec9ef */ 162 4.41534310525166673322e-01, /* 0x3fdc42191ff11eb6 */ 163 4.44722423960939305942e-01, /* 0x3fdc76550aad71f8 */ 164 4.47900879150937292206e-01, /* 0x3fdcaa6872f3631b */ 165 4.51069655988523443568e-01, /* 0x3fdcde53432c1350 */ 166 4.54228735266762495559e-01, /* 0x3fdd121566b7f2ad */ 167 4.57378098670320809571e-01, /* 0x3fdd45aec9ec862b */ 168 4.60517728767271039558e-01, /* 0x3fdd791f5a1226f4 */ 169 4.63647609000806093515e-01, /* 0x3fddac670561bb4f */ 170 4.66767723680866497560e-01, /* 0x3fdddf85bb026974 */ 171 4.69878057975686880265e-01, /* 0x3fde127b6b0744af */ 172 4.72978597903265574054e-01, /* 0x3fde4548066cf51a */ 173 4.76069330322761219421e-01, /* 0x3fde77eb7f175a34 */ 174 4.79150242925822533735e-01, /* 0x3fdeaa65c7cf28c4 */ 175 4.82221324227853687105e-01, /* 0x3fdedcb6d43f8434 */ 176 4.85282563559221225002e-01, /* 0x3fdf0ede98f393cf */ 177 4.88333951056405479729e-01, /* 0x3fdf40dd0b541417 */ 178 4.91375477653101910835e-01, /* 0x3fdf72b221a4e495 */ 179 4.94407135071275316562e-01, /* 0x3fdfa45dd3029258 */ 180 4.97428915812172245392e-01, /* 0x3fdfd5e0175fdf83 */ 181 5.00440813147294050189e-01, /* 0x3fe0039c73c1a40b */ 182 5.03442821109336358099e-01, /* 0x3fe01c341e82422d */ 183 5.06434934483096732549e-01, /* 0x3fe034b709250488 */ 184 5.09417148796356245022e-01, /* 0x3fe04d25314342e5 */ 185 5.12389460310737621107e-01, /* 0x3fe0657e94db30cf */ 186 5.15351866012543347040e-01, /* 0x3fe07dc3324e9b38 */ 187 5.18304363603577900044e-01, /* 0x3fe095f30861a58f */ 188 5.21246951491958210312e-01, /* 0x3fe0ae0e1639866c */ 189 5.24179628782913242802e-01, /* 0x3fe0c6145b5b43da */ 190 5.27102395269579471204e-01, /* 0x3fe0de05d7aa6f7c */ 191 5.30015251423793132268e-01, /* 0x3fe0f5e28b67e295 */ 192 5.32918198386882147055e-01, /* 0x3fe10daa77307a0d */ 193 5.35811237960463593311e-01, /* 0x3fe1255d9bfbd2a8 */ 194 5.38694372597246617929e-01, /* 0x3fe13cfbfb1b056e */ 195 5.41567605391844897333e-01, /* 0x3fe1548596376469 */ 196 5.44430940071603086672e-01, /* 0x3fe16bfa6f5137e1 */ 197 5.47284380987436924748e-01, /* 0x3fe1835a88be7c13 */ 198 5.50127933104692989907e-01, /* 0x3fe19aa5e5299f99 */ 199 5.52961601994028217888e-01, /* 0x3fe1b1dc87904284 */ 200 5.55785393822313511514e-01, /* 0x3fe1c8fe7341f64f */ 201 5.58599315343562330405e-01, /* 0x3fe1e00babdefeb3 */ 202 5.61403373889889367732e-01, /* 0x3fe1f7043557138a */ 203 5.64197577362497537656e-01, /* 0x3fe20de813e823b1 */ 204 5.66981934222700489912e-01, /* 0x3fe224b74c1d192a */ 205 5.69756453482978431069e-01, /* 0x3fe23b71e2cc9e6a */ 206 5.72521144698072359525e-01, /* 0x3fe25217dd17e501 */ 207 5.75276017956117824426e-01, /* 0x3fe268a940696da6 */ 208 5.78021083869819540801e-01, /* 0x3fe27f261273d1b3 */ 209 5.80756353567670302596e-01, /* 0x3fe2958e59308e30 */ 210 5.83481838685214859730e-01, /* 0x3fe2abe21aded073 */ 211 5.86197551356360535557e-01, /* 0x3fe2c2215e024465 */ 212 5.88903504204738026395e-01, /* 0x3fe2d84c2961e48b */ 213 5.91599710335111383941e-01, /* 0x3fe2ee628406cbca */ 214 5.94286183324841177367e-01, /* 0x3fe30464753b090a */ 215 5.96962937215401501234e-01, /* 0x3fe31a52048874be */ 216 5.99629986503951384336e-01, /* 0x3fe3302b39b78856 */ 217 6.02287346134964152178e-01, /* 0x3fe345f01cce37bb */ 218 6.04935031491913965951e-01, /* 0x3fe35ba0b60eccce */ 219 6.07573058389022313541e-01, /* 0x3fe3713d0df6c503 */ 220 6.10201443063065118722e-01, /* 0x3fe386c52d3db11e */ 221 6.12820202165241245673e-01, /* 0x3fe39c391cd41719 */ 222 6.15429352753104952356e-01, /* 0x3fe3b198e5e2564a */ 223 6.18028912282561737612e-01, /* 0x3fe3c6e491c78dc4 */ 224 6.20618898599929469384e-01, /* 0x3fe3dc1c2a188504 */ 225 6.23199329934065904268e-01, /* 0x3fe3f13fb89e96f4 */ 226 6.25770224888563042498e-01, /* 0x3fe4064f47569f48 */ 227 6.28331602434009650615e-01, /* 0x3fe41b4ae06fea41 */ 228 6.30883481900321840818e-01, /* 0x3fe430328e4b26d5 */ 229 6.33425882969144482537e-01, /* 0x3fe445065b795b55 */ 230 6.35958825666321447834e-01, /* 0x3fe459c652badc7f */ 231 6.38482330354437466191e-01, /* 0x3fe46e727efe4715 */ 232 6.40996417725432032775e-01, /* 0x3fe4830aeb5f7bfd */ 233 6.43501108793284370968e-01, /* 0x3fe4978fa3269ee1 */ 234 6.45996424886771558604e-01, /* 0x3fe4ac00b1c71762 */ 235 6.48482387642300484032e-01, /* 0x3fe4c05e22de94e4 */ 236 6.50959018996812410762e-01, /* 0x3fe4d4a8023414e8 */ 237 6.53426341180761927063e-01, /* 0x3fe4e8de5bb6ec04 */ 238 6.55884376711170835605e-01, /* 0x3fe4fd013b7dd17e */ 239 6.58333148384755983962e-01, /* 0x3fe51110adc5ed81 */ 240 6.60772679271132590273e-01, /* 0x3fe5250cbef1e9fa */ 241 6.63202992706093175102e-01, /* 0x3fe538f57b89061e */ 242 6.65624112284960989250e-01, /* 0x3fe54ccaf0362c8f */ 243 6.68036061856020157990e-01, /* 0x3fe5608d29c70c34 */ 244 6.70438865514021320458e-01, /* 0x3fe5743c352b33b9 */ 245 6.72832547593763097282e-01, /* 0x3fe587d81f732fba */ 246 6.75217132663749830535e-01, /* 0x3fe59b60f5cfab9d */ 247 6.77592645519925151909e-01, /* 0x3fe5aed6c5909517 */ 248 6.79959111179481823228e-01, /* 0x3fe5c2399c244260 */ 249 6.82316554874748071313e-01, /* 0x3fe5d58987169b18 */ 250 6.84665002047148862907e-01, /* 0x3fe5e8c6941043cf */ 251 6.87004478341244895212e-01, /* 0x3fe5fbf0d0d5cc49 */ 252 6.89335009598845749323e-01, /* 0x3fe60f084b46e05e */ 253 6.91656621853199760075e-01, /* 0x3fe6220d115d7b8d */ 254 6.93969341323259825138e-01, /* 0x3fe634ff312d1f3b */ 255 6.96273194408023488045e-01, /* 0x3fe647deb8e20b8f */ 256 6.98568207680949848637e-01, /* 0x3fe65aabb6c07b02 */ 257 7.00854407884450081312e-01, /* 0x3fe66d663923e086 */ 258 7.03131821924453670469e-01, /* 0x3fe6800e4e7e2857 */ 259 7.05400476865049030906e-01, /* 0x3fe692a40556fb6a */ 260 7.07660399923197958039e-01, /* 0x3fe6a5276c4b0575 */ 261 7.09911618463524796141e-01, /* 0x3fe6b798920b3d98 */ 262 7.12154159993178659249e-01, /* 0x3fe6c9f7855c3198 */ 263 7.14388052156768926793e-01, /* 0x3fe6dc44551553ae */ 264 7.16613322731374569052e-01, /* 0x3fe6ee7f10204aef */ 265 7.18829999621624415873e-01, /* 0x3fe700a7c5784633 */ 266 7.21038110854851588272e-01, /* 0x3fe712be84295198 */ 267 7.23237684576317874097e-01, /* 0x3fe724c35b4fae7b */ 268 7.25428749044510712274e-01, /* 0x3fe736b65a172dff */ 269 7.27611332626510676214e-01, /* 0x3fe748978fba8e0f */ 270 7.29785463793429123314e-01, /* 0x3fe75a670b82d8d8 */ 271 7.31951171115916565668e-01, /* 0x3fe76c24dcc6c6c0 */ 272 7.34108483259739652560e-01, /* 0x3fe77dd112ea22c7 */ 273 7.36257428981428097003e-01, /* 0x3fe78f6bbd5d315e */ 274 7.38398037123989547936e-01, /* 0x3fe7a0f4eb9c19a2 */ 275 7.40530336612692630105e-01, /* 0x3fe7b26cad2e50fd */ 276 7.42654356450917929600e-01, /* 0x3fe7c3d311a6092b */ 277 7.44770125716075148681e-01, /* 0x3fe7d528289fa093 */ 278 7.46877673555587429099e-01, /* 0x3fe7e66c01c114fd */ 279 7.48977029182941400620e-01, /* 0x3fe7f79eacb97898 */ 280 7.51068221873802288613e-01, /* 0x3fe808c03940694a */ 281 7.53151280962194302759e-01, /* 0x3fe819d0b7158a4c */ 282 7.55226235836744863583e-01, /* 0x3fe82ad036000005 */ 283 7.57293115936992444759e-01, /* 0x3fe83bbec5cdee22 */ 284 7.59351950749757920178e-01, /* 0x3fe84c9c7653f7ea */ 285 7.61402769805578416573e-01, /* 0x3fe85d69576cc2c5 */ 286 7.63445602675201784315e-01, /* 0x3fe86e2578f87ae5 */ 287 7.65480478966144461950e-01, /* 0x3fe87ed0eadc5a2a */ 288 7.67507428319308182552e-01, /* 0x3fe88f6bbd023118 */ 289 7.69526480405658186434e-01, /* 0x3fe89ff5ff57f1f7 */ 290 7.71537664922959498526e-01, /* 0x3fe8b06fc1cf3dfe */ 291 7.73541011592573490852e-01, /* 0x3fe8c0d9145cf49d */ 292 7.75536550156311621507e-01, /* 0x3fe8d13206f8c4ca */ 293 7.77524310373347682379e-01, /* 0x3fe8e17aa99cc05d */ 294 7.79504322017186335181e-01, /* 0x3fe8f1b30c44f167 */ 295 7.81476614872688268854e-01, /* 0x3fe901db3eeef187 */ 296 7.83441218733151756304e-01, /* 0x3fe911f35199833b */ 297 7.85398163397448278999e-01}; /* 0x3fe921fb54442d18 */ 298 299 /* Some constants. */ 300 301 static double pi = 3.1415926535897932e+00, /* 0x400921fb54442d18 */ 302 piby2 = 1.5707963267948966e+00, /* 0x3ff921fb54442d18 */ 303 piby4 = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */ 304 three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */ 305 306 double u, v, vbyu, q, s, uu, r; 307 unsigned int swap_vu, index, xzero, yzero, xnan, ynan, xinf, yinf; 308 int xexp, yexp, diffexp; 309 310 double x = fx; 311 double y = fy; 312 313 /* Find properties of arguments x and y. */ 314 315 unsigned long long ux, aux, xneg, uy, auy, yneg; 316 317 GET_BITS_DP64(x, ux); 318 GET_BITS_DP64(y, uy); 319 aux = ux & ~SIGNBIT_DP64; 320 auy = uy & ~SIGNBIT_DP64; 321 xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); 322 yexp = (int)((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); 323 xneg = ux & SIGNBIT_DP64; 324 yneg = uy & SIGNBIT_DP64; 325 xzero = (aux == 0); 326 yzero = (auy == 0); 327 xnan = (aux > PINFBITPATT_DP64); 328 ynan = (auy > PINFBITPATT_DP64); 329 xinf = (aux == PINFBITPATT_DP64); 330 yinf = (auy == PINFBITPATT_DP64); 331 332 diffexp = yexp - xexp; 333 334 /* Special cases */ 335 336 if (xnan) 337 { 338 unsigned int ufx; 339 GET_BITS_SP32(fx, ufx); 340 return _handle_errorf("atan2f", OP_ATAN2, ufx|0x00400000, _DOMAIN, 0, 341 EDOM, fx, fy, 2); 342 } 343 else if (ynan) 344 { 345 unsigned int ufy; 346 GET_BITS_SP32(fy, ufy); 347 return _handle_errorf("atan2f", OP_ATAN2, ufy|0x00400000, _DOMAIN, 0, 348 EDOM, fx, fy, 2); 349 } 350 else if (yzero) 351 { /* Zero y gives +-0 for positive x 352 and +-pi for negative x */ 353 if (xneg) 354 { 355 if (yneg) return valf_with_flags((float)-pi, AMD_F_INEXACT); 356 else return valf_with_flags((float)pi, AMD_F_INEXACT); 357 } 358 else return (float)y; 359 } 360 else if (xzero) 361 { /* Zero x gives +- pi/2 362 depending on sign of y */ 363 if (yneg) return valf_with_flags((float)-piby2, AMD_F_INEXACT); 364 else valf_with_flags((float)piby2, AMD_F_INEXACT); 365 } 366 367 if (diffexp > 26) 368 { /* abs(y)/abs(x) > 2^26 => arctan(x/y) 369 is insignificant compared to piby2 */ 370 if (yneg) return valf_with_flags((float)-piby2, AMD_F_INEXACT); 371 else return valf_with_flags((float)piby2, AMD_F_INEXACT); 372 } 373 else if (diffexp < -13 && (!xneg)) 374 { /* x positive and dominant over y by a factor of 2^13. 375 In this case atan(y/x) is y/x to machine accuracy. */ 376 377 if (diffexp < -150) /* Result underflows */ 378 { 379 if (yneg) 380 return valf_with_flags(-0.0F, AMD_F_INEXACT | AMD_F_UNDERFLOW); 381 else 382 return valf_with_flags(0.0F, AMD_F_INEXACT | AMD_F_UNDERFLOW); 383 } 384 else 385 { 386 if (diffexp < -126) 387 { 388 /* Result will likely be denormalized */ 389 y = scaleDouble_1(y, 100); 390 y /= x; 391 /* Now y is 2^100 times the true result. Scale it back down. */ 392 GET_BITS_DP64(y, uy); 393 scaleDownDouble(uy, 100, &uy); 394 PUT_BITS_DP64(uy, y); 395 if ((uy & EXPBITS_DP64) == 0) 396 return valf_with_flags((float)y, AMD_F_INEXACT | AMD_F_UNDERFLOW); 397 else 398 return (float)y; 399 } 400 else 401 return (float)(y / x); 402 } 403 } 404 else if (diffexp < -26 && xneg) 405 { /* abs(x)/abs(y) > 2^56 and x < 0 => arctan(y/x) 406 is insignificant compared to pi */ 407 if (yneg) return valf_with_flags((float)-pi, AMD_F_INEXACT); 408 else return valf_with_flags((float)pi, AMD_F_INEXACT); 409 } 410 else if (yinf && xinf) 411 { /* If abs(x) and abs(y) are both infinity 412 return +-pi/4 or +- 3pi/4 according to 413 signs. */ 414 if (xneg) 415 { 416 if (yneg) return valf_with_flags((float)-three_piby4, AMD_F_INEXACT); 417 else return valf_with_flags((float)three_piby4, AMD_F_INEXACT); 418 } 419 else 420 { 421 if (yneg) return valf_with_flags((float)-piby4, AMD_F_INEXACT); 422 else return valf_with_flags((float)piby4, AMD_F_INEXACT); 423 } 424 } 425 426 /* General case: take absolute values of arguments */ 427 428 u = x; v = y; 429 if (xneg) u = -x; 430 if (yneg) v = -y; 431 432 /* Swap u and v if necessary to obtain 0 < v < u. Compute v/u. */ 433 434 swap_vu = (u < v); 435 if (swap_vu) { uu = u; u = v; v = uu; } 436 vbyu = v/u; 437 438 if (vbyu > 0.0625) 439 { /* General values of v/u. Use a look-up 440 table and series expansion. */ 441 442 index = (int)(256*vbyu + 0.5); 443 r = (256*v-index*u)/(256*u+index*v); 444 445 /* Polynomial approximation to atan(vbyu) */ 446 447 s = r*r; 448 q = atan_jby256[index-16] + r - r*s*0.33333333333224095522; 449 } 450 else if (vbyu < 1.e-4) 451 { /* v/u is small enough that atan(v/u) = v/u */ 452 q = vbyu; 453 } 454 else /* vbyu <= 0.0625 */ 455 { 456 /* Small values of v/u. Use a series expansion */ 457 458 s = vbyu*vbyu; 459 q = vbyu - 460 vbyu*s*(0.33333333333333170500 - 461 s*(0.19999999999393223405 - 462 s*0.14285713561807169030)); 463 } 464 465 /* Tidy-up according to which quadrant the arguments lie in */ 466 467 if (swap_vu) {q = piby2 - q;} 468 if (xneg) {q = pi - q;} 469 if (yneg) q = - q; 470 return (float)q; 471 } 472