/* ============================================================ Copyright (c) 2002-2015 Advanced Micro Devices, Inc. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: + Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. + Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. + Neither the name of Advanced Micro Devices, Inc. nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL ADVANCED MICRO DEVICES, INC. OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. It is licensee's responsibility to comply with any export regulations applicable in licensee's jurisdiction. ============================================================ */ #include "libm_amd.h" #include "libm_util_amd.h" #define USE_VALF_WITH_FLAGS #define USE_NAN_WITH_FLAGS #define USE_SCALEDOUBLE_1 #define USE_SCALEDOWNDOUBLE #define USE_HANDLE_ERRORF #include "libm_inlines_amd.h" #undef USE_VALF_WITH_FLAGS #undef USE_NAN_WITH_FLAGS #undef USE_SCALEDOUBLE_1 #undef USE_SCALEDOWNDOUBLE #undef USE_HANDLE_ERRORF #include "libm_errno_amd.h" float FN_PROTOTYPE(mth_i_atan2)(float fy, float fx) { /* Array atan_jby256 contains precomputed values of atan(j/256), for j = 16, 17, ..., 256. */ static const double atan_jby256[241] = { 6.24188099959573430842e-02, /* 0x3faff55bb72cfde9 */ 6.63088949198234745008e-02, /* 0x3fb0f99ea71d52a6 */ 7.01969710718705064423e-02, /* 0x3fb1f86dbf082d58 */ 7.40829225490337306415e-02, /* 0x3fb2f719318a4a9a */ 7.79666338315423007588e-02, /* 0x3fb3f59f0e7c559d */ 8.18479898030765457007e-02, /* 0x3fb4f3fd677292fb */ 8.57268757707448092464e-02, /* 0x3fb5f2324fd2d7b2 */ 8.96031774848717321724e-02, /* 0x3fb6f03bdcea4b0c */ 9.34767811585894559112e-02, /* 0x3fb7ee182602f10e */ 9.73475734872236708739e-02, /* 0x3fb8ebc54478fb28 */ 1.01215441667466668485e-01, /* 0x3fb9e94153cfdcf1 */ 1.05080273416329528224e-01, /* 0x3fbae68a71c722b8 */ 1.08941956989865793015e-01, /* 0x3fbbe39ebe6f07c3 */ 1.12800381201659388752e-01, /* 0x3fbce07c5c3cca32 */ 1.16655435441069349478e-01, /* 0x3fbddd21701eba6e */ 1.20507009691224548087e-01, /* 0x3fbed98c2190043a */ 1.24354994546761424279e-01, /* 0x3fbfd5ba9aac2f6d */ 1.28199281231298117811e-01, /* 0x3fc068d584212b3d */ 1.32039761614638734288e-01, /* 0x3fc0e6adccf40881 */ 1.35876328229701304195e-01, /* 0x3fc1646541060850 */ 1.39708874289163620386e-01, /* 0x3fc1e1fafb043726 */ 1.43537293701821222491e-01, /* 0x3fc25f6e171a535c */ 1.47361481088651630200e-01, /* 0x3fc2dcbdb2fba1ff */ 1.51181331798580037562e-01, /* 0x3fc359e8edeb99a3 */ 1.54996741923940972718e-01, /* 0x3fc3d6eee8c6626c */ 1.58807608315631065832e-01, /* 0x3fc453cec6092a9e */ 1.62613828597948567589e-01, /* 0x3fc4d087a9da4f17 */ 1.66415301183114927586e-01, /* 0x3fc54d18ba11570a */ 1.70211925285474380276e-01, /* 0x3fc5c9811e3ec269 */ 1.74003600935367680469e-01, /* 0x3fc645bfffb3aa73 */ 1.77790228992676047071e-01, /* 0x3fc6c1d4898933d8 */ 1.81571711160032150945e-01, /* 0x3fc73dbde8a7d201 */ 1.85347949995694760705e-01, /* 0x3fc7b97b4bce5b02 */ 1.89118848926083965578e-01, /* 0x3fc8350be398ebc7 */ 1.92884312257974643856e-01, /* 0x3fc8b06ee2879c28 */ 1.96644245190344985064e-01, /* 0x3fc92ba37d050271 */ 2.00398553825878511514e-01, /* 0x3fc9a6a8e96c8626 */ 2.04147145182116990236e-01, /* 0x3fca217e601081a5 */ 2.07889927202262986272e-01, /* 0x3fca9c231b403279 */ 2.11626808765629753628e-01, /* 0x3fcb1696574d780b */ 2.15357699697738047551e-01, /* 0x3fcb90d7529260a2 */ 2.19082510780057748701e-01, /* 0x3fcc0ae54d768466 */ 2.22801153759394493514e-01, /* 0x3fcc84bf8a742e6d */ 2.26513541356919617664e-01, /* 0x3fccfe654e1d5395 */ 2.30219587276843717927e-01, /* 0x3fcd77d5df205736 */ 2.33919206214733416127e-01, /* 0x3fcdf110864c9d9d */ 2.37612313865471241892e-01, /* 0x3fce6a148e96ec4d */ 2.41298826930858800743e-01, /* 0x3fcee2e1451d980c */ 2.44978663126864143473e-01, /* 0x3fcf5b75f92c80dd */ 2.48651741190513253521e-01, /* 0x3fcfd3d1fc40dbe4 */ 2.52317980886427151166e-01, /* 0x3fd025fa510665b5 */ 2.55977303013005474952e-01, /* 0x3fd061eea03d6290 */ 2.59629629408257511791e-01, /* 0x3fd09dc597d86362 */ 2.63274882955282396590e-01, /* 0x3fd0d97ee509acb3 */ 2.66912987587400396539e-01, /* 0x3fd1151a362431c9 */ 2.70543868292936529052e-01, /* 0x3fd150973a9ce546 */ 2.74167451119658789338e-01, /* 0x3fd18bf5a30bf178 */ 2.77783663178873208022e-01, /* 0x3fd1c735212dd883 */ 2.81392432649178403370e-01, /* 0x3fd2025567e47c95 */ 2.84993688779881237938e-01, /* 0x3fd23d562b381041 */ 2.88587361894077354396e-01, /* 0x3fd278372057ef45 */ 2.92173383391398755471e-01, /* 0x3fd2b2f7fd9b5fe2 */ 2.95751685750431536626e-01, /* 0x3fd2ed987a823cfe */ 2.99322202530807379706e-01, /* 0x3fd328184fb58951 */ 3.02884868374971361060e-01, /* 0x3fd362773707ebcb */ 3.06439619009630070945e-01, /* 0x3fd39cb4eb76157b */ 3.09986391246883430384e-01, /* 0x3fd3d6d129271134 */ 3.13525122985043869228e-01, /* 0x3fd410cbad6c7d32 */ 3.17055753209146973237e-01, /* 0x3fd44aa436c2af09 */ 3.20578221991156986359e-01, /* 0x3fd4845a84d0c21b */ 3.24092470489871664618e-01, /* 0x3fd4bdee586890e6 */ 3.27598440950530811477e-01, /* 0x3fd4f75f73869978 */ 3.31096076704132047386e-01, /* 0x3fd530ad9951cd49 */ 3.34585322166458920545e-01, /* 0x3fd569d88e1b4cd7 */ 3.38066122836825466713e-01, /* 0x3fd5a2e0175e0f4e */ 3.41538425296541714449e-01, /* 0x3fd5dbc3fbbe768d */ 3.45002177207105076295e-01, /* 0x3fd614840309cfe1 */ 3.48457327308122011278e-01, /* 0x3fd64d1ff635c1c5 */ 3.51903825414964732676e-01, /* 0x3fd685979f5fa6fd */ 3.55341622416168290144e-01, /* 0x3fd6bdeac9cbd76c */ 3.58770670270572189509e-01, /* 0x3fd6f61941e4def0 */ 3.62190922004212156882e-01, /* 0x3fd72e22d53aa2a9 */ 3.65602331706966821034e-01, /* 0x3fd7660752817501 */ 3.69004854528964421068e-01, /* 0x3fd79dc6899118d1 */ 3.72398446676754202311e-01, /* 0x3fd7d5604b63b3f7 */ 3.75783065409248884237e-01, /* 0x3fd80cd46a14b1d0 */ 3.79158669033441808605e-01, /* 0x3fd84422b8df95d7 */ 3.82525216899905096124e-01, /* 0x3fd87b4b0c1ebedb */ 3.85882669398073752109e-01, /* 0x3fd8b24d394a1b25 */ 3.89230987951320717144e-01, /* 0x3fd8e92916f5cde8 */ 3.92570135011828580396e-01, /* 0x3fd91fde7cd0c662 */ 3.95900074055262896078e-01, /* 0x3fd9566d43a34907 */ 3.99220769575252543149e-01, /* 0x3fd98cd5454d6b18 */ 4.02532187077682512832e-01, /* 0x3fd9c3165cc58107 */ 4.05834293074804064450e-01, /* 0x3fd9f93066168001 */ 4.09127055079168300278e-01, /* 0x3fda2f233e5e530b */ 4.12410441597387267265e-01, /* 0x3fda64eec3cc23fc */ 4.15684422123729413467e-01, /* 0x3fda9a92d59e98cf */ 4.18948967133552840902e-01, /* 0x3fdad00f5422058b */ 4.22204048076583571270e-01, /* 0x3fdb056420ae9343 */ 4.25449637370042266227e-01, /* 0x3fdb3a911da65c6c */ 4.28685708391625730496e-01, /* 0x3fdb6f962e737efb */ 4.31912235472348193799e-01, /* 0x3fdba473378624a5 */ 4.35129193889246812521e-01, /* 0x3fdbd9281e528191 */ 4.38336559857957774877e-01, /* 0x3fdc0db4c94ec9ef */ 4.41534310525166673322e-01, /* 0x3fdc42191ff11eb6 */ 4.44722423960939305942e-01, /* 0x3fdc76550aad71f8 */ 4.47900879150937292206e-01, /* 0x3fdcaa6872f3631b */ 4.51069655988523443568e-01, /* 0x3fdcde53432c1350 */ 4.54228735266762495559e-01, /* 0x3fdd121566b7f2ad */ 4.57378098670320809571e-01, /* 0x3fdd45aec9ec862b */ 4.60517728767271039558e-01, /* 0x3fdd791f5a1226f4 */ 4.63647609000806093515e-01, /* 0x3fddac670561bb4f */ 4.66767723680866497560e-01, /* 0x3fdddf85bb026974 */ 4.69878057975686880265e-01, /* 0x3fde127b6b0744af */ 4.72978597903265574054e-01, /* 0x3fde4548066cf51a */ 4.76069330322761219421e-01, /* 0x3fde77eb7f175a34 */ 4.79150242925822533735e-01, /* 0x3fdeaa65c7cf28c4 */ 4.82221324227853687105e-01, /* 0x3fdedcb6d43f8434 */ 4.85282563559221225002e-01, /* 0x3fdf0ede98f393cf */ 4.88333951056405479729e-01, /* 0x3fdf40dd0b541417 */ 4.91375477653101910835e-01, /* 0x3fdf72b221a4e495 */ 4.94407135071275316562e-01, /* 0x3fdfa45dd3029258 */ 4.97428915812172245392e-01, /* 0x3fdfd5e0175fdf83 */ 5.00440813147294050189e-01, /* 0x3fe0039c73c1a40b */ 5.03442821109336358099e-01, /* 0x3fe01c341e82422d */ 5.06434934483096732549e-01, /* 0x3fe034b709250488 */ 5.09417148796356245022e-01, /* 0x3fe04d25314342e5 */ 5.12389460310737621107e-01, /* 0x3fe0657e94db30cf */ 5.15351866012543347040e-01, /* 0x3fe07dc3324e9b38 */ 5.18304363603577900044e-01, /* 0x3fe095f30861a58f */ 5.21246951491958210312e-01, /* 0x3fe0ae0e1639866c */ 5.24179628782913242802e-01, /* 0x3fe0c6145b5b43da */ 5.27102395269579471204e-01, /* 0x3fe0de05d7aa6f7c */ 5.30015251423793132268e-01, /* 0x3fe0f5e28b67e295 */ 5.32918198386882147055e-01, /* 0x3fe10daa77307a0d */ 5.35811237960463593311e-01, /* 0x3fe1255d9bfbd2a8 */ 5.38694372597246617929e-01, /* 0x3fe13cfbfb1b056e */ 5.41567605391844897333e-01, /* 0x3fe1548596376469 */ 5.44430940071603086672e-01, /* 0x3fe16bfa6f5137e1 */ 5.47284380987436924748e-01, /* 0x3fe1835a88be7c13 */ 5.50127933104692989907e-01, /* 0x3fe19aa5e5299f99 */ 5.52961601994028217888e-01, /* 0x3fe1b1dc87904284 */ 5.55785393822313511514e-01, /* 0x3fe1c8fe7341f64f */ 5.58599315343562330405e-01, /* 0x3fe1e00babdefeb3 */ 5.61403373889889367732e-01, /* 0x3fe1f7043557138a */ 5.64197577362497537656e-01, /* 0x3fe20de813e823b1 */ 5.66981934222700489912e-01, /* 0x3fe224b74c1d192a */ 5.69756453482978431069e-01, /* 0x3fe23b71e2cc9e6a */ 5.72521144698072359525e-01, /* 0x3fe25217dd17e501 */ 5.75276017956117824426e-01, /* 0x3fe268a940696da6 */ 5.78021083869819540801e-01, /* 0x3fe27f261273d1b3 */ 5.80756353567670302596e-01, /* 0x3fe2958e59308e30 */ 5.83481838685214859730e-01, /* 0x3fe2abe21aded073 */ 5.86197551356360535557e-01, /* 0x3fe2c2215e024465 */ 5.88903504204738026395e-01, /* 0x3fe2d84c2961e48b */ 5.91599710335111383941e-01, /* 0x3fe2ee628406cbca */ 5.94286183324841177367e-01, /* 0x3fe30464753b090a */ 5.96962937215401501234e-01, /* 0x3fe31a52048874be */ 5.99629986503951384336e-01, /* 0x3fe3302b39b78856 */ 6.02287346134964152178e-01, /* 0x3fe345f01cce37bb */ 6.04935031491913965951e-01, /* 0x3fe35ba0b60eccce */ 6.07573058389022313541e-01, /* 0x3fe3713d0df6c503 */ 6.10201443063065118722e-01, /* 0x3fe386c52d3db11e */ 6.12820202165241245673e-01, /* 0x3fe39c391cd41719 */ 6.15429352753104952356e-01, /* 0x3fe3b198e5e2564a */ 6.18028912282561737612e-01, /* 0x3fe3c6e491c78dc4 */ 6.20618898599929469384e-01, /* 0x3fe3dc1c2a188504 */ 6.23199329934065904268e-01, /* 0x3fe3f13fb89e96f4 */ 6.25770224888563042498e-01, /* 0x3fe4064f47569f48 */ 6.28331602434009650615e-01, /* 0x3fe41b4ae06fea41 */ 6.30883481900321840818e-01, /* 0x3fe430328e4b26d5 */ 6.33425882969144482537e-01, /* 0x3fe445065b795b55 */ 6.35958825666321447834e-01, /* 0x3fe459c652badc7f */ 6.38482330354437466191e-01, /* 0x3fe46e727efe4715 */ 6.40996417725432032775e-01, /* 0x3fe4830aeb5f7bfd */ 6.43501108793284370968e-01, /* 0x3fe4978fa3269ee1 */ 6.45996424886771558604e-01, /* 0x3fe4ac00b1c71762 */ 6.48482387642300484032e-01, /* 0x3fe4c05e22de94e4 */ 6.50959018996812410762e-01, /* 0x3fe4d4a8023414e8 */ 6.53426341180761927063e-01, /* 0x3fe4e8de5bb6ec04 */ 6.55884376711170835605e-01, /* 0x3fe4fd013b7dd17e */ 6.58333148384755983962e-01, /* 0x3fe51110adc5ed81 */ 6.60772679271132590273e-01, /* 0x3fe5250cbef1e9fa */ 6.63202992706093175102e-01, /* 0x3fe538f57b89061e */ 6.65624112284960989250e-01, /* 0x3fe54ccaf0362c8f */ 6.68036061856020157990e-01, /* 0x3fe5608d29c70c34 */ 6.70438865514021320458e-01, /* 0x3fe5743c352b33b9 */ 6.72832547593763097282e-01, /* 0x3fe587d81f732fba */ 6.75217132663749830535e-01, /* 0x3fe59b60f5cfab9d */ 6.77592645519925151909e-01, /* 0x3fe5aed6c5909517 */ 6.79959111179481823228e-01, /* 0x3fe5c2399c244260 */ 6.82316554874748071313e-01, /* 0x3fe5d58987169b18 */ 6.84665002047148862907e-01, /* 0x3fe5e8c6941043cf */ 6.87004478341244895212e-01, /* 0x3fe5fbf0d0d5cc49 */ 6.89335009598845749323e-01, /* 0x3fe60f084b46e05e */ 6.91656621853199760075e-01, /* 0x3fe6220d115d7b8d */ 6.93969341323259825138e-01, /* 0x3fe634ff312d1f3b */ 6.96273194408023488045e-01, /* 0x3fe647deb8e20b8f */ 6.98568207680949848637e-01, /* 0x3fe65aabb6c07b02 */ 7.00854407884450081312e-01, /* 0x3fe66d663923e086 */ 7.03131821924453670469e-01, /* 0x3fe6800e4e7e2857 */ 7.05400476865049030906e-01, /* 0x3fe692a40556fb6a */ 7.07660399923197958039e-01, /* 0x3fe6a5276c4b0575 */ 7.09911618463524796141e-01, /* 0x3fe6b798920b3d98 */ 7.12154159993178659249e-01, /* 0x3fe6c9f7855c3198 */ 7.14388052156768926793e-01, /* 0x3fe6dc44551553ae */ 7.16613322731374569052e-01, /* 0x3fe6ee7f10204aef */ 7.18829999621624415873e-01, /* 0x3fe700a7c5784633 */ 7.21038110854851588272e-01, /* 0x3fe712be84295198 */ 7.23237684576317874097e-01, /* 0x3fe724c35b4fae7b */ 7.25428749044510712274e-01, /* 0x3fe736b65a172dff */ 7.27611332626510676214e-01, /* 0x3fe748978fba8e0f */ 7.29785463793429123314e-01, /* 0x3fe75a670b82d8d8 */ 7.31951171115916565668e-01, /* 0x3fe76c24dcc6c6c0 */ 7.34108483259739652560e-01, /* 0x3fe77dd112ea22c7 */ 7.36257428981428097003e-01, /* 0x3fe78f6bbd5d315e */ 7.38398037123989547936e-01, /* 0x3fe7a0f4eb9c19a2 */ 7.40530336612692630105e-01, /* 0x3fe7b26cad2e50fd */ 7.42654356450917929600e-01, /* 0x3fe7c3d311a6092b */ 7.44770125716075148681e-01, /* 0x3fe7d528289fa093 */ 7.46877673555587429099e-01, /* 0x3fe7e66c01c114fd */ 7.48977029182941400620e-01, /* 0x3fe7f79eacb97898 */ 7.51068221873802288613e-01, /* 0x3fe808c03940694a */ 7.53151280962194302759e-01, /* 0x3fe819d0b7158a4c */ 7.55226235836744863583e-01, /* 0x3fe82ad036000005 */ 7.57293115936992444759e-01, /* 0x3fe83bbec5cdee22 */ 7.59351950749757920178e-01, /* 0x3fe84c9c7653f7ea */ 7.61402769805578416573e-01, /* 0x3fe85d69576cc2c5 */ 7.63445602675201784315e-01, /* 0x3fe86e2578f87ae5 */ 7.65480478966144461950e-01, /* 0x3fe87ed0eadc5a2a */ 7.67507428319308182552e-01, /* 0x3fe88f6bbd023118 */ 7.69526480405658186434e-01, /* 0x3fe89ff5ff57f1f7 */ 7.71537664922959498526e-01, /* 0x3fe8b06fc1cf3dfe */ 7.73541011592573490852e-01, /* 0x3fe8c0d9145cf49d */ 7.75536550156311621507e-01, /* 0x3fe8d13206f8c4ca */ 7.77524310373347682379e-01, /* 0x3fe8e17aa99cc05d */ 7.79504322017186335181e-01, /* 0x3fe8f1b30c44f167 */ 7.81476614872688268854e-01, /* 0x3fe901db3eeef187 */ 7.83441218733151756304e-01, /* 0x3fe911f35199833b */ 7.85398163397448278999e-01}; /* 0x3fe921fb54442d18 */ /* Some constants. */ static double pi = 3.1415926535897932e+00, /* 0x400921fb54442d18 */ piby2 = 1.5707963267948966e+00, /* 0x3ff921fb54442d18 */ piby4 = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */ three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */ double u, v, vbyu, q, s, uu, r; unsigned int swap_vu, index, xzero, yzero, xnan, ynan, xinf, yinf; int xexp, yexp, diffexp; double x = fx; double y = fy; /* Find properties of arguments x and y. */ __UINT8_T ux, aux, xneg, uy, auy, yneg; GET_BITS_DP64(x, ux); GET_BITS_DP64(y, uy); aux = ux & ~SIGNBIT_DP64; auy = uy & ~SIGNBIT_DP64; xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); yexp = (int)((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); xneg = ux & SIGNBIT_DP64; yneg = uy & SIGNBIT_DP64; xzero = (aux == 0); yzero = (auy == 0); xnan = (aux > PINFBITPATT_DP64); ynan = (auy > PINFBITPATT_DP64); xinf = (aux == PINFBITPATT_DP64); yinf = (auy == PINFBITPATT_DP64); diffexp = yexp - xexp; /* Special cases */ if (xnan) return fx + fx; /* Raise invalid if it's a signalling NaN */ else if (ynan) return (float)(y + y); /* Raise invalid if it's a signalling NaN */ else if (yzero) { /* Zero y gives +-0 for positive x and +-pi for negative x */ if (xneg) { if (yneg) return valf_with_flags((float)-pi, AMD_F_INEXACT); else return valf_with_flags((float)pi, AMD_F_INEXACT); } else return (float)y; } else if (xzero) { /* Zero x gives +- pi/2 depending on sign of y */ if (yneg) return valf_with_flags((float)-piby2, AMD_F_INEXACT); else valf_with_flags((float)piby2, AMD_F_INEXACT); } if (diffexp > 26) { /* abs(y)/abs(x) > 2^26 => arctan(x/y) is insignificant compared to piby2 */ if (yneg) return valf_with_flags((float)-piby2, AMD_F_INEXACT); else return valf_with_flags((float)piby2, AMD_F_INEXACT); } else if (diffexp < -13 && (!xneg)) { /* x positive and dominant over y by a factor of 2^13. In this case atan(y/x) is y/x to machine accuracy. */ if (diffexp < -150) /* Result underflows */ { if (yneg) return valf_with_flags(-0.0F, AMD_F_INEXACT | AMD_F_UNDERFLOW); else return valf_with_flags(0.0F, AMD_F_INEXACT | AMD_F_UNDERFLOW); } else { if (diffexp < -126) { /* Result will likely be denormalized */ y = scaleDouble_1(y, 100); y /= x; /* Now y is 2^100 times the true result. Scale it back down. */ GET_BITS_DP64(y, uy); scaleDownDouble(uy, 100, &uy); PUT_BITS_DP64(uy, y); if ((uy & EXPBITS_DP64) == 0) return valf_with_flags((float)y, AMD_F_INEXACT | AMD_F_UNDERFLOW); else return (float)y; } else return (float)(y / x); } } else if (diffexp < -26 && xneg) { /* abs(x)/abs(y) > 2^56 and x < 0 => arctan(y/x) is insignificant compared to pi */ if (yneg) return valf_with_flags((float)-pi, AMD_F_INEXACT); else return valf_with_flags((float)pi, AMD_F_INEXACT); } else if (yinf && xinf) { /* If abs(x) and abs(y) are both infinity return +-pi/4 or +- 3pi/4 according to signs. */ if (xneg) { if (yneg) return valf_with_flags((float)-three_piby4, AMD_F_INEXACT); else return valf_with_flags((float)three_piby4, AMD_F_INEXACT); } else { if (yneg) return valf_with_flags((float)-piby4, AMD_F_INEXACT); else return valf_with_flags((float)piby4, AMD_F_INEXACT); } } /* General case: take absolute values of arguments */ u = x; v = y; if (xneg) u = -x; if (yneg) v = -y; /* Swap u and v if necessary to obtain 0 < v < u. Compute v/u. */ swap_vu = (u < v); if (swap_vu) { uu = u; u = v; v = uu; } vbyu = v / u; if (vbyu > 0.0625) { /* General values of v/u. Use a look-up table and series expansion. */ index = (int)(256 * vbyu + 0.5); r = (256 * v - index * u) / (256 * u + index * v); /* Polynomial approximation to atan(vbyu) */ s = r * r; q = atan_jby256[index - 16] + r - r * s * 0.33333333333224095522; } else if (vbyu < 1.e-4) { /* v/u is small enough that atan(v/u) = v/u */ q = vbyu; } else /* vbyu <= 0.0625 */ { /* Small values of v/u. Use a series expansion */ s = vbyu * vbyu; q = vbyu - vbyu * s * (0.33333333333333170500 - s * (0.19999999999393223405 - s * 0.14285713561807169030)); } /* Tidy-up according to which quadrant the arguments lie in */ if (swap_vu) { q = piby2 - q; } if (xneg) { q = pi - q; } if (yneg) q = -q; return (float)q; }