atan2f.c

Go to the documentation of this file.

 
/*******************************************************************************
MIT License
-----------
 
Copyright (c) 2002-2019 Advanced Micro Devices, Inc.
 
Permission is hereby granted, free of charge, to any person obtaining a copy
of this Software and associated documentaon files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
 
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
 
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
*******************************************************************************/
 
#include "libm.h"
#include "libm_util.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.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.h"
 
#ifdef _MSC_VER
// Disable "C4163: not available as intrinsic function" warning that older
// compilers may issue here.
#pragma warning(disable:4163)
#pragma function(atan2f)
#endif
 
float FN_PROTOTYPE(atan2f)(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. */
 
  unsigned long long 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)
    {
      unsigned int ufx;
      GET_BITS_SP32(fx, ufx);
      return _handle_errorf("atan2f", OP_ATAN2, ufx|0x00400000, _DOMAIN, 0, 
                    EDOM, fx, fy, 2);
    }
  else if (ynan)
    {
      unsigned int ufy;
      GET_BITS_SP32(fy, ufy);
      return _handle_errorf("atan2f", OP_ATAN2, ufy|0x00400000, _DOMAIN, 0, 
                    EDOM, fx, fy, 2);
    }
  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;
}