mathf.c File Reference

#include <corecrt.h>
#include <wine/asm.h>

Include dependency graph for mathf.c:

Go to the source code of this file.

Functions
double __cdecl	sin (double)
double __cdecl	cos (double)
double __cdecl	tan (double)
double __cdecl	atan2 (double, double)
double __cdecl	exp (double)
double __cdecl	log (double)
double __cdecl	pow (double, double)
double __cdecl	sqrt (double)
double __cdecl	floor (double)
double __cdecl	ceil (double)
float __cdecl	powf (float, float)
double	exp2 (double x)
float	exp2f (float x)

Function Documentation

atan2()

double __cdecl atan2	(	double	y,
		double	x
	)

Definition at line 52 of file atan2.c.

{
  /* Arrays atan_jby256_lead and atan_jby256_tail contain
     leading and trailing parts respectively of precomputed
     values of atan(j/256), for j = 16, 17, ..., 256.
     atan_jby256_lead contains the first 21 bits of precision,
     and atan_jby256_tail contains a further 53 bits precision. */
 
  static const double atan_jby256_lead[  241] = {
    6.24187886714935302734e-02,  /* 0x3faff55b00000000 */
    6.63088560104370117188e-02,  /* 0x3fb0f99e00000000 */
    7.01969265937805175781e-02,  /* 0x3fb1f86d00000000 */
    7.40829110145568847656e-02,  /* 0x3fb2f71900000000 */
    7.79666304588317871094e-02,  /* 0x3fb3f59f00000000 */
    8.18479657173156738281e-02,  /* 0x3fb4f3fd00000000 */
    8.57268571853637695312e-02,  /* 0x3fb5f23200000000 */
    8.96031260490417480469e-02,  /* 0x3fb6f03b00000000 */
    9.34767723083496093750e-02,  /* 0x3fb7ee1800000000 */
    9.73475575447082519531e-02,  /* 0x3fb8ebc500000000 */
    1.01215422153472900391e-01,  /* 0x3fb9e94100000000 */
    1.05080246925354003906e-01,  /* 0x3fbae68a00000000 */
    1.08941912651062011719e-01,  /* 0x3fbbe39e00000000 */
    1.12800359725952148438e-01,  /* 0x3fbce07c00000000 */
    1.16655409336090087891e-01,  /* 0x3fbddd2100000000 */
    1.20507001876831054688e-01,  /* 0x3fbed98c00000000 */
    1.24354958534240722656e-01,  /* 0x3fbfd5ba00000000 */
    1.28199219703674316406e-01,  /* 0x3fc068d500000000 */
    1.32039666175842285156e-01,  /* 0x3fc0e6ad00000000 */
    1.35876297950744628906e-01,  /* 0x3fc1646500000000 */
    1.39708757400512695312e-01,  /* 0x3fc1e1fa00000000 */
    1.43537282943725585938e-01,  /* 0x3fc25f6e00000000 */
    1.47361397743225097656e-01,  /* 0x3fc2dcbd00000000 */
    1.51181221008300781250e-01,  /* 0x3fc359e800000000 */
    1.54996633529663085938e-01,  /* 0x3fc3d6ee00000000 */
    1.58807516098022460938e-01,  /* 0x3fc453ce00000000 */
    1.62613749504089355469e-01,  /* 0x3fc4d08700000000 */
    1.66415214538574218750e-01,  /* 0x3fc54d1800000000 */
    1.70211911201477050781e-01,  /* 0x3fc5c98100000000 */
    1.74003481864929199219e-01,  /* 0x3fc645bf00000000 */
    1.77790164947509765625e-01,  /* 0x3fc6c1d400000000 */
    1.81571602821350097656e-01,  /* 0x3fc73dbd00000000 */
    1.85347914695739746094e-01,  /* 0x3fc7b97b00000000 */
    1.89118742942810058594e-01,  /* 0x3fc8350b00000000 */
    1.92884206771850585938e-01,  /* 0x3fc8b06e00000000 */
    1.96644186973571777344e-01,  /* 0x3fc92ba300000000 */
    2.00398445129394531250e-01,  /* 0x3fc9a6a800000000 */
    2.04147100448608398438e-01,  /* 0x3fca217e00000000 */
    2.07889914512634277344e-01,  /* 0x3fca9c2300000000 */
    2.11626768112182617188e-01,  /* 0x3fcb169600000000 */
    2.15357661247253417969e-01,  /* 0x3fcb90d700000000 */
    2.19082474708557128906e-01,  /* 0x3fcc0ae500000000 */
    2.22801089286804199219e-01,  /* 0x3fcc84bf00000000 */
    2.26513504981994628906e-01,  /* 0x3fccfe6500000000 */
    2.30219483375549316406e-01,  /* 0x3fcd77d500000000 */
    2.33919143676757812500e-01,  /* 0x3fcdf11000000000 */
    2.37612247467041015625e-01,  /* 0x3fce6a1400000000 */
    2.41298794746398925781e-01,  /* 0x3fcee2e100000000 */
    2.44978547096252441406e-01,  /* 0x3fcf5b7500000000 */
    2.48651623725891113281e-01,  /* 0x3fcfd3d100000000 */
    2.52317905426025390625e-01,  /* 0x3fd025fa00000000 */
    2.55977153778076171875e-01,  /* 0x3fd061ee00000000 */
    2.59629487991333007812e-01,  /* 0x3fd09dc500000000 */
    2.63274669647216796875e-01,  /* 0x3fd0d97e00000000 */
    2.66912937164306640625e-01,  /* 0x3fd1151a00000000 */
    2.70543813705444335938e-01,  /* 0x3fd1509700000000 */
    2.74167299270629882812e-01,  /* 0x3fd18bf500000000 */
    2.77783632278442382812e-01,  /* 0x3fd1c73500000000 */
    2.81392335891723632812e-01,  /* 0x3fd2025500000000 */
    2.84993648529052734375e-01,  /* 0x3fd23d5600000000 */
    2.88587331771850585938e-01,  /* 0x3fd2783700000000 */
    2.92173147201538085938e-01,  /* 0x3fd2b2f700000000 */
    2.95751571655273437500e-01,  /* 0x3fd2ed9800000000 */
    2.99322128295898437500e-01,  /* 0x3fd3281800000000 */
    3.02884817123413085938e-01,  /* 0x3fd3627700000000 */
    3.06439399719238281250e-01,  /* 0x3fd39cb400000000 */
    3.09986352920532226562e-01,  /* 0x3fd3d6d100000000 */
    3.13524961471557617188e-01,  /* 0x3fd410cb00000000 */
    3.17055702209472656250e-01,  /* 0x3fd44aa400000000 */
    3.20578098297119140625e-01,  /* 0x3fd4845a00000000 */
    3.24092388153076171875e-01,  /* 0x3fd4bdee00000000 */
    3.27598333358764648438e-01,  /* 0x3fd4f75f00000000 */
    3.31095933914184570312e-01,  /* 0x3fd530ad00000000 */
    3.34585189819335937500e-01,  /* 0x3fd569d800000000 */
    3.38066101074218750000e-01,  /* 0x3fd5a2e000000000 */
    3.41538190841674804688e-01,  /* 0x3fd5dbc300000000 */
    3.45002174377441406250e-01,  /* 0x3fd6148400000000 */
    3.48457098007202148438e-01,  /* 0x3fd64d1f00000000 */
    3.51903676986694335938e-01,  /* 0x3fd6859700000000 */
    3.55341434478759765625e-01,  /* 0x3fd6bdea00000000 */
    3.58770608901977539062e-01,  /* 0x3fd6f61900000000 */
    3.62190723419189453125e-01,  /* 0x3fd72e2200000000 */
    3.65602254867553710938e-01,  /* 0x3fd7660700000000 */
    3.69004726409912109375e-01,  /* 0x3fd79dc600000000 */
    3.72398376464843750000e-01,  /* 0x3fd7d56000000000 */
    3.75782966613769531250e-01,  /* 0x3fd80cd400000000 */
    3.79158496856689453125e-01,  /* 0x3fd8442200000000 */
    3.82525205612182617188e-01,  /* 0x3fd87b4b00000000 */
    3.85882616043090820312e-01,  /* 0x3fd8b24d00000000 */
    3.89230966567993164062e-01,  /* 0x3fd8e92900000000 */
    3.92570018768310546875e-01,  /* 0x3fd91fde00000000 */
    3.95900011062622070312e-01,  /* 0x3fd9566d00000000 */
    3.99220705032348632812e-01,  /* 0x3fd98cd500000000 */
    4.02532100677490234375e-01,  /* 0x3fd9c31600000000 */
    4.05834197998046875000e-01,  /* 0x3fd9f93000000000 */
    4.09126996994018554688e-01,  /* 0x3fda2f2300000000 */
    4.12410259246826171875e-01,  /* 0x3fda64ee00000000 */
    4.15684223175048828125e-01,  /* 0x3fda9a9200000000 */
    4.18948888778686523438e-01,  /* 0x3fdad00f00000000 */
    4.22204017639160156250e-01,  /* 0x3fdb056400000000 */
    4.25449609756469726562e-01,  /* 0x3fdb3a9100000000 */
    4.28685665130615234375e-01,  /* 0x3fdb6f9600000000 */
    4.31912183761596679688e-01,  /* 0x3fdba47300000000 */
    4.35129165649414062500e-01,  /* 0x3fdbd92800000000 */
    4.38336372375488281250e-01,  /* 0x3fdc0db400000000 */
    4.41534280776977539062e-01,  /* 0x3fdc421900000000 */
    4.44722414016723632812e-01,  /* 0x3fdc765500000000 */
    4.47900772094726562500e-01,  /* 0x3fdcaa6800000000 */
    4.51069593429565429688e-01,  /* 0x3fdcde5300000000 */
    4.54228639602661132812e-01,  /* 0x3fdd121500000000 */
    4.57377910614013671875e-01,  /* 0x3fdd45ae00000000 */
    4.60517644882202148438e-01,  /* 0x3fdd791f00000000 */
    4.63647603988647460938e-01,  /* 0x3fddac6700000000 */
    4.66767549514770507812e-01,  /* 0x3fdddf8500000000 */
    4.69877958297729492188e-01,  /* 0x3fde127b00000000 */
    4.72978591918945312500e-01,  /* 0x3fde454800000000 */
    4.76069211959838867188e-01,  /* 0x3fde77eb00000000 */
    4.79150056838989257812e-01,  /* 0x3fdeaa6500000000 */
    4.82221126556396484375e-01,  /* 0x3fdedcb600000000 */
    4.85282421112060546875e-01,  /* 0x3fdf0ede00000000 */
    4.88333940505981445312e-01,  /* 0x3fdf40dd00000000 */
    4.91375446319580078125e-01,  /* 0x3fdf72b200000000 */
    4.94406938552856445312e-01,  /* 0x3fdfa45d00000000 */
    4.97428894042968750000e-01,  /* 0x3fdfd5e000000000 */
    5.00440597534179687500e-01,  /* 0x3fe0039c00000000 */
    5.03442764282226562500e-01,  /* 0x3fe01c3400000000 */
    5.06434917449951171875e-01,  /* 0x3fe034b700000000 */
    5.09417057037353515625e-01,  /* 0x3fe04d2500000000 */
    5.12389183044433593750e-01,  /* 0x3fe0657e00000000 */
    5.15351772308349609375e-01,  /* 0x3fe07dc300000000 */
    5.18304347991943359375e-01,  /* 0x3fe095f300000000 */
    5.21246910095214843750e-01,  /* 0x3fe0ae0e00000000 */
    5.24179458618164062500e-01,  /* 0x3fe0c61400000000 */
    5.27101993560791015625e-01,  /* 0x3fe0de0500000000 */
    5.30014991760253906250e-01,  /* 0x3fe0f5e200000000 */
    5.32917976379394531250e-01,  /* 0x3fe10daa00000000 */
    5.35810947418212890625e-01,  /* 0x3fe1255d00000000 */
    5.38693904876708984375e-01,  /* 0x3fe13cfb00000000 */
    5.41567325592041015625e-01,  /* 0x3fe1548500000000 */
    5.44430732727050781250e-01,  /* 0x3fe16bfa00000000 */
    5.47284126281738281250e-01,  /* 0x3fe1835a00000000 */
    5.50127506256103515625e-01,  /* 0x3fe19aa500000000 */
    5.52961349487304687500e-01,  /* 0x3fe1b1dc00000000 */
    5.55785179138183593750e-01,  /* 0x3fe1c8fe00000000 */
    5.58598995208740234375e-01,  /* 0x3fe1e00b00000000 */
    5.61403274536132812500e-01,  /* 0x3fe1f70400000000 */
    5.64197540283203125000e-01,  /* 0x3fe20de800000000 */
    5.66981792449951171875e-01,  /* 0x3fe224b700000000 */
    5.69756031036376953125e-01,  /* 0x3fe23b7100000000 */
    5.72520732879638671875e-01,  /* 0x3fe2521700000000 */
    5.75275897979736328125e-01,  /* 0x3fe268a900000000 */
    5.78021049499511718750e-01,  /* 0x3fe27f2600000000 */
    5.80756187438964843750e-01,  /* 0x3fe2958e00000000 */
    5.83481788635253906250e-01,  /* 0x3fe2abe200000000 */
    5.86197376251220703125e-01,  /* 0x3fe2c22100000000 */
    5.88903427124023437500e-01,  /* 0x3fe2d84c00000000 */
    5.91599464416503906250e-01,  /* 0x3fe2ee6200000000 */
    5.94285964965820312500e-01,  /* 0x3fe3046400000000 */
    5.96962928771972656250e-01,  /* 0x3fe31a5200000000 */
    5.99629878997802734375e-01,  /* 0x3fe3302b00000000 */
    6.02287292480468750000e-01,  /* 0x3fe345f000000000 */
    6.04934692382812500000e-01,  /* 0x3fe35ba000000000 */
    6.07573032379150390625e-01,  /* 0x3fe3713d00000000 */
    6.10201358795166015625e-01,  /* 0x3fe386c500000000 */
    6.12820148468017578125e-01,  /* 0x3fe39c3900000000 */
    6.15428924560546875000e-01,  /* 0x3fe3b19800000000 */
    6.18028640747070312500e-01,  /* 0x3fe3c6e400000000 */
    6.20618820190429687500e-01,  /* 0x3fe3dc1c00000000 */
    6.23198986053466796875e-01,  /* 0x3fe3f13f00000000 */
    6.25770092010498046875e-01,  /* 0x3fe4064f00000000 */
    6.28331184387207031250e-01,  /* 0x3fe41b4a00000000 */
    6.30883216857910156250e-01,  /* 0x3fe4303200000000 */
    6.33425712585449218750e-01,  /* 0x3fe4450600000000 */
    6.35958671569824218750e-01,  /* 0x3fe459c600000000 */
    6.38482093811035156250e-01,  /* 0x3fe46e7200000000 */
    6.40995979309082031250e-01,  /* 0x3fe4830a00000000 */
    6.43500804901123046875e-01,  /* 0x3fe4978f00000000 */
    6.45996093750000000000e-01,  /* 0x3fe4ac0000000000 */
    6.48482322692871093750e-01,  /* 0x3fe4c05e00000000 */
    6.50959014892578125000e-01,  /* 0x3fe4d4a800000000 */
    6.53426170349121093750e-01,  /* 0x3fe4e8de00000000 */
    6.55884265899658203125e-01,  /* 0x3fe4fd0100000000 */
    6.58332824707031250000e-01,  /* 0x3fe5111000000000 */
    6.60772323608398437500e-01,  /* 0x3fe5250c00000000 */
    6.63202762603759765625e-01,  /* 0x3fe538f500000000 */
    6.65623664855957031250e-01,  /* 0x3fe54cca00000000 */
    6.68035984039306640625e-01,  /* 0x3fe5608d00000000 */
    6.70438766479492187500e-01,  /* 0x3fe5743c00000000 */
    6.72832489013671875000e-01,  /* 0x3fe587d800000000 */
    6.75216674804687500000e-01,  /* 0x3fe59b6000000000 */
    6.77592277526855468750e-01,  /* 0x3fe5aed600000000 */
    6.79958820343017578125e-01,  /* 0x3fe5c23900000000 */
    6.82316303253173828125e-01,  /* 0x3fe5d58900000000 */
    6.84664726257324218750e-01,  /* 0x3fe5e8c600000000 */
    6.87004089355468750000e-01,  /* 0x3fe5fbf000000000 */
    6.89334869384765625000e-01,  /* 0x3fe60f0800000000 */
    6.91656589508056640625e-01,  /* 0x3fe6220d00000000 */
    6.93969249725341796875e-01,  /* 0x3fe634ff00000000 */
    6.96272850036621093750e-01,  /* 0x3fe647de00000000 */
    6.98567867279052734375e-01,  /* 0x3fe65aab00000000 */
    7.00854301452636718750e-01,  /* 0x3fe66d6600000000 */
    7.03131675720214843750e-01,  /* 0x3fe6800e00000000 */
    7.05400466918945312500e-01,  /* 0x3fe692a400000000 */
    7.07660198211669921875e-01,  /* 0x3fe6a52700000000 */
    7.09911346435546875000e-01,  /* 0x3fe6b79800000000 */
    7.12153911590576171875e-01,  /* 0x3fe6c9f700000000 */
    7.14387893676757812500e-01,  /* 0x3fe6dc4400000000 */
    7.16613292694091796875e-01,  /* 0x3fe6ee7f00000000 */
    7.18829631805419921875e-01,  /* 0x3fe700a700000000 */
    7.21037864685058593750e-01,  /* 0x3fe712be00000000 */
    7.23237514495849609375e-01,  /* 0x3fe724c300000000 */
    7.25428581237792968750e-01,  /* 0x3fe736b600000000 */
    7.27611064910888671875e-01,  /* 0x3fe7489700000000 */
    7.29785442352294921875e-01,  /* 0x3fe75a6700000000 */
    7.31950759887695312500e-01,  /* 0x3fe76c2400000000 */
    7.34108448028564453125e-01,  /* 0x3fe77dd100000000 */
    7.36257076263427734375e-01,  /* 0x3fe78f6b00000000 */
    7.38397598266601562500e-01,  /* 0x3fe7a0f400000000 */
    7.40530014038085937500e-01,  /* 0x3fe7b26c00000000 */
    7.42654323577880859375e-01,  /* 0x3fe7c3d300000000 */
    7.44770050048828125000e-01,  /* 0x3fe7d52800000000 */
    7.46877670288085937500e-01,  /* 0x3fe7e66c00000000 */
    7.48976707458496093750e-01,  /* 0x3fe7f79e00000000 */
    7.51068115234375000000e-01,  /* 0x3fe808c000000000 */
    7.53150939941406250000e-01,  /* 0x3fe819d000000000 */
    7.55226135253906250000e-01,  /* 0x3fe82ad000000000 */
    7.57292747497558593750e-01,  /* 0x3fe83bbe00000000 */
    7.59351730346679687500e-01,  /* 0x3fe84c9c00000000 */
    7.61402606964111328125e-01,  /* 0x3fe85d6900000000 */
    7.63445377349853515625e-01,  /* 0x3fe86e2500000000 */
    7.65480041503906250000e-01,  /* 0x3fe87ed000000000 */
    7.67507076263427734375e-01,  /* 0x3fe88f6b00000000 */
    7.69526004791259765625e-01,  /* 0x3fe89ff500000000 */
    7.71537303924560546875e-01,  /* 0x3fe8b06f00000000 */
    7.73540973663330078125e-01,  /* 0x3fe8c0d900000000 */
    7.75536537170410156250e-01,  /* 0x3fe8d13200000000 */
    7.77523994445800781250e-01,  /* 0x3fe8e17a00000000 */
    7.79504299163818359375e-01,  /* 0x3fe8f1b300000000 */
    7.81476497650146484375e-01,  /* 0x3fe901db00000000 */
    7.83441066741943359375e-01,  /* 0x3fe911f300000000 */
    7.85398006439208984375e-01}; /* 0x3fe921fb00000000 */
 
  static const double atan_jby256_tail[  241] = {
    2.13244638182005395671e-08,  /* 0x3e56e59fbd38db2c */
    3.89093864761712760656e-08,  /* 0x3e64e3aa54dedf96 */
    4.44780900009437454576e-08,  /* 0x3e67e105ab1bda88 */
    1.15344768460112754160e-08,  /* 0x3e48c5254d013fd0 */
    3.37271051945395312705e-09,  /* 0x3e2cf8ab3ad62670 */
    2.40857608736109859459e-08,  /* 0x3e59dca4bec80468 */
    1.85853810450623807768e-08,  /* 0x3e53f4b5ec98a8da */
    5.14358299969225078306e-08,  /* 0x3e6b9d49619d81fe */
    8.85023985412952486748e-09,  /* 0x3e43017887460934 */
    1.59425154214358432060e-08,  /* 0x3e511e3eca0b9944 */
    1.95139937737755753164e-08,  /* 0x3e54f3f73c5a332e */
    2.64909755273544319715e-08,  /* 0x3e5c71c8ae0e00a6 */
    4.43388037881231070144e-08,  /* 0x3e67cde0f86fbdc7 */
    2.14757072421821274557e-08,  /* 0x3e570f328c889c72 */
    2.61049792670754218852e-08,  /* 0x3e5c07ae9b994efe */
    7.81439350674466302231e-09,  /* 0x3e40c8021d7b1698 */
    3.60125207123751024094e-08,  /* 0x3e635585edb8cb22 */
    6.15276238179343767917e-08,  /* 0x3e70842567b30e96 */
    9.54387964641184285058e-08,  /* 0x3e799e811031472e */
    3.02789566851502754129e-08,  /* 0x3e6041821416bcee */
    1.16888650949870856331e-07,  /* 0x3e7f6086e4dc96f4 */
    1.07580956468653338863e-08,  /* 0x3e471a535c5f1b58 */
    8.33454265379535427653e-08,  /* 0x3e765f743fe63ca1 */
    1.10790279272629526068e-07,  /* 0x3e7dbd733472d014 */
    1.08394277896366207424e-07,  /* 0x3e7d18cc4d8b0d1d */
    9.22176086126841098800e-08,  /* 0x3e78c12553c8fb29 */
    7.90938592199048786990e-08,  /* 0x3e753b49e2e8f991 */
    8.66445407164293125637e-08,  /* 0x3e77422ae148c141 */
    1.40839973537092438671e-08,  /* 0x3e4e3ec269df56a8 */
    1.19070438507307600689e-07,  /* 0x3e7ff6754e7e0ac9 */
    6.40451663051716197071e-08,  /* 0x3e7131267b1b5aad */
    1.08338682076343674522e-07,  /* 0x3e7d14fa403a94bc */
    3.52999550187922736222e-08,  /* 0x3e62f396c089a3d8 */
    1.05983273930043077202e-07,  /* 0x3e7c731d78fa95bb */
    1.05486124078259553339e-07,  /* 0x3e7c50f385177399 */
    5.82167732281776477773e-08,  /* 0x3e6f41409c6f2c20 */
    1.08696483983403942633e-07,  /* 0x3e7d2d90c4c39ec0 */
    4.47335086122377542835e-08,  /* 0x3e680420696f2106 */
    1.26896287162615723528e-08,  /* 0x3e4b40327943a2e8 */
    4.06534471589151404531e-08,  /* 0x3e65d35e02f3d2a2 */
    3.84504846300557026690e-08,  /* 0x3e64a498288117b0 */
    3.60715006404807269080e-08,  /* 0x3e635da119afb324 */
    6.44725903165522722801e-08,  /* 0x3e714e85cdb9a908 */
    3.63749249976409461305e-08,  /* 0x3e638754e5547b9a */
    1.03901294413833913794e-07,  /* 0x3e7be40ae6ce3246 */
    6.25379756302167880580e-08,  /* 0x3e70c993b3bea7e7 */
    6.63984302368488828029e-08,  /* 0x3e71d2dd89ac3359 */
    3.21844598971548278059e-08,  /* 0x3e61476603332c46 */
    1.16030611712765830905e-07,  /* 0x3e7f25901bac55b7 */
    1.17464622142347730134e-07,  /* 0x3e7f881b7c826e28 */
    7.54604017965808996596e-08,  /* 0x3e7441996d698d20 */
    1.49234929356206556899e-07,  /* 0x3e8407ac521ea089 */
    1.41416924523217430259e-07,  /* 0x3e82fb0c6c4b1723 */
    2.13308065617483489011e-07,  /* 0x3e8ca135966a3e18 */
    5.04230937933302320146e-08,  /* 0x3e6b1218e4d646e4 */
    5.45874922281655519035e-08,  /* 0x3e6d4e72a350d288 */
    1.51849028914786868886e-07,  /* 0x3e84617e2f04c329 */
    3.09004308703769273010e-08,  /* 0x3e6096ec41e82650 */
    9.67574548184738317664e-08,  /* 0x3e79f91f25773e6e */
    4.02508285529322212824e-08,  /* 0x3e659c0820f1d674 */
    3.01222268096861091157e-08,  /* 0x3e602bf7a2df1064 */
    2.36189860670079288680e-07,  /* 0x3e8fb36bfc40508f */
    1.14095158111080887695e-07,  /* 0x3e7ea08f3f8dc892 */
    7.42349089746573467487e-08,  /* 0x3e73ed6254656a0e */
    5.12515583196230380184e-08,  /* 0x3e6b83f5e5e69c58 */
    2.19290391828763918102e-07,  /* 0x3e8d6ec2af768592 */
    3.83263512187553886471e-08,  /* 0x3e6493889a226f94 */
    1.61513486284090523855e-07,  /* 0x3e85ad8fa65279ba */
    5.09996743535589922261e-08,  /* 0x3e6b615784d45434 */
    1.23694037861246766534e-07,  /* 0x3e809a184368f145 */
    8.23367955351123783984e-08,  /* 0x3e761a2439b0d91c */
    1.07591766213053694014e-07,  /* 0x3e7ce1a65e39a978 */
    1.42789947524631815640e-07,  /* 0x3e832a39a93b6a66 */
    1.32347123024711878538e-07,  /* 0x3e81c3699af804e7 */
    2.17626067316598149229e-08,  /* 0x3e575e0f4e44ede8 */
    2.34454866923044288656e-07,  /* 0x3e8f77ced1a7a83b */
    2.82966370261766916053e-09,  /* 0x3e284e7f0cb1b500 */
    2.29300919890907632975e-07,  /* 0x3e8ec6b838b02dfe */
    1.48428270450261284915e-07,  /* 0x3e83ebf4dfbeda87 */
    1.87937408574313982512e-07,  /* 0x3e89397aed9cb475 */
    6.13685946813334055347e-08,  /* 0x3e707937bc239c54 */
    1.98585022733583817493e-07,  /* 0x3e8aa754553131b6 */
    7.68394131623752961662e-08,  /* 0x3e74a05d407c45dc */
    1.28119052312436745644e-07,  /* 0x3e8132231a206dd0 */
    7.02119104719236502733e-08,  /* 0x3e72d8ecfdd69c88 */
    9.87954793820636301943e-08,  /* 0x3e7a852c74218606 */
    1.72176752381034986217e-07,  /* 0x3e871bf2baeebb50 */
    1.12877225146169704119e-08,  /* 0x3e483d7db7491820 */
    5.33549829555851737993e-08,  /* 0x3e6ca50d92b6da14 */
    2.13833275710816521345e-08,  /* 0x3e56f5cde8530298 */
    1.16243518048290556393e-07,  /* 0x3e7f343198910740 */
    6.29926408369055877943e-08,  /* 0x3e70e8d241ccd80a */
    6.45429039328021963791e-08,  /* 0x3e71535ac619e6c8 */
    8.64001922814281933403e-08,  /* 0x3e77316041c36cd2 */
    9.50767572202325800240e-08,  /* 0x3e7985a000637d8e */
    5.80851497508121135975e-08,  /* 0x3e6f2f29858c0a68 */
    1.82350561135024766232e-07,  /* 0x3e8879847f96d909 */
    1.98948680587390608655e-07,  /* 0x3e8ab3d319e12e42 */
    7.83548663450197659846e-08,  /* 0x3e75088162dfc4c2 */
    3.04374234486798594427e-08,  /* 0x3e605749a1cd9d8c */
    2.76135725629797411787e-08,  /* 0x3e5da65c6c6b8618 */
    4.32610105454203065470e-08,  /* 0x3e6739bf7df1ad64 */
    5.17107515324127256994e-08,  /* 0x3e6bc31252aa3340 */
    2.82398327875841444660e-08,  /* 0x3e5e528191ad3aa8 */
    1.87482469524195595399e-07,  /* 0x3e8929d93df19f18 */
    2.97481891662714096139e-08,  /* 0x3e5ff11eb693a080 */
    9.94421570843584316402e-09,  /* 0x3e455ae3f145a3a0 */
    1.07056210730391848428e-07,  /* 0x3e7cbcd8c6c0ca82 */
    6.25589580466881163081e-08,  /* 0x3e70cb04d425d304 */
    9.56641013869464593803e-08,  /* 0x3e79adfcab5be678 */
    1.88056307148355440276e-07,  /* 0x3e893d90c5662508 */
    8.38850689379557880950e-08,  /* 0x3e768489bd35ff40 */
    5.01215865527674122924e-09,  /* 0x3e3586ed3da2b7e0 */
    1.74166095998522089762e-07,  /* 0x3e87604d2e850eee */
    9.96779574395363585849e-08,  /* 0x3e7ac1d12bfb53d8 */
    5.98432026368321460686e-09,  /* 0x3e39b3d468274740 */
    1.18362922366887577169e-07,  /* 0x3e7fc5d68d10e53c */
    1.86086833284154215946e-07,  /* 0x3e88f9e51884becb */
    1.97671457251348941011e-07,  /* 0x3e8a87f0869c06d1 */
    1.42447160717199237159e-07,  /* 0x3e831e7279f685fa */
    1.05504240785546574184e-08,  /* 0x3e46a8282f9719b0 */
    3.13335218371639189324e-08,  /* 0x3e60d2724a8a44e0 */
    1.96518418901914535399e-07,  /* 0x3e8a60524b11ad4e */
    2.17692035039173536059e-08,  /* 0x3e575fdf832750f0 */
    2.15613114426529981675e-07,  /* 0x3e8cf06902e4cd36 */
    5.68271098300441214948e-08,  /* 0x3e6e82422d4f6d10 */
    1.70331455823369124256e-08,  /* 0x3e524a091063e6c0 */
    9.17590028095709583247e-08,  /* 0x3e78a1a172dc6f38 */
    2.77266304112916566247e-07,  /* 0x3e929b6619f8a92d */
    9.37041937614656939690e-08,  /* 0x3e79274d9c1b70c8 */
    1.56116346368316796511e-08,  /* 0x3e50c34b1fbb7930 */
    4.13967433808382727413e-08,  /* 0x3e6639866c20eb50 */
    1.70164749185821616276e-07,  /* 0x3e86d6d0f6832e9e */
    4.01708788545600086008e-07,  /* 0x3e9af54def99f25e */
    2.59663539226050551563e-07,  /* 0x3e916cfc52a00262 */
    2.22007487655027469542e-07,  /* 0x3e8dcc1e83569c32 */
    2.90542250809644081369e-07,  /* 0x3e937f7a551ed425 */
    4.67720537666628903341e-07,  /* 0x3e9f6360adc98887 */
    2.79799803956772554802e-07,  /* 0x3e92c6ec8d35a2c1 */
    2.07344552327432547723e-07,  /* 0x3e8bd44df84cb036 */
    2.54705698692735196368e-07,  /* 0x3e9117cf826e310e */
    4.26848589539548450728e-07,  /* 0x3e9ca533f332cfc9 */
    2.52506723633552216197e-07,  /* 0x3e90f208509dbc2e */
    2.14684129933849704964e-07,  /* 0x3e8cd07d93c945de */
    3.20134822201596505431e-07,  /* 0x3e957bdfd67e6d72 */
    9.93537565749855712134e-08,  /* 0x3e7aab89c516c658 */
    3.70792944827917252327e-08,  /* 0x3e63e823b1a1b8a0 */
    1.41772749369083698972e-07,  /* 0x3e8307464a9d6d3c */
    4.22446601490198804306e-07,  /* 0x3e9c5993cd438843 */
    4.11818433724801511540e-07,  /* 0x3e9ba2fca02ab554 */
    1.19976381502605310519e-07,  /* 0x3e801a5b6983a268 */
    3.43703078571520905265e-08,  /* 0x3e6273d1b350efc8 */
    1.66128705555453270379e-07,  /* 0x3e864c238c37b0c6 */
    5.00499610023283006540e-08,  /* 0x3e6aded07370a300 */
    1.75105139941208062123e-07,  /* 0x3e878091197eb47e */
    7.70807146729030327334e-08,  /* 0x3e74b0f245e0dabc */
    2.45918607526895836121e-07,  /* 0x3e9080d9794e2eaf */
    2.18359020958626199345e-07,  /* 0x3e8d4ec242b60c76 */
    8.44342887976445333569e-09,  /* 0x3e4221d2f940caa0 */
    1.07506148687888629299e-07,  /* 0x3e7cdbc42b2bba5c */
    5.36544954316820904572e-08,  /* 0x3e6cce37bb440840 */
    3.39109101518396596341e-07,  /* 0x3e96c1d999cf1dd0 */
    2.60098720293920613340e-08,  /* 0x3e5bed8a07eb0870 */
    8.42678991664621455827e-08,  /* 0x3e769ed88f490e3c */
    5.36972237470183633197e-08,  /* 0x3e6cd41719b73ef0 */
    4.28192558171921681288e-07,  /* 0x3e9cbc4ac95b41b7 */
    2.71535491483955143294e-07,  /* 0x3e9238f1b890f5d7 */
    7.84094998145075780203e-08,  /* 0x3e750c4282259cc4 */
    3.43880599134117431863e-07,  /* 0x3e9713d2de87b3e2 */
    1.32878065060366481043e-07,  /* 0x3e81d5a7d2255276 */
    4.18046802627967629428e-07,  /* 0x3e9c0dfd48227ac1 */
    2.65042411765766019424e-07,  /* 0x3e91c964dab76753 */
    1.70383695347518643694e-07,  /* 0x3e86de56d5704496 */
    1.54096497259613515678e-07,  /* 0x3e84aeb71fd19968 */
    2.36543402412459813461e-07,  /* 0x3e8fbf91c57b1918 */
    4.38416350106876736790e-07,  /* 0x3e9d6bef7fbe5d9a */
    3.03892161339927775731e-07,  /* 0x3e9464d3dc249066 */
    3.31136771605664899240e-07,  /* 0x3e9638e2ec4d9073 */
    6.49494294526590682218e-08,  /* 0x3e716f4a7247ea7c */
    4.10423429887181345747e-09,  /* 0x3e31a0a740f1d440 */
    1.70831640869113847224e-07,  /* 0x3e86edbb0114a33c */
    1.10811512657909180966e-07,  /* 0x3e7dbee8bf1d513c */
    3.23677724749783611964e-07,  /* 0x3e95b8bdb0248f73 */
    3.55662734259192678528e-07,  /* 0x3e97de3d3f5eac64 */
    2.30102333489738219140e-07,  /* 0x3e8ee24187ae448a */
    4.47429004000738629714e-07,  /* 0x3e9e06c591ec5192 */
    7.78167135617329598659e-08,  /* 0x3e74e3861a332738 */
    9.90345291908535415737e-08,  /* 0x3e7a9599dcc2bfe4 */
    5.85800913143113728314e-08,  /* 0x3e6f732fbad43468 */
    4.57859062410871843857e-07,  /* 0x3e9eb9f573b727d9 */
    3.67993069723390929794e-07,  /* 0x3e98b212a2eb9897 */
    2.90836464322977276043e-07,  /* 0x3e9384884c167215 */
    2.51621574250131388318e-07,  /* 0x3e90e2d363020051 */
    2.75789824740652815545e-07,  /* 0x3e92820879fbd022 */
    3.88985776250314403593e-07,  /* 0x3e9a1ab9893e4b30 */
    1.40214080183768019611e-07,  /* 0x3e82d1b817a24478 */
    3.23451432223550478373e-08,  /* 0x3e615d7b8ded4878 */
    9.15979180730608444470e-08,  /* 0x3e78968f9db3a5e4 */
    3.44371402498640470421e-07,  /* 0x3e971c4171fe135f */
    3.40401897215059498077e-07,  /* 0x3e96d80f605d0d8c */
    1.06431813453707950243e-07,  /* 0x3e7c91f043691590 */
    1.46204238932338846248e-07,  /* 0x3e839f8a15fce2b2 */
    9.94610376972039046878e-09,  /* 0x3e455beda9d94b80 */
    2.01711528092681771039e-07,  /* 0x3e8b12c15d60949a */
    2.72027977986191568296e-07,  /* 0x3e924167b312bfe3 */
    2.48402602511693757964e-07,  /* 0x3e90ab8633070277 */
    1.58480011219249621715e-07,  /* 0x3e854554ebbc80ee */
    3.00372828113368713281e-08,  /* 0x3e60204aef5a4bb8 */
    3.67816204583541976394e-07,  /* 0x3e98af08c679cf2c */
    2.46169793032343824291e-07,  /* 0x3e90852a330ae6c8 */
    1.70080468270204253247e-07,  /* 0x3e86d3eb9ec32916 */
    1.67806717763872914315e-07,  /* 0x3e8685cb7fcbbafe */
    2.67715622006907942620e-07,  /* 0x3e91f751c1e0bd95 */
    2.14411342550299170574e-08,  /* 0x3e5705b1b0f72560 */
    4.11228221283669073277e-07,  /* 0x3e9b98d8d808ca92 */
    3.52311752396749662260e-08,  /* 0x3e62ea22c75cc980 */
    3.52718000397367821054e-07,  /* 0x3e97aba62bca0350 */
    4.38857387992911129814e-07,  /* 0x3e9d73833442278c */
    3.22574606753482540743e-07,  /* 0x3e95a5ca1fb18bf9 */
    3.28730371182804296828e-08,  /* 0x3e61a6092b6ecf28 */
    7.56672470607639279700e-08,  /* 0x3e744fd049aac104 */
    3.26750155316369681821e-09,  /* 0x3e2c114fd8df5180 */
    3.21724445362095284743e-07,  /* 0x3e95972f130feae5 */
    1.06639427371776571151e-07,  /* 0x3e7ca034a55fe198 */
    3.41020788139524715063e-07,  /* 0x3e96e2b149990227 */
    1.00582838631232552824e-07,  /* 0x3e7b00000294592c */
    3.68439433859276640065e-07,  /* 0x3e98b9bdc442620e */
    2.20403078342388012027e-07,  /* 0x3e8d94fdfabf3e4e */
    1.62841467098298142534e-07,  /* 0x3e85db30b145ad9a */
    2.25325348296680733838e-07,  /* 0x3e8e3e1eb95022b0 */
    4.37462238226421614339e-07,  /* 0x3e9d5b8b45442bd6 */
    3.52055880555040706500e-07,  /* 0x3e97a046231ecd2e */
    4.75614398494781776825e-07,  /* 0x3e9feafe3ef55232 */
    3.60998399033215317516e-07,  /* 0x3e9839e7bfd78267 */
    3.79292434611513945954e-08,  /* 0x3e645cf49d6fa900 */
    1.29859015528549300061e-08,  /* 0x3e4be3132b27f380 */
    3.15927546985474913188e-07,  /* 0x3e9533980bb84f9f */
    2.28533679887379668031e-08,  /* 0x3e5889e2ce3ba390 */
    1.17222541823553133877e-07,  /* 0x3e7f7778c3ad0cc8 */
    1.51991208405464415857e-07,  /* 0x3e846660cec4eba2 */
    1.56958239325240655564e-07}; /* 0x3e85110b4611a626 */
 
  /* Some constants and split constants. */
 
  static double pi = 3.1415926535897932e+00, /* 0x400921fb54442d18 */
             piby2 = 1.5707963267948966e+00, /* 0x3ff921fb54442d18 */
             piby4 = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */
       three_piby4 = 2.3561944901923449e+00, /* 0x4002d97c7f3321d2 */
           pi_head = 3.1415926218032836e+00, /* 0x400921fb50000000 */
           pi_tail = 3.1786509547056392e-08, /* 0x3e6110b4611a6263 */
        piby2_head = 1.5707963267948965e+00, /* 0x3ff921fb54442d18 */
        piby2_tail = 6.1232339957367660e-17; /* 0x3c91a62633145c07 */
 
  double u, v, vbyu, q1, q2, s, u1, vu1, u2, vu2, uu, c, r;
  unsigned int swap_vu, index, xzero, yzero, xnan, ynan, xinf, yinf;
  int m, xexp, yexp, diffexp;
 
  /* Find properties of arguments x and y. */
 
  unsigned long long ux, ui, 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 _handle_error("atan2", OP_ATAN2, ux|0x0008000000000000, _DOMAIN, 0,
                        EDOM, x, y, 2);
  else if (ynan)
    return _handle_error("atan2", OP_ATAN2, uy|0x0008000000000000, _DOMAIN, 0,
                        EDOM, x, y, 2);
  else if (yzero)
    { /* Zero y gives +-0 for positive x
         and +-pi for negative x */
      if (xneg)
    {
      if (yneg) return val_with_flags(-pi,AMD_F_INEXACT);
          else return val_with_flags(pi,AMD_F_INEXACT);
    }
      else return y;
    }
  else if (xzero)
    { /* Zero x gives +- pi/2
         depending on sign of y */
      if (yneg) return val_with_flags(-piby2,AMD_F_INEXACT);
      else val_with_flags(piby2,AMD_F_INEXACT);
    }
 
  /* Scale up both x and y if they are both below 1/4.
     This avoids any possible later denormalised arithmetic. */
 
  if ((xexp < 1021 && yexp < 1021))
    {
      scaleUpDouble1024(ux, &ux);
      scaleUpDouble1024(uy, &uy);
      PUT_BITS_DP64(ux, x);
      PUT_BITS_DP64(uy, y);
      xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64);
      yexp = (int)((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64);
      diffexp = yexp - xexp;
    }
 
  if (diffexp > 56)
    { /* abs(y)/abs(x) > 2^56 => arctan(x/y)
         is insignificant compared to piby2 */
      if (yneg) return val_with_flags(-piby2,AMD_F_INEXACT);
      else return val_with_flags(piby2,AMD_F_INEXACT);
    }
  else if (diffexp < -28 && (!xneg))
    { /* x positive and dominant over y by a factor of 2^28.
         In this case atan(y/x) is y/x to machine accuracy. */
 
      if (diffexp < -1074) /* Result underflows */
        {
          if (yneg)
            return val_with_flags(-0.0,AMD_F_INEXACT | AMD_F_UNDERFLOW);
          else
            return val_with_flags(0.0,AMD_F_INEXACT | AMD_F_UNDERFLOW);
        }
      else
        {
          if (diffexp < -1022)
            {
              /* 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 val_with_flags(y, AMD_F_INEXACT | AMD_F_UNDERFLOW);
          else
        return y;
             }
          else
            return y / x;
        }
    }
  else if (diffexp < -56 && xneg)
    { /* abs(x)/abs(y) > 2^56 and x < 0 => arctan(y/x)
         is insignificant compared to pi */
    if (yneg) return val_with_flags(-pi,AMD_F_INEXACT);
    else return val_with_flags(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 val_with_flags(-three_piby4,AMD_F_INEXACT);
      else return val_with_flags(three_piby4,AMD_F_INEXACT);
      }
    else
      {
      if (yneg) return val_with_flags(-piby4,AMD_F_INEXACT);
      else return val_with_flags(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);
      q1 = atan_jby256_lead[index-16];
      q2 = atan_jby256_tail[index-16];
      c = index*1./256;
      GET_BITS_DP64(u, ui);
      m = (int)((ui & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64;
      u = scaleDouble_2(u,-m);
      v = scaleDouble_2(v,-m);
      GET_BITS_DP64(u, ui);
      PUT_BITS_DP64(0xfffffffff8000000 & ui, u1); /* 26 leading bits of u */
      u2 = u - u1;
 
      r = ((v-c*u1)-c*u2)/(u+c*v);
 
      /* Polynomial approximation to atan(r) */
 
      s = r*r;
      q2 = q2 + r - r*(s * (0.33333333333224095522 - s*(0.19999918038989143496)));
    }
  else if (vbyu < 1.e-8)
    { /* v/u is small enough that atan(v/u) = v/u */
      q1 = 0.0;
      q2 = vbyu;
    }
  else  /* vbyu <= 0.0625 */
    {
      /* Small values of v/u. Use a series expansion
     computed carefully to minimise cancellation */
 
      GET_BITS_DP64(u, ui);
      PUT_BITS_DP64(0xffffffff00000000 & ui, u1);
      GET_BITS_DP64(vbyu, ui);
      PUT_BITS_DP64(0xffffffff00000000 & ui, vu1);
      u2 = u - u1;
      vu2 = vbyu - vu1;
 
      q1 = 0.0;
      s  = vbyu*vbyu;
      q2 = vbyu +
    ((((v - u1*vu1) - u2*vu1) - u*vu2)/u -
     (vbyu*s*(0.33333333333333170500 -
          s*(0.19999999999393223405 -
             s*(0.14285713561807169030 -
            s*(0.11110736283514525407 -
               s*(0.90029810285449784439E-01)))))));
    }
 
  /* Tidy-up according to which quadrant the arguments lie in */
 
  if (swap_vu) {q1 = piby2_head - q1; q2 = piby2_tail - q2;}
  if (xneg) {q1 = pi_head - q1; q2 = pi_tail - q2;}
  q1 = q1 + q2;
 
  if (yneg) q1 = - q1;
 
  return q1;
}

ceil()

double __cdecl ceil

(

double

x

)

Definition at line 18 of file ceil.c.

{
    /* Load the value as uint64 */
    unsigned long long u64 = *(unsigned long long*)&x;
 
    /* Check for NAN */
    if ((u64 & ~(1ULL << 63)) > 0x7FF0000000000000ull)
    {
        /* Set error bit */
        u64 |= 0x0008000000000000ull;
        return *(double*)&u64;
    }
 
    /* Check if x is positive */
    if ((u64 & (1ULL << 63)) == 0)
    {
        /* Check if it fits into an int64 */
        if (x < (double)_I64_MAX)
        {
            /* Cast to int64 to truncate towards 0. If this matches the
               input, return it as is, otherwise add 1 */
            double y = (double)(long long)x;
            return (x > y) ? y + 1 : y;
        }
        else
        {
            /* The exponent is larger than the fraction bits.
               This means the number is already an integer. */
            return x;
        }
    }
    else
    {
        /* Check if it fits into an int64 */
        if (x > (double)_I64_MIN)
        {
            /* Cast to int64 to truncate towards 0. */
            x = (double)(long long)x;
            return (x == 0.) ? -0.0 : x;
        }
        else
        {
            /* The exponent is larger than the fraction bits.
               This means the number is already an integer. */
            return x;
        }
    }
}

cos()

double __cdecl cos

(

double

x

)

Definition at line 21 of file cos.c.

{
    int quadrant;
    double x2, result;
 
    /* Calculate the quadrant */
    quadrant = (int)(x * (2./M_PI));
 
    /* Get offset inside quadrant */
    x = x - quadrant * (M_PI/2.);
 
    /* Normalize quadrant to [0..3] */
    quadrant = quadrant & 0x3;
 
    /* Fixup value for the generic function */
    x += cos_off_tbl[quadrant];
 
    /* Calculate the negative of the square of x */
    x2 = - (x * x);
 
    /* This is an unrolled taylor series using <PRECISION> iterations
     * Example with 4 iterations:
     * result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
     * To save multiplications and to keep the precision high, it's performed
     * like this:
     * result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
     */
 
    /* Start with 0, compiler will optimize this away */
    result = 0;
 
#if (PRECISION >= 10)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
    result *= x2;
#endif
#if (PRECISION >= 9)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
    result *= x2;
#endif
#if (PRECISION >= 8)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
    result *= x2;
#endif
#if (PRECISION >= 7)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
    result *= x2;
#endif
#if (PRECISION >= 6)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
    result *= x2;
#endif
#if (PRECISION >= 5)
    result += 1./(1.*2*3*4*5*6*7*8*9*10);
    result *= x2;
#endif
    result += 1./(1.*2*3*4*5*6*7*8);
    result *= x2;
 
    result += 1./(1.*2*3*4*5*6);
    result *= x2;
 
    result += 1./(1.*2*3*4);
    result *= x2;
 
    result += 1./(1.*2);
    result *= x2;
 
    result += 1;
 
    /* Apply correct sign */
    result *= cos_sign_tbl[quadrant];
 
    return result;
}

exp()

double __cdecl exp

(

double

)

exp2()

double exp2

(

double

x

)

Definition at line 68 of file mathf.c.

{ return pow(2.0, x); }

exp2f()

float exp2f

(

float

x

)

Definition at line 69 of file mathf.c.

{ return powf(2.0f, x); }

floor()

double __cdecl floor

(

double

x

)

Definition at line 18 of file floor.c.

{
    /* Load the value as uint64 */
    unsigned long long u64 = *(unsigned long long*)&x;
 
    /* Check for NAN */
    if ((u64 & ~(1ULL << 63)) > 0x7FF0000000000000ull)
    {
        /* Set error bit */
        u64 |= 0x0008000000000000ull;
        return *(double*)&u64;
    }
 
    /* Check if x is positive */
    if ((u64 & (1ULL << 63)) == 0)
    {
        /* Check if it fits into an int64 */
        if (x < (double)_I64_MAX)
        {
            /* Just cast to int64, which will truncate towards 0,
               which is what we want here.*/
            return (double)(long long)x;
        }
        else
        {
            /* The exponent is larger than the fraction bits.
               This means the number is already an integer. */
            return x;
        }
    }
    else
    {
        /* Check if it fits into an int64 */
        if (x > (double)_I64_MIN)
        {
            /* Check if it is -0 */
            if (x == -0.)
            {
                return -0.;
            }
 
            /* Cast to int64 to truncate towards 0. If this matches the
               input, return it as is, otherwise subtract 1 */
            double y = (double)(long long)x;
            return (x == y) ? y : y - 1;
        }
        else
        {
            /* The exponent is larger than the fraction bits.
               This means the number is already an integer. */
            return x;
        }
    }
}

log()

double __cdecl log

(

double

x

)

Definition at line 184 of file freeldr.c.

{
    __debugbreak();
    return 0.0;
}

pow()

double __cdecl pow	(	double	x,
		double	y
	)

Definition at line 178 of file freeldr.c.

{
    __debugbreak();
    return 0.0;
}

Referenced by exp2().

powf()

float __cdecl powf	(	float	x,
		float	y
	)

Definition at line 14 of file powf.c.

{
    return (float)pow((double)x, (double)y);
}

Referenced by exp2f().

sin()

double __cdecl sin

(

double

x

)

Definition at line 21 of file sin.c.

{
    int quadrant;
    double x2, result;
 
    /* Calculate the quadrant */
    quadrant = (int)(x * (2./M_PI));
 
    /* Get offset inside quadrant */
    x = x - quadrant * (M_PI/2.);
 
    /* Normalize quadrant to [0..3] */
    quadrant = (quadrant - 1) & 0x3;
 
    /* Fixup value for the generic function */
    x += sin_off_tbl[quadrant];
 
    /* Calculate the negative of the square of x */
    x2 = - (x * x);
 
    /* This is an unrolled taylor series using <PRECISION> iterations
     * Example with 4 iterations:
     * result = 1 - x^2/2! + x^4/4! - x^6/6! + x^8/8!
     * To save multiplications and to keep the precision high, it's performed
     * like this:
     * result = 1 - x^2 * (1/2! - x^2 * (1/4! - x^2 * (1/6! - x^2 * (1/8!))))
     */
 
    /* Start with 0, compiler will optimize this away */
    result = 0;
 
#if (PRECISION >= 10)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18*19*20);
    result *= x2;
#endif
#if (PRECISION >= 9)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17*18);
    result *= x2;
#endif
#if (PRECISION >= 8)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16);
    result *= x2;
#endif
#if (PRECISION >= 7)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12*13*14);
    result *= x2;
#endif
#if (PRECISION >= 6)
    result += 1./(1.*2*3*4*5*6*7*8*9*10*11*12);
    result *= x2;
#endif
#if (PRECISION >= 5)
    result += 1./(1.*2*3*4*5*6*7*8*9*10);
    result *= x2;
#endif
    result += 1./(1.*2*3*4*5*6*7*8);
    result *= x2;
 
    result += 1./(1.*2*3*4*5*6);
    result *= x2;
 
    result += 1./(1.*2*3*4);
    result *= x2;
 
    result += 1./(1.*2);
    result *= x2;
 
    result += 1;
 
    /* Apply correct sign */
    result *= sin_sign_tbl[quadrant];
 
    return result;
}

sqrt()

double __cdecl sqrt

(

double

x

)

Definition at line 5 of file sqrt.c.

{
    register union
    {
        __m128d x128d;
        __m128i x128i;
    } u ;
    register union
    {
        unsigned long long ullx;
        double dbl;
    } u2;
 
    /* Set the lower double-precision value of u to x.
       All that we want, is that the compiler understands that we have the
       function parameter in a register that we can address as an __m128.
       Sadly there is no obvious way to do that. If we use the union, VS will
       generate code to store xmm0 in memory and the read it into a GPR.
       We avoid memory access by using a direct move. But even here we won't
       get a simple MOVSD. We can either do:
       a) _mm_set_sd: move x into the lower part of an xmm register and zero
          out the upper part (XORPD+MOVSD)
       b) _mm_set1_pd: move x into the lower and higher part of an xmm register
         (MOVSD+UNPCKLPD)
       c) _mm_set_pd, which either generates a memory access, when we try to
          tell it to keep the upper 64 bits, or generate 2 MOVAPS + UNPCKLPD
       We choose a, which is probably the fastest.
    */
    u.x128d = _mm_set_sd(x);
 
    /* Move the contents of the lower 64 bit into a 64 bit GPR using MOVD */
    u2.ullx = _mm_cvtsi128_si64(u.x128i);
 
    /* Check for negative values */
    if (u2.ullx & 0x8000000000000000ULL)
    {
        /* Check if this is *really* negative and not just -0.0 */
        if (u2.ullx != 0x8000000000000000ULL)
        {
            /* Return -1.#IND00 */
            u2.ullx = 0xfff8000000000000ULL;
        }
 
        /* Return what we have */
        return u2.dbl;
    }
 
    /* Check if this is a NaN (bits 52-62 are 1, bit 0-61 are not all 0) or
       negative (bit 63 is 1) */
    if (u2.ullx > 0x7FF0000000000000ULL)
    {
        /* Set this bit. That's what MS function does. */
        u2.ullx |= 0x8000000000000ULL;
        return u2.dbl;
    }
 
    /* Calculate the square root. */
#ifdef _MSC_VER
    /* Another YAY for the MS compiler. There are 2 instructions we could use:
       SQRTPD (computes sqrt for 2 double values) or SQRTSD (computes sqrt for
       only the lower 64 bit double value). Obviously we only need 1. And on
       Some architectures SQRTPD is twice as slow as SQRTSD. On the other hand
       the MS compiler is stupid and always generates an additional MOVAPS
       instruction when SQRTSD is used. We choose to use SQRTPD here since on
       modern hardware it's as fast as SQRTSD. */
    u.x128d = _mm_sqrt_pd(u.x128d); // SQRTPD
#else
    u.x128d = _mm_sqrt_sd(u.x128d, u.x128d); // SQRTSD
#endif
 
    return u.x128d.m128d_f64[0];
}

tan()

double __cdecl tan

(

double

x

)

Definition at line 122 of file tan.c.

{
  double r, rr;
  int region, xneg;
 
  unsigned long long ux, ax;
  GET_BITS_DP64(x, ux);
  ax = (ux & ~SIGNBIT_DP64);
  if (ax <= 0x3fe921fb54442d18) /* abs(x) <= pi/4 */
    {
      if (ax < 0x3f20000000000000) /* abs(x) < 2.0^(-13) */
        {
          if (ax < 0x3e40000000000000) /* abs(x) < 2.0^(-27) */
        {
          if (ax == 0x0000000000000000) return x;
              else return val_with_flags(x, AMD_F_INEXACT);
        }
          else
            {
              /* Using a temporary variable prevents 64-bit VC++ from
                 rearranging
                    x + x*x*x*0.333333333333333333;
                 into
                    x * (1 + x*x*0.333333333333333333);
                 The latter results in an incorrectly rounded answer. */
              double tmp;
              tmp = x*x*x*0.333333333333333333;
              return x + tmp;
            }
        }
      else
        return tan_piby4(x, 0.0, 0);
    }
  else if ((ux & EXPBITS_DP64) == EXPBITS_DP64)
    {
      /* x is either NaN or infinity */
      if (ux & MANTBITS_DP64)
        /* x is NaN */
        return _handle_error("tan", OP_TAN, ux|0x0008000000000000, _DOMAIN, 0,
                            EDOM, x, 0.0, 1);
      else
        /* x is infinity. Return a NaN */
        return _handle_error("tan", OP_TAN, INDEFBITPATT_DP64, _DOMAIN, AMD_F_INVALID,
                            EDOM, x, 0.0, 1);
    }
  xneg = (ax != ux);
 
 
  if (xneg)
    x = -x;
 
  if (x < 5.0e5)
    {
      /* For these size arguments we can just carefully subtract the
         appropriate multiple of pi/2, using extra precision where
         x is close to an exact multiple of pi/2 */
      static const double
        twobypi =  6.36619772367581382433e-01, /* 0x3fe45f306dc9c883 */
        piby2_1  =  1.57079632673412561417e+00, /* 0x3ff921fb54400000 */
        piby2_1tail =  6.07710050650619224932e-11, /* 0x3dd0b4611a626331 */
        piby2_2  =  6.07710050630396597660e-11, /* 0x3dd0b4611a600000 */
        piby2_2tail =  2.02226624879595063154e-21, /* 0x3ba3198a2e037073 */
        piby2_3  =  2.02226624871116645580e-21, /* 0x3ba3198a2e000000 */
        piby2_3tail =  8.47842766036889956997e-32; /* 0x397b839a252049c1 */
      double t, rhead, rtail;
      int npi2;
      unsigned long long uy, xexp, expdiff;
      xexp  = ax >> EXPSHIFTBITS_DP64;
      /* How many pi/2 is x a multiple of? */
      if (ax <= 0x400f6a7a2955385e) /* 5pi/4 */
        {
          if (ax <= 0x4002d97c7f3321d2) /* 3pi/4 */
            npi2 = 1;
          else
            npi2 = 2;
        }
      else if (ax <= 0x401c463abeccb2bb) /* 9pi/4 */
        {
          if (ax <= 0x4015fdbbe9bba775) /* 7pi/4 */
            npi2 = 3;
          else
            npi2 = 4;
        }
      else
        npi2  = (int)(x * twobypi + 0.5);
      /* Subtract the multiple from x to get an extra-precision remainder */
      rhead  = x - npi2 * piby2_1;
      rtail  = npi2 * piby2_1tail;
      GET_BITS_DP64(rhead, uy);
      expdiff = xexp - ((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64);
      if (expdiff > 15)
        {
          /* The remainder is pretty small compared with x, which
             implies that x is a near multiple of pi/2
             (x matches the multiple to at least 15 bits) */
          t  = rhead;
          rtail  = npi2 * piby2_2;
          rhead  = t - rtail;
          rtail  = npi2 * piby2_2tail - ((t - rhead) - rtail);
          if (expdiff > 48)
            {
              /* x matches a pi/2 multiple to at least 48 bits */
              t  = rhead;
              rtail  = npi2 * piby2_3;
              rhead  = t - rtail;
              rtail  = npi2 * piby2_3tail - ((t - rhead) - rtail);
            }
        }
      r = rhead - rtail;
      rr = (rhead - r) - rtail;
      region = npi2 & 3;
    }
  else
    {
      /* Reduce x into range [-pi/4,pi/4] */
      __remainder_piby2(x, &r, &rr, &region);
    }
 
  if (xneg)
    return -tan_piby4(r, rr, region & 1);
  else
    return tan_piby4(r, rr, region & 1);
}