xref: /third_party/musl/libc-test/src/math/ucb/atan2.h (revision 570af302)
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36// that they be sent to fdlibm-comments@sunpro.sun.com.
37// atan2d(+-0,+anything but nan) is +-0
38T(RN,                  0x0p+0,                  0x0p+0,                  0x0p+0,          0x0p+0, 0)
39T(RN,                  0x0p+0,               0x1p-1074,                  0x0p+0,          0x0p+0, 0)
40T(RN,                  0x0p+0,               0x1p-1022,                  0x0p+0,          0x0p+0, 0)
41T(RN,                  0x0p+0, 0x1.fffffffffffffp+1023,                  0x0p+0,          0x0p+0, 0)
42T(RN,                  0x0p+0,                     inf,                  0x0p+0,          0x0p+0, 0)
43T(RN,                 -0x0p+0,                  0x0p+0,                 -0x0p+0,          0x0p+0, 0)
44T(RN,                 -0x0p+0,               0x1p-1074,                 -0x0p+0,          0x0p+0, 0)
45T(RN,                 -0x0p+0,               0x1p-1022,                 -0x0p+0,          0x0p+0, 0)
46T(RN,                 -0x0p+0, 0x1.fffffffffffffp+1023,                 -0x0p+0,          0x0p+0, 0)
47T(RN,                 -0x0p+0,                     inf,                 -0x0p+0,          0x0p+0, 0)
48T(RZ,                  0x0p+0,                  0x0p+0,                  0x0p+0,          0x0p+0, 0)
49T(RZ,                  0x0p+0,               0x1p-1074,                  0x0p+0,          0x0p+0, 0)
50T(RZ,                  0x0p+0,               0x1p-1022,                  0x0p+0,          0x0p+0, 0)
51T(RZ,                  0x0p+0, 0x1.fffffffffffffp+1023,                  0x0p+0,          0x0p+0, 0)
52T(RZ,                  0x0p+0,                     inf,                  0x0p+0,          0x0p+0, 0)
53T(RZ,                 -0x0p+0,                  0x0p+0,                 -0x0p+0,          0x0p+0, 0)
54T(RZ,                 -0x0p+0,               0x1p-1074,                 -0x0p+0,          0x0p+0, 0)
55T(RZ,                 -0x0p+0,               0x1p-1022,                 -0x0p+0,          0x0p+0, 0)
56T(RZ,                 -0x0p+0, 0x1.fffffffffffffp+1023,                 -0x0p+0,          0x0p+0, 0)
57T(RZ,                 -0x0p+0,                     inf,                 -0x0p+0,          0x0p+0, 0)
58T(RU,                  0x0p+0,                  0x0p+0,                  0x0p+0,          0x0p+0, 0)
59T(RU,                  0x0p+0,               0x1p-1074,                  0x0p+0,          0x0p+0, 0)
60T(RU,                  0x0p+0,               0x1p-1022,                  0x0p+0,          0x0p+0, 0)
61T(RU,                  0x0p+0, 0x1.fffffffffffffp+1023,                  0x0p+0,          0x0p+0, 0)
62T(RU,                  0x0p+0,                     inf,                  0x0p+0,          0x0p+0, 0)
63T(RU,                 -0x0p+0,                  0x0p+0,                 -0x0p+0,          0x0p+0, 0)
64T(RU,                 -0x0p+0,               0x1p-1074,                 -0x0p+0,          0x0p+0, 0)
65T(RU,                 -0x0p+0,               0x1p-1022,                 -0x0p+0,          0x0p+0, 0)
66T(RU,                 -0x0p+0, 0x1.fffffffffffffp+1023,                 -0x0p+0,          0x0p+0, 0)
67T(RU,                 -0x0p+0,                     inf,                 -0x0p+0,          0x0p+0, 0)
68T(RD,                  0x0p+0,                  0x0p+0,                  0x0p+0,          0x0p+0, 0)
69T(RD,                  0x0p+0,               0x1p-1074,                  0x0p+0,          0x0p+0, 0)
70T(RD,                  0x0p+0,               0x1p-1022,                  0x0p+0,          0x0p+0, 0)
71T(RD,                  0x0p+0, 0x1.fffffffffffffp+1023,                  0x0p+0,          0x0p+0, 0)
72T(RD,                  0x0p+0,                     inf,                  0x0p+0,          0x0p+0, 0)
73T(RD,                 -0x0p+0,                  0x0p+0,                 -0x0p+0,          0x0p+0, 0)
74T(RD,                 -0x0p+0,               0x1p-1074,                 -0x0p+0,          0x0p+0, 0)
75T(RD,                 -0x0p+0,               0x1p-1022,                 -0x0p+0,          0x0p+0, 0)
76T(RD,                 -0x0p+0, 0x1.fffffffffffffp+1023,                 -0x0p+0,          0x0p+0, 0)
77T(RD,                 -0x0p+0,                     inf,                 -0x0p+0,          0x0p+0, 0)
78// atan2d(+-0,-anything but nan) is +-pi
79T(RN,                  0x0p+0,                    -inf,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
80T(RN,                  0x0p+0,-0x1.fffffffffffffp+1023,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
81T(RN,                  0x0p+0,              -0x1p-1022,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
82T(RN,                  0x0p+0,              -0x1p-1074,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
83T(RN,                  0x0p+0,                 -0x0p+0,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
84T(RN,                 -0x0p+0,                    -inf,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
85T(RN,                 -0x0p+0,-0x1.fffffffffffffp+1023,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
86T(RN,                 -0x0p+0,              -0x1p-1022,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
87T(RN,                 -0x0p+0,              -0x1p-1074,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
88T(RN,                 -0x0p+0,                 -0x0p+0,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
89//  atan2d(+-anything but 0 and nan, 0) is +- pi/2
90T(RN,                     inf,                  0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
91T(RN,                     inf,                 -0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
92T(RN, 0x1.fffffffffffffp+1023,                  0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
93T(RN, 0x1.fffffffffffffp+1023,                 -0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
94T(RN,               0x1p-1022,                  0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
95T(RN,               0x1p-1022,                 -0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
96T(RN,               0x1p-1074,                  0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
97T(RN,               0x1p-1074,                 -0x0p+0,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
98T(RN,                    -inf,                  0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
99T(RN,                    -inf,                 -0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
100T(RN,-0x1.fffffffffffffp+1023,                  0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
101T(RN,-0x1.fffffffffffffp+1023,                 -0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
102T(RN,              -0x1p-1074,                  0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
103T(RN,              -0x1p-1074,                 -0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
104T(RN,              -0x1p-1022,                  0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
105T(RN,              -0x1p-1022,                 -0x0p+0,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
106// atan2d(big,small) :=: +-pi/2
107T(RN, 0x1.fffffffffffffp+1023,               0x1p-1022,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
108T(RN, 0x1.fffffffffffffp+1023,              -0x1p-1022,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
109T(RN,-0x1.fffffffffffffp+1023,               0x1p-1022,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
110T(RN,-0x1.fffffffffffffp+1023,              -0x1p-1022,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
111T(RZ, 0x1.fffffffffffffp+1023,               0x1p-1022,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
112T(RZ, 0x1.fffffffffffffp+1023,              -0x1p-1022,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
113T(RZ,-0x1.fffffffffffffp+1023,               0x1p-1022,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
114T(RZ,-0x1.fffffffffffffp+1023,              -0x1p-1022,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
115T(RU, 0x1.fffffffffffffp+1023,               0x1p-1022,    0x1.921fb54442d19p+0,   0x1.72cecep-1, INEXACT)
116T(RU, 0x1.fffffffffffffp+1023,              -0x1p-1022,    0x1.921fb54442d19p+0,   0x1.72cecep-1, INEXACT)
117T(RU,-0x1.fffffffffffffp+1023,               0x1p-1022,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
118T(RU,-0x1.fffffffffffffp+1023,              -0x1p-1022,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
119T(RD, 0x1.fffffffffffffp+1023,               0x1p-1022,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
120T(RD, 0x1.fffffffffffffp+1023,              -0x1p-1022,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
121T(RD,-0x1.fffffffffffffp+1023,               0x1p-1022,   -0x1.921fb54442d19p+0,  -0x1.72cecep-1, INEXACT)
122T(RD,-0x1.fffffffffffffp+1023,              -0x1p-1022,   -0x1.921fb54442d19p+0,  -0x1.72cecep-1, INEXACT)
123// atan2d(small,big) = small/big (big>0)
124T(RN,               0x1p-1022, 0x1.fffffffffffffp+1023,                  0x0p+0,         -0x0p+0, INEXACT|UNDERFLOW)
125T(RN,              -0x1p-1022, 0x1.fffffffffffffp+1023,                 -0x0p+0,          0x0p+0, INEXACT|UNDERFLOW)
126T(RN,               0x1p-1022,-0x1.fffffffffffffp+1023,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
127T(RN,              -0x1p-1022,-0x1.fffffffffffffp+1023,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
128T(RZ,               0x1p-1022, 0x1.fffffffffffffp+1023,                  0x0p+0,         -0x0p+0, INEXACT|UNDERFLOW)
129T(RZ,              -0x1p-1022, 0x1.fffffffffffffp+1023,                 -0x0p+0,          0x0p+0, INEXACT|UNDERFLOW)
130T(RZ,               0x1p-1022,-0x1.fffffffffffffp+1023,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
131T(RZ,              -0x1p-1022,-0x1.fffffffffffffp+1023,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
132T(RU,               0x1p-1022, 0x1.fffffffffffffp+1023,               0x1p-1074,          0x1p+0, INEXACT|UNDERFLOW)
133T(RU,              -0x1p-1022, 0x1.fffffffffffffp+1023,                 -0x0p+0,          0x0p+0, INEXACT|UNDERFLOW)
134T(RU,               0x1p-1022,-0x1.fffffffffffffp+1023,    0x1.921fb54442d19p+1,   0x1.72cecep-1, INEXACT)
135T(RU,              -0x1p-1022,-0x1.fffffffffffffp+1023,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
136T(RD,               0x1p-1022, 0x1.fffffffffffffp+1023,                  0x0p+0,         -0x0p+0, INEXACT|UNDERFLOW)
137T(RD,              -0x1p-1022, 0x1.fffffffffffffp+1023,              -0x1p-1074,         -0x1p+0, INEXACT|UNDERFLOW)
138T(RD,               0x1p-1022,-0x1.fffffffffffffp+1023,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
139T(RD,              -0x1p-1022,-0x1.fffffffffffffp+1023,   -0x1.921fb54442d19p+1,  -0x1.72cecep-1, INEXACT)
140// atan2d(+-x,+x) = +-pi/4 for normal x
141T(RN,               0x1p-1022,               0x1p-1022,    0x1.921fb54442d18p-1,  -0x1.1a6264p-2, INEXACT)
142T(RN,              -0x1p-1022,               0x1p-1022,   -0x1.921fb54442d18p-1,   0x1.1a6264p-2, INEXACT)
143T(RN, 0x1.fffffffffffffp+1023, 0x1.fffffffffffffp+1023,    0x1.921fb54442d18p-1,  -0x1.1a6264p-2, INEXACT)
144T(RN,-0x1.fffffffffffffp+1023, 0x1.fffffffffffffp+1023,   -0x1.921fb54442d18p-1,   0x1.1a6264p-2, INEXACT)
145// atan2d(+-x,-x) = +-3pi/4 for normal x
146T(RN,               0x1p-1022,              -0x1p-1022,    0x1.2d97c7f3321d2p+1,  -0x1.a79394p-3, INEXACT)
147T(RN,              -0x1p-1022,              -0x1p-1022,   -0x1.2d97c7f3321d2p+1,   0x1.a79394p-3, INEXACT)
148T(RN,                  0x1p+0,                 -0x1p+0,    0x1.2d97c7f3321d2p+1,  -0x1.a79394p-3, INEXACT)
149T(RN,                 -0x1p+0,                 -0x1p+0,   -0x1.2d97c7f3321d2p+1,   0x1.a79394p-3, INEXACT)
150T(RN, 0x1.fffffffffffffp+1023,-0x1.fffffffffffffp+1023,    0x1.2d97c7f3321d2p+1,  -0x1.a79394p-3, INEXACT)
151T(RN,-0x1.fffffffffffffp+1023,-0x1.fffffffffffffp+1023,   -0x1.2d97c7f3321d2p+1,   0x1.a79394p-3, INEXACT)
152// random arguments between -2.0 and 2.0
153T(RN,   -0x1.13284b2b5006dp-1,    0x1.6ca8dfb825911p+0,    -0x1.716d1fa13dd6p-2,  -0x1.31471ap-3, INEXACT)
154T(RN,    0x1.c2ca609de7505p+0,   -0x1.55f11fba96889p+0,    0x1.1c206d50867f1p+1,  -0x1.d982d2p-2, INEXACT)
155T(RN,   -0x1.15679e27084ddp-1,   -0x1.41e131b093c41p-4,   -0x1.b6ff43cc0fa03p+0,   0x1.428fe2p-3, INEXACT)
156T(RN,    0x1.281b0d18455f5p+0,    0x1.b5ce34a51b239p+0,    0x1.30789aa67a7b1p-1,   0x1.e13b2ap-2, INEXACT)
157T(RN,   -0x1.583481079de4dp-2,   -0x1.ea8223103b871p+0,   -0x1.7be5087e43d19p+1,   0x1.a6c422p-2, INEXACT)
158T(RN,   -0x1.aae17f24163e5p-1,    0x1.7a9da1468cce9p-4,   -0x1.75db7c098be45p+0,   0x1.e9c708p-2, INEXACT)
159T(RN,   -0x1.844fff258fcbdp+0,    0x1.6ca321ace7da1p+0,   -0x1.a237b131b62afp-1,  -0x1.d5b568p-2, INEXACT)
160T(RN,   -0x1.fe09befde0ed5p+0,   -0x1.ff6c7e8e5e899p+0,   -0x1.2dc43c18871b1p+1,   0x1.ece6e2p-7, INEXACT)
161T(RN,   -0x1.d24c81412d02dp-1,    0x1.29b6828273bd1p+0,   -0x1.5428a1a6caecfp-1,    0x1.9211bp-2, INEXACT)
162T(RN,    0x1.25ea7e8b7c6c5p-1,    0x1.f99598e193549p-1,    0x1.0d9c960b4dda9p-1,   -0x1.000c7p-3, INEXACT)
163// atan2d involve nan
164T(RN,                  0x0p+0,                     nan,                     nan,          0x0p+0, 0)
165T(RN,                  0x1p+0,                     nan,                     nan,          0x0p+0, 0)
166T(RN,                     nan,               0x1p-1074,                     nan,          0x0p+0, 0)
167T(RN,                     nan,-0x1.fffffffffffffp+1023,                     nan,          0x0p+0, 0)
168T(RN,                     nan,                     nan,                     nan,          0x0p+0, 0)
169T(RN,                     nan,                     nan,                     nan,          0x0p+0, 0)
170T(RZ,                  0x0p+0,                     nan,                     nan,          0x0p+0, 0)
171T(RZ,                  0x1p+0,                     nan,                     nan,          0x0p+0, 0)
172T(RZ,                     nan,               0x1p-1074,                     nan,          0x0p+0, 0)
173T(RZ,                     nan,-0x1.fffffffffffffp+1023,                     nan,          0x0p+0, 0)
174T(RZ,                     nan,                     nan,                     nan,          0x0p+0, 0)
175T(RZ,                     nan,                     nan,                     nan,          0x0p+0, 0)
176T(RU,                  0x0p+0,                     nan,                     nan,          0x0p+0, 0)
177T(RU,                  0x1p+0,                     nan,                     nan,          0x0p+0, 0)
178T(RU,                     nan,               0x1p-1074,                     nan,          0x0p+0, 0)
179T(RU,                     nan,-0x1.fffffffffffffp+1023,                     nan,          0x0p+0, 0)
180T(RU,                     nan,                     nan,                     nan,          0x0p+0, 0)
181T(RU,                     nan,                     nan,                     nan,          0x0p+0, 0)
182T(RD,                  0x0p+0,                     nan,                     nan,          0x0p+0, 0)
183T(RD,                  0x1p+0,                     nan,                     nan,          0x0p+0, 0)
184T(RD,                     nan,               0x1p-1074,                     nan,          0x0p+0, 0)
185T(RD,                     nan,-0x1.fffffffffffffp+1023,                     nan,          0x0p+0, 0)
186T(RD,                     nan,                     nan,                     nan,          0x0p+0, 0)
187T(RD,                     nan,                     nan,                     nan,          0x0p+0, 0)
188//  atan2d(+-(anything but inf and nan), +inf) is +-0
189T(RN,               0x1p-1074,                     inf,                  0x0p+0,          0x0p+0, 0)
190T(RN, 0x1.fffffffffffffp+1023,                     inf,                  0x0p+0,          0x0p+0, 0)
191T(RN,              -0x1p-1074,                     inf,                 -0x0p+0,          0x0p+0, 0)
192T(RN,-0x1.fffffffffffffp+1023,                     inf,                 -0x0p+0,          0x0p+0, 0)
193T(RZ,               0x1p-1074,                     inf,                  0x0p+0,          0x0p+0, 0)
194T(RZ, 0x1.fffffffffffffp+1023,                     inf,                  0x0p+0,          0x0p+0, 0)
195T(RZ,              -0x1p-1074,                     inf,                 -0x0p+0,          0x0p+0, 0)
196T(RZ,-0x1.fffffffffffffp+1023,                     inf,                 -0x0p+0,          0x0p+0, 0)
197T(RU,               0x1p-1074,                     inf,                  0x0p+0,          0x0p+0, 0)
198T(RU, 0x1.fffffffffffffp+1023,                     inf,                  0x0p+0,          0x0p+0, 0)
199T(RU,              -0x1p-1074,                     inf,                 -0x0p+0,          0x0p+0, 0)
200T(RU,-0x1.fffffffffffffp+1023,                     inf,                 -0x0p+0,          0x0p+0, 0)
201T(RD,               0x1p-1074,                     inf,                  0x0p+0,          0x0p+0, 0)
202T(RD, 0x1.fffffffffffffp+1023,                     inf,                  0x0p+0,          0x0p+0, 0)
203T(RD,              -0x1p-1074,                     inf,                 -0x0p+0,          0x0p+0, 0)
204T(RD,-0x1.fffffffffffffp+1023,                     inf,                 -0x0p+0,          0x0p+0, 0)
205//  atan2d(+-(anything but inf and nan), -inf) is +-pi
206T(RN,               0x1p-1074,                    -inf,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
207T(RN, 0x1.fffffffffffffp+1023,                    -inf,    0x1.921fb54442d18p+1,  -0x1.1a6264p-2, INEXACT)
208T(RN,              -0x1p-1074,                    -inf,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
209T(RN,-0x1.fffffffffffffp+1023,                    -inf,   -0x1.921fb54442d18p+1,   0x1.1a6264p-2, INEXACT)
210//  atan2d(+-inf,+inf ) is +-pi/4
211T(RN,                     inf,                     inf,    0x1.921fb54442d18p-1,  -0x1.1a6264p-2, INEXACT)
212T(RN,                    -inf,                     inf,   -0x1.921fb54442d18p-1,   0x1.1a6264p-2, INEXACT)
213//  atan2d(+-inf,-inf ) is +-3pi/4
214T(RN,                     inf,                    -inf,    0x1.2d97c7f3321d2p+1,  -0x1.a79394p-3, INEXACT)
215T(RN,                    -inf,                    -inf,   -0x1.2d97c7f3321d2p+1,   0x1.a79394p-3, INEXACT)
216//  atan2d(+-inf, (anything but,0,nan, and inf)) is +-pi/2
217T(RN,                     inf,               0x1p-1074,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
218T(RN,                     inf,              -0x1p-1074,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
219T(RN,                     inf, 0x1.fffffffffffffp+1023,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
220T(RN,                     inf,-0x1.fffffffffffffp+1023,    0x1.921fb54442d18p+0,  -0x1.1a6264p-2, INEXACT)
221T(RN,                    -inf,               0x1p-1074,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
222T(RN,                    -inf,              -0x1p-1074,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
223T(RN,                    -inf, 0x1.fffffffffffffp+1023,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
224T(RN,                    -inf,-0x1.fffffffffffffp+1023,   -0x1.921fb54442d18p+0,   0x1.1a6264p-2, INEXACT)
225