1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
|
# Data test file for mpc_tan.
# Copyright (C) INRIA, 2008, 2010
# This file is part of the MPC Library.
#
# The MPC Library is free software; you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation; either version 2.1 of the License, or (at your
# option) any later version.
#
# The MPC Library is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
# License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with the MPC Library; see the file COPYING.LIB. If not, write to
# the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
# MA 02111-1307, USA.
# See file sin.dat for the format description.
# Special values, following ISO C99 standard, Annex G,
# more precisely Section G.6.2.6 "The ctanh functions"
# since G.6 defines ctan(z) as -i * ctanh(i*z)
# Rule [conj]: tan(conj(z)) = conj(tan(z))
# Rule [odd]: tan(-z) = -tan(z)
# Note: for each rule, we cite the rule for tanh from C99,
# and below the translated rule for tan, using tanh(z) = i tan(-iz),
# thus tanh(a+i*b) = c+i*d translates to tan(b-i*a) = d-i*c
# tanh(+0 + i*0) = +0 + i*0
# tan (+0 - i*0) = +0 - i*0
0 0 2 +0 2 -0 2 +0 2 -0 N N
# [conj]: tan(+0 + i*0) = +0 + i*0
0 0 2 +0 2 +0 2 +0 2 +0 N N
# [odd]: tan(-0 + i*0) = -0 + i*0
0 0 2 -0 2 +0 2 -0 2 +0 N N
# [odd+conj]: tan(-0 - i*0) = -0 - i*0
0 0 2 -0 2 -0 2 -0 2 -0 N N
# tanh(x + i*inf) = nan + i*nan for finite x
# tan (inf - i*x) = nan + i*nan for finite x
0 0 2 nan 2 nan 2 +inf 2 +1 N N
0 0 2 nan 2 nan 2 +inf 2 +0 N N
0 0 2 nan 2 nan 2 +inf 2 -0 N N
0 0 2 nan 2 nan 2 +inf 2 -1 N N
# [conj] does not make sense since we already considered x < 0
# [odd]: tan(-inf + i*x) = nan + i*nan for finite x
0 0 2 nan 2 nan 2 -inf 2 +1 N N
0 0 2 nan 2 nan 2 -inf 2 +0 N N
0 0 2 nan 2 nan 2 -inf 2 -0 N N
0 0 2 nan 2 nan 2 -inf 2 -1 N N
# tanh(x + i*nan) = nan + i*nan for finite x
# tan (nan + i*x) = nan + i*nan for finite x
0 0 2 nan 2 nan 2 nan 2 1 N N
0 0 2 nan 2 nan 2 nan 2 +0 N N
0 0 2 nan 2 nan 2 nan 2 -0 N N
0 0 2 nan 2 nan 2 nan 2 -1 N N
# [conj] makes no sense since we already considered x < 0
# idem for [odd] since nan has no sign
# tanh(+inf + i*y) = 1 + i*0*sin(2y) for positive-signed finite y
# tan (y - i*inf) = 0*sin(2*y) - i*1 for positive-signed finite y
0 0 2 +0 2 -1 2 1 2 -inf N N
0 0 2 -0 2 -1 2 2 2 -inf N N
# [conj]: tan (y + i*inf) = 0*sin(2*y) + i*1
0 0 2 +0 2 +1 2 1 2 +inf N N
0 0 2 -0 2 +1 2 2 2 +inf N N
# [odd]: tan (-y + i*inf) = -0*sin(2*y) + i*1
0 0 2 -0 2 +1 2 -1 2 +inf N N
0 0 2 +0 2 +1 2 -2 2 +inf N N
# [odd+conj]: tan (-y - i*inf) = -0*sin(2*y) - i*1
0 0 2 -0 2 -1 2 -1 2 -inf N N
0 0 2 +0 2 -1 2 -2 2 -inf N N
# tanh(+inf + i*inf) = 1 +/- i*0 (unspecified sign of zero for C99)
# tan (+inf - i*inf) = +/-0 - i*1
0 0 2 0 2 -1 2 +inf 2 -inf N N
# [conj]: tan (+inf + i*inf) = +/-0 + i*1
0 0 2 0 2 +1 2 +inf 2 +inf N N
# [odd]: tan (-inf + i*inf) = +/-0 + i*1
0 0 2 0 2 +1 2 -inf 2 +inf N N
# [odd+conj]: tan (-inf - i*inf) = +/-0 - i*1
0 0 2 0 2 -1 2 -inf 2 -inf N N
# tanh(+inf + i*nan) = 1 +/- i*0 (unspecified sign of zero for C99)
# tan (nan - i*inf) = +/-0 - i*1
0 0 2 0 2 -1 2 nan 2 -inf N N
# [conj]: tan (nan + i*inf) = +/-0 + i*1
0 0 2 0 2 +1 2 nan 2 +inf N N
# [odd] = [conj] since nan has no sign, and -(+/-0) = +/-0
# tanh(nan + i*0) = nan + i*0
# tan(+0 + i*nan) = +0 + i*nan
0 0 2 +0 2 nan 2 +0 2 nan N N
# [conj] gives the same identity since nan has no sign
# [odd]: tan(-0 + i*nan) = -0 + i*nan
0 0 2 -0 2 nan 2 -0 2 nan N N
# tanh(nan + i*y) = nan + i*nan for all nonzero y
# tan (y + i*nan) = nan + i*nan
0 0 2 nan 2 nan 2 +inf 2 nan N N
0 0 2 nan 2 nan 2 +1 2 nan N N
0 0 2 nan 2 nan 2 -1 2 nan N N
0 0 2 nan 2 nan 2 -inf 2 nan N N
# [conj] gives no new relation since nan has no sign
# [odd] gives no new relation since we already considered y < 0
# tanh(nan + i*nan) = nan + i*nan
0 0 2 nan 2 nan 2 nan 2 nan N N
# corner case: op = atan (2^(-k) + i*2^k) for k=200 and k=1000
+ + 100 0x1@-50 100 0x1@50 1000 0x1.921fb54442d18469898cc51701b839a252049c1114cf98e804177d4c76273644a29410f31c6809bbdf2a33679a748636605614dbe4be286e9fc26adadaa3848bc90b6aecc4bcfd8de89884d34c6fdad617feb96de80d6fdbdc70d7f6b5133f4b5d3e4822f8963fcc9250cca3d9c8b67b8400f97142c77e0b31b4906c38 1000 0x1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555548888888888888888888888888888888888888888888888888a@-50 N N
+ + 100 0x1@-250 100 0x1@250 4000 0x1.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 4000 0x1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000055555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555556@-250 N N
# yet another absurd case: op = atan (2^200) + 2^(-200000)*I;
# expensive to compute
#- - 50 0x1@50 50 0x1@-49900 1000 0x1.921fb54442d18469898cc51701b839a252049c1114cf98e803177d4c76273644a29410f31c6809bbdf2a33679a748636605614dbe4be286e9fc26adadaa3848bc90b6aecc4bcfd8de8988628a1c5302b6d540ec33d62c53131c62d4c0a6894a0b2939d784deb9521e7a621f92f1e0bd0d9564ec6981cd3608709e5c18e 1000 0x1@-50000 N N
# corner case
- + 9 -0x9bp-51 9 -1 9 -0x16dp-8 9 -0x77p-3 N N
# huge values
+ - 53 -0 53 -1 53 0x4580CBF242683p-3 53 -0x1B3E8A3660D279p-3 N N
+ + 53 -0 53 +1 53 -0x1B3E8A3660D279p-3 53 0x4580CBF242683p-3 N N
|
