tests/tan.dat - master - niceSOFT/mpc

tests/tan.dat
150 строк9 KB
Andreas Enge
Add copyright year 2024.
10 сен 2024, 10:48
10 сен 2024, 10:482e0838c
# Data test file for mpc_tan.
#
# Copyright (C) 2008, 2010, 2011, 2024 INRIA
#
# This file is part of GNU MPC.
#
# GNU MPC 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 3 of the License, or (at your
#o ption) any later version.
#
# GNU MPC 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 this program. If not, see http://www.gnu.org/licenses/ .

# 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 0x1.921fb54442d18469898cc51701b839a252049c1114cf98e804177d4c76273644a29410f31c6809bbdf2a33679a748636605614dbe4be286e9fc26adadaa3848bc90b6aecc4bcfd8de89885d34c6fdad617feb96de80d6fdbdc70d7f6b5133f4b5d3e4822f8963fcc9250cca3d9c8b67b8400f97142c77e0b31b4906c38aba734d22c7f51fa499ebf06caba47b9475b2c38c5e6ac410aa5773daa520ee12d2cdace186a9c95793009e2e8d811943042f86520bc8c5c6d9c77c73cee58301d0c07364f0745d80f451f6b8abbe0de98a593bc5797ed2ab02e30732a92f9d52ad5ca2ba44c3131f40a202ae51cb51555885b5a662e1a08a0f46750aa4357be3974c9d9f70a08b1b7de1515d4e2aeba0c18fb672e1f0b4dc3c98f57eb5d19b61267ae3d1929c0944ac33b9dc7a44c35a5dcd7e25ff40db31410c9b0ec04e67d90d4c8a43e56302ef6401977c22eaef4c2bad8ee13118175b28dc411c49f40e9cb566287b6b7f9c1fa211c9705a2415242100234e478254f0fccaf10e334217b74b64d33864e30d5e9c4783528d0696c2a17b44b07d39455a899d1b77785b609bd1df25d1df8283f7d954c50f8b28e9cd780bb33652c9f412187444677430ca2b7cfda3ec252e19dc5af5f7037baec42e09039a00d224fab60b5532769d5311b1fbb830dff6fb9214d811e9be86b92680509246d87f56a 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 -0x4580CBF242683p-3 53 -0x1B3E8A3660D279p-3 N N
+ + 53 -0 53 +1  53 -0x1B3E8A3660D279p-3 53 0x4580CBF242683p-3 N N

# some values taken from ttan.c
+ + 53 0x1D02967C31CDB5 53 0x1D02967C31CDB5  53 0x3243F6A8885A30p-53 53 0x11A62633145C07p-106 N N
- + 53 0x1D02967C31CDB4 53 0x1D02967C31CDB5  53 0x3243F6A8885A30p-53 53 0x11A62633145C07p-106 D U
- - 53 0x1D02967C31CDB4 53 0x1D02967C31CDB4  53 0x3243F6A8885A30p-53 53 0x11A62633145C07p-106 Z D
- + 53 -0xB0BD0AA4A3B3D 53 -0xB0BD0AA4A3B3D  53 0x1921FB54442D19p-52 53 -0x172CECE675D1FDp-105 N N

# bug reported by Joseph Myers (07 Apr 2015)
- - 2 0 2 0.75 2 0x1p-10 2 0x1p1000 Z Z

# the following inputs are slow in MPC 1.3.1
# (missing return and ternary values have to be computed)
- + 24 0xd.d9be7p-418493112 24 0x1p+0 24 0x1.f0afa6p-104 24 0x1.14a3a4p+27 N N
+ + 24 -0x2.06619cp-8561088 24 -0x1p+0 24 0x1.1643e6p+4 24 -0x1.6a3032p+21 N N
+ + 24 0x9.9be8cp-8572004 24 0x1p+0 24 0x1.620458p-7 24 0x1.6aa65cp+21 N N
+ - 24 -0x7.b66c9p-33391980 24 -0x1p+0 24 -0x1.e9956p-4 24 -0x1.612c52p+23 N N
+ - 24 -0x4.f20ebp-374976548 24 -0x1p+0 24 -0x1.eae722p+50 24 -0x1.efbf1ap+26 N N
+ + 24 0xb.51234p-265969608 24 0x1p+0 24 0x1.d6425ap-5 24 0x1.5fa19ep+26 N N
+ + 24 -0xa.15bd1p-22703900 24 0x1p+0 24 -0x1.a7d67ap-7 24 0x1.e04266p+22 N N
+ + 24 -0x1.ac13a2p-10422968 24 0x1p+0 24 -0x1.5e41b2p+121 24 0x1.b8f52ap+21 N N
- + 24 0x0p+0 24 0x1p+0 24 0x1.870846p-1 24 0x1.386458p+61 N N