head 1.1; branch 1.1.1; access; symbols netbsd-11-0-RC4:1.1.1.2 netbsd-11-0-RC3:1.1.1.2 netbsd-11-0-RC2:1.1.1.2 netbsd-11-0-RC1:1.1.1.2 perseant-exfatfs-base-20250801:1.1.1.2 netbsd-11:1.1.1.2.0.14 netbsd-11-base:1.1.1.2 netbsd-10-1-RELEASE:1.1.1.2 perseant-exfatfs-base-20240630:1.1.1.2 perseant-exfatfs:1.1.1.2.0.12 perseant-exfatfs-base:1.1.1.2 netbsd-8-3-RELEASE:1.1.1.1 netbsd-9-4-RELEASE:1.1.1.2 netbsd-10-0-RELEASE:1.1.1.2 netbsd-10-0-RC6:1.1.1.2 netbsd-10-0-RC5:1.1.1.2 netbsd-10-0-RC4:1.1.1.2 netbsd-10-0-RC3:1.1.1.2 netbsd-10-0-RC2:1.1.1.2 netbsd-10-0-RC1:1.1.1.2 mpc-1-3-1:1.1.1.2 netbsd-10:1.1.1.2.0.10 netbsd-10-base:1.1.1.2 netbsd-9-3-RELEASE:1.1.1.2 mpc-1-2-1:1.1.1.2 cjep_sun2x-base1:1.1.1.2 cjep_sun2x:1.1.1.2.0.8 cjep_sun2x-base:1.1.1.2 cjep_staticlib_x-base1:1.1.1.2 netbsd-9-2-RELEASE:1.1.1.2 cjep_staticlib_x:1.1.1.2.0.6 cjep_staticlib_x-base:1.1.1.2 netbsd-9-1-RELEASE:1.1.1.2 mpc-1-2-0:1.1.1.2 phil-wifi-20200421:1.1.1.2 phil-wifi-20200411:1.1.1.2 is-mlppp:1.1.1.2.0.4 is-mlppp-base:1.1.1.2 phil-wifi-20200406:1.1.1.2 netbsd-8-2-RELEASE:1.1.1.1 netbsd-9-0-RELEASE:1.1.1.2 netbsd-9-0-RC2:1.1.1.2 netbsd-9-0-RC1:1.1.1.2 phil-wifi-20191119:1.1.1.2 netbsd-9:1.1.1.2.0.2 netbsd-9-base:1.1.1.2 phil-wifi-20190609:1.1.1.2 netbsd-8-1-RELEASE:1.1.1.1 netbsd-8-1-RC1:1.1.1.1 pgoyette-compat-merge-20190127:1.1.1.1.28.1 pgoyette-compat-20190127:1.1.1.2 pgoyette-compat-20190118:1.1.1.2 pgoyette-compat-1226:1.1.1.2 pgoyette-compat-1126:1.1.1.2 pgoyette-compat-1020:1.1.1.2 pgoyette-compat-0930:1.1.1.2 pgoyette-compat-0906:1.1.1.2 mpc-1-1-0:1.1.1.2 netbsd-7-2-RELEASE:1.1.1.1 pgoyette-compat-0728:1.1.1.1 netbsd-8-0-RELEASE:1.1.1.1 phil-wifi:1.1.1.1.0.30 phil-wifi-base:1.1.1.1 pgoyette-compat-0625:1.1.1.1 netbsd-8-0-RC2:1.1.1.1 pgoyette-compat-0521:1.1.1.1 pgoyette-compat-0502:1.1.1.1 pgoyette-compat-0422:1.1.1.1 netbsd-8-0-RC1:1.1.1.1 pgoyette-compat-0415:1.1.1.1 pgoyette-compat-0407:1.1.1.1 pgoyette-compat-0330:1.1.1.1 pgoyette-compat-0322:1.1.1.1 pgoyette-compat-0315:1.1.1.1 netbsd-7-1-2-RELEASE:1.1.1.1 pgoyette-compat:1.1.1.1.0.28 pgoyette-compat-base:1.1.1.1 netbsd-7-1-1-RELEASE:1.1.1.1 matt-nb8-mediatek:1.1.1.1.0.26 matt-nb8-mediatek-base:1.1.1.1 mpc-1-0-3:1.1.1.1 perseant-stdc-iso10646:1.1.1.1.0.24 perseant-stdc-iso10646-base:1.1.1.1 netbsd-8:1.1.1.1.0.22 netbsd-8-base:1.1.1.1 prg-localcount2-base3:1.1.1.1 prg-localcount2-base2:1.1.1.1 prg-localcount2-base1:1.1.1.1 prg-localcount2:1.1.1.1.0.20 prg-localcount2-base:1.1.1.1 pgoyette-localcount-20170426:1.1.1.1 bouyer-socketcan-base1:1.1.1.1 pgoyette-localcount-20170320:1.1.1.1 netbsd-7-1:1.1.1.1.0.18 netbsd-7-1-RELEASE:1.1.1.1 netbsd-7-1-RC2:1.1.1.1 netbsd-7-nhusb-base-20170116:1.1.1.1 bouyer-socketcan:1.1.1.1.0.16 bouyer-socketcan-base:1.1.1.1 pgoyette-localcount-20170107:1.1.1.1 netbsd-7-1-RC1:1.1.1.1 pgoyette-localcount-20161104:1.1.1.1 netbsd-7-0-2-RELEASE:1.1.1.1 localcount-20160914:1.1.1.1 netbsd-7-nhusb:1.1.1.1.0.14 netbsd-7-nhusb-base:1.1.1.1 pgoyette-localcount-20160806:1.1.1.1 pgoyette-localcount-20160726:1.1.1.1 pgoyette-localcount:1.1.1.1.0.12 pgoyette-localcount-base:1.1.1.1 netbsd-7-0-1-RELEASE:1.1.1.1 netbsd-7-0:1.1.1.1.0.10 netbsd-7-0-RELEASE:1.1.1.1 netbsd-7-0-RC3:1.1.1.1 netbsd-7-0-RC2:1.1.1.1 netbsd-7-0-RC1:1.1.1.1 tls-maxphys-base:1.1.1.1 tls-maxphys:1.1.1.1.0.8 netbsd-7:1.1.1.1.0.6 netbsd-7-base:1.1.1.1 yamt-pagecache:1.1.1.1.0.4 yamt-pagecache-base9:1.1.1.1 tls-earlyentropy:1.1.1.1.0.2 tls-earlyentropy-base:1.1.1.1 riastradh-xf86-video-intel-2-7-1-pre-2-21-15:1.1.1.1 riastradh-drm2-base3:1.1.1.1 mpc-1-0-1:1.1.1.1 mpc:1.1.1; locks; strict; comment @# @; 1.1 date 2013.11.28.10.32.39; author mrg; state Exp; branches 1.1.1.1; next ; commitid q22cPE2uoE8G02fx; 1.1.1.1 date 2013.11.28.10.32.39; author mrg; state Exp; branches 1.1.1.1.4.1 1.1.1.1.8.1 1.1.1.1.28.1 1.1.1.1.30.1; next 1.1.1.2; commitid q22cPE2uoE8G02fx; 1.1.1.2 date 2018.09.04.04.28.12; author mrg; state Exp; branches; next ; commitid oOC0vQcFoJw32KQA; 1.1.1.1.4.1 date 2013.11.28.10.32.39; author yamt; state dead; branches; next 1.1.1.1.4.2; commitid nx2BSsHy0NPeAxBx; 1.1.1.1.4.2 date 2014.05.22.14.09.14; author yamt; state Exp; branches; next ; commitid nx2BSsHy0NPeAxBx; 1.1.1.1.8.1 date 2013.11.28.10.32.39; author tls; state dead; branches; next 1.1.1.1.8.2; commitid jTnpym9Qu0o4R1Nx; 1.1.1.1.8.2 date 2014.08.20.00.00.02; author tls; state Exp; branches; next ; commitid jTnpym9Qu0o4R1Nx; 1.1.1.1.28.1 date 2018.09.06.06.53.44; author pgoyette; state Exp; branches; next ; commitid HCi1bXD317XIK0RA; 1.1.1.1.30.1 date 2019.06.10.22.02.25; author christos; state Exp; branches; next ; commitid jtc8rnCzWiEEHGqB; desc @@ 1.1 log @Initial revision @ text @# Data test file for mpc_tan. # # Copyright (C) 2008, 2010, 2011 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.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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 -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 @ 1.1.1.1 log @initial import of MPC 1.0.1 package. changes since 0.9: Changes in version 1.0.1: - Switched to automake 1.11.6, see https://lists.gnu.org/archive/html/automake/2012-07/msg00023.html - #14669: Fixed extraction of CC from gmp.h - Fixed case of intermediate zero real or imaginary part in mpc_fma, found by hydra with GMP_CHECK_RANDOMIZE=1346362345 Changes in version 1.0: - First release as a GNU package - License change: LGPLv3+ for code, GFDLv1.3+ (with no invariant sections) for documentation - 100% of all lines are covered by tests - Functions renamed: mpc_mul_2exp to mpc_mul_2ui, mpc_div_2exp to mpc_div_2ui - 0^0, which returned (NaN,NaN) previously, now returns (1,+0) - Removed compatibility with K&R compilers, untestable due to lack of such compilers - New functions: mpc_log10, mpc_mul_2si, mpc_div_2si - Speed-ups: - mpc_fma - Bug fixes: - mpc_div and mpc_norm now return a value indicating the effective rounding direction, as the other functions - mpc_mul, mpc_sqr and mpc_norm now return correct results even if there are over- or underflows during the computation - mpc_asin, mpc_proj, mpc_sqr: Wrong result when input variable has infinite part and equals output variable is corrected - mpc_fr_sub: Wrong return value for imaginary part is corrected @ text @@ 1.1.1.1.30.1 log @Sync with HEAD @ text @a135 3 # bug reported by Joseph Myers (07 Apr 2015) - - 2 0 2 0.75 2 0x1p-10 2 0x1p1000 Z Z @ 1.1.1.1.28.1 log @Sync with HEAD Resolve a couple of conflicts (result of the uimin/uimax changes) @ text @a135 3 # bug reported by Joseph Myers (07 Apr 2015) - - 2 0 2 0.75 2 0x1p-10 2 0x1p1000 Z Z @ 1.1.1.2 log @import MPC 1.1.0. from their NEWS: Changes in version 1.1.0: - Minimally required library versions: GMP 5.0.0 and MPFR 3.0.0 - Fixed issues with MPFR 4.0.0 - New functions: mpc_cmp_abs, mpc_rootofunity - Improved speed for corner cases of mpc_asin, mpc_sin, see http://lists.gforge.inria.fr/pipermail/mpc-discuss/2013-December/001266.html - Rewrite of the testing framework - New mpcbench tool, used with "make bench" - Fixed handling of over- and underflows with directed rounding in the "other direction" for mpc_cos, mpc_sin, mpc_exp and mpc_pow, see http://lists.gforge.inria.fr/pipermail/mpc-discuss/2015-March/001336.html - Fixed a bug in mpc_atan(0,y) with |y| near 1, see http://lists.gforge.inria.fr/pipermail/mpc-discuss/2017-March/001404.html @ text @a135 3 # bug reported by Joseph Myers (07 Apr 2015) - - 2 0 2 0.75 2 0x1p-10 2 0x1p1000 Z Z @ 1.1.1.1.8.1 log @file tan.dat was added on branch tls-maxphys on 2014-08-20 00:00:02 +0000 @ text @d1 135 @ 1.1.1.1.8.2 log @Rebase to HEAD as of a few days ago. @ text @a0 135 # Data test file for mpc_tan. # # Copyright (C) 2008, 2010, 2011 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.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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 -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 @ 1.1.1.1.4.1 log @file tan.dat was added on branch yamt-pagecache on 2014-05-22 14:09:14 +0000 @ text @d1 135 @ 1.1.1.1.4.2 log @sync with head. for a reference, the tree before this commit was tagged as yamt-pagecache-tag8. this commit was splitted into small chunks to avoid a limitation of cvs. ("Protocol error: too many arguments") @ text @a0 135 # Data test file for mpc_tan. # # Copyright (C) 2008, 2010, 2011 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.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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 -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 @