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tests/pow.dat
495 строк
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Andreas Enge
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25 июл 2025, 17:53
25 июл 2025, 17:53
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# Data file for mpc_pow. # # Copyright (C) 2009, 2011, 2012, 2014, 2015, 2016, 2024, 2025 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/ . # # For explanations on the file format, see add.dat. 0 0 53 +1 53 0 53 nan 53 +0 53 +0 53 +0 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 +0 53 -1 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 +1 53 +0 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 +1 53 +1 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 -1 53 +0 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 +inf 53 +0 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 +inf 53 +1 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 +inf 53 -1 N N 0 0 53 nan 53 nan 53 nan 53 +0 53 -inf 53 +0 N N 0 0 53 nan 53 nan 53 +inf 53 +0 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 +inf 53 +0 53 +0 53 -1 N N 0 0 53 inf 53 nan 53 +inf 53 +0 53 +1 53 +0 N N 0 0 53 +inf 53 nan 53 +inf 53 +0 53 +1 53 +1 N N 0 0 53 +inf 53 nan 53 +inf 53 +0 53 +1 53 -1 N N 0 0 53 0 53 0 53 +inf 53 +0 53 -1 53 +0 N N 0 0 53 0 53 0 53 +inf 53 +0 53 -1 53 +1 N N 0 0 53 0 53 0 53 +inf 53 +0 53 -1 53 -1 N N 0 0 53 nan 53 nan 53 +inf 53 +0 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 +inf 53 +0 53 nan 53 +1 N N 0 0 53 nan 53 nan 53 +inf 53 +0 53 nan 53 -1 N N 0 0 53 +inf 53 nan 53 +inf 53 +0 53 +inf 53 +0 N N 0 0 53 +inf 53 nan 53 +inf 53 +0 53 +inf 53 +1 N N 0 0 53 +inf 53 nan 53 +inf 53 +0 53 +inf 53 -1 N N 0 0 53 0 53 0 53 +inf 53 +0 53 -inf 53 +0 N N 0 0 53 0 53 0 53 +inf 53 +0 53 -inf 53 +1 N N 0 0 53 0 53 0 53 +inf 53 +0 53 -inf 53 -1 N N 0 0 53 nan 53 nan 53 +inf 53 +1 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 +inf 53 +1 53 +0 53 -1 N N 0 0 53 +inf 53 nan 53 +inf 53 +1 53 +1 53 +0 N N 0 0 53 +inf 53 nan 53 +inf 53 +1 53 +1 53 +1 N N 0 0 53 +inf 53 nan 53 +inf 53 +1 53 +1 53 -1 N N 0 0 53 0 53 0 53 +inf 53 +1 53 -1 53 +0 N N 0 0 53 0 53 0 53 +inf 53 +1 53 -1 53 +1 N N 0 0 53 0 53 0 53 +inf 53 +1 53 -1 53 -1 N N 0 0 53 nan 53 nan 53 +inf 53 +1 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 +inf 53 +1 53 nan 53 +1 N N 0 0 53 nan 53 nan 53 +inf 53 +1 53 nan 53 -1 N N 0 0 53 +inf 53 nan 53 +inf 53 +1 53 +inf 53 +0 N N 0 0 53 +inf 53 nan 53 +inf 53 +1 53 +inf 53 +1 N N 0 0 53 +inf 53 nan 53 +inf 53 +1 53 +inf 53 -1 N N 0 0 53 0 53 0 53 +inf 53 +1 53 -inf 53 +0 N N 0 0 53 0 53 0 53 +inf 53 +1 53 -inf 53 +1 N N 0 0 53 0 53 0 53 +inf 53 +1 53 -inf 53 -1 N N 0 0 53 nan 53 nan 53 +inf 53 -1 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 +inf 53 -1 53 +0 53 -1 N N 0 0 53 +inf 53 nan 53 +inf 53 -1 53 +1 53 +0 N N 0 0 53 +inf 53 nan 53 +inf 53 -1 53 +1 53 +1 N N 0 0 53 +inf 53 nan 53 +inf 53 -1 53 +1 53 -1 N N 0 0 53 0 53 0 53 +inf 53 -1 53 -1 53 +0 N N 0 0 53 0 53 0 53 +inf 53 -1 53 -1 53 +1 N N 0 0 53 0 53 0 53 +inf 53 -1 53 -1 53 -1 N N 0 0 53 nan 53 nan 53 +inf 53 -1 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 +inf 53 -1 53 nan 53 +1 N N 0 0 53 nan 53 nan 53 +inf 53 -1 53 nan 53 -1 N N 0 0 53 +inf 53 nan 53 +inf 53 -1 53 +inf 53 +0 N N 0 0 53 +inf 53 nan 53 +inf 53 -1 53 +inf 53 +1 N N 0 0 53 +inf 53 nan 53 +inf 53 -1 53 +inf 53 -1 N N 0 0 53 0 53 0 53 +inf 53 -1 53 -inf 53 +0 N N 0 0 53 0 53 0 53 +inf 53 -1 53 -inf 53 +1 N N 0 0 53 0 53 0 53 +inf 53 -1 53 -inf 53 -1 N N 0 0 53 nan 53 nan 53 -inf 53 +0 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 -inf 53 +0 53 +0 53 -1 N N 0 0 53 +inf 53 nan 53 -inf 53 +0 53 +1 53 +0 N N 0 0 53 +inf 53 nan 53 -inf 53 +0 53 +1 53 +1 N N 0 0 53 +inf 53 nan 53 -inf 53 +0 53 +1 53 -1 N N 0 0 53 0 53 0 53 -inf 53 +0 53 -1 53 +0 N N 0 0 53 0 53 0 53 -inf 53 +0 53 -1 53 +1 N N 0 0 53 0 53 0 53 -inf 53 +0 53 -1 53 -1 N N 0 0 53 nan 53 nan 53 -inf 53 +0 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 -inf 53 +0 53 nan 53 +1 N N 0 0 53 nan 53 nan 53 -inf 53 +0 53 nan 53 -1 N N 0 0 53 +inf 53 nan 53 -inf 53 +0 53 +inf 53 +0 N N 0 0 53 +inf 53 nan 53 -inf 53 +0 53 +inf 53 +1 N N 0 0 53 +inf 53 nan 53 -inf 53 +0 53 +inf 53 -1 N N 0 0 53 0 53 0 53 -inf 53 +0 53 -inf 53 +0 N N 0 0 53 0 53 0 53 -inf 53 +0 53 -inf 53 +1 N N 0 0 53 0 53 0 53 -inf 53 +0 53 -inf 53 -1 N N 0 0 53 nan 53 nan 53 -inf 53 +1 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 -inf 53 +1 53 +0 53 -1 N N 0 0 53 +inf 53 nan 53 -inf 53 +1 53 +1 53 +0 N N 0 0 53 +inf 53 nan 53 -inf 53 +1 53 +1 53 +1 N N 0 0 53 +inf 53 nan 53 -inf 53 +1 53 +1 53 -1 N N 0 0 53 0 53 0 53 -inf 53 +1 53 -1 53 +0 N N 0 0 53 0 53 0 53 -inf 53 +1 53 -1 53 +1 N N 0 0 53 0 53 0 53 -inf 53 +1 53 -1 53 -1 N N 0 0 53 nan 53 nan 53 -inf 53 +1 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 -inf 53 +1 53 nan 53 +1 N N 0 0 53 nan 53 nan 53 -inf 53 +1 53 nan 53 -1 N N 0 0 53 +inf 53 nan 53 -inf 53 +1 53 +inf 53 +0 N N 0 0 53 +inf 53 nan 53 -inf 53 +1 53 +inf 53 +1 N N 0 0 53 +inf 53 nan 53 -inf 53 +1 53 +inf 53 -1 N N 0 0 53 0 53 0 53 -inf 53 +1 53 -inf 53 +0 N N 0 0 53 0 53 0 53 -inf 53 +1 53 -inf 53 +1 N N 0 0 53 0 53 0 53 -inf 53 +1 53 -inf 53 -1 N N 0 0 53 nan 53 nan 53 -inf 53 -1 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 -inf 53 -1 53 +0 53 -1 N N 0 0 53 +inf 53 nan 53 -inf 53 -1 53 +1 53 +0 N N 0 0 53 +inf 53 nan 53 -inf 53 -1 53 +1 53 +1 N N 0 0 53 +inf 53 nan 53 -inf 53 -1 53 +1 53 -1 N N 0 0 53 0 53 0 53 -inf 53 -1 53 -1 53 +0 N N 0 0 53 0 53 0 53 -inf 53 -1 53 -1 53 +1 N N 0 0 53 0 53 0 53 -inf 53 -1 53 -1 53 -1 N N 0 0 53 nan 53 nan 53 -inf 53 -1 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 -inf 53 -1 53 nan 53 +1 N N 0 0 53 nan 53 nan 53 -inf 53 -1 53 nan 53 -1 N N 0 0 53 +inf 53 nan 53 -inf 53 -1 53 +inf 53 +0 N N 0 0 53 +inf 53 nan 53 -inf 53 -1 53 +inf 53 +1 N N 0 0 53 +inf 53 nan 53 -inf 53 -1 53 +inf 53 -1 N N 0 0 53 0 53 0 53 -inf 53 -1 53 -inf 53 +0 N N 0 0 53 0 53 0 53 -inf 53 -1 53 -inf 53 +1 N N 0 0 53 0 53 0 53 -inf 53 -1 53 -inf 53 -1 N N 0 0 53 1 53 +0 53 +0 53 +0 53 +0 53 +0 N N 0 0 53 1 53 +0 53 +0 53 +0 53 -0 53 +0 N N 0 0 53 1 53 +0 53 +0 53 -0 53 +0 53 +0 N N 0 0 53 1 53 +0 53 +0 53 -0 53 -0 53 +0 N N 0 0 53 1 53 +0 53 -0 53 +0 53 +0 53 +0 N N 0 0 53 1 53 +0 53 -0 53 +0 53 -0 53 +0 N N 0 0 53 1 53 +0 53 -0 53 -0 53 +0 53 +0 N N 0 0 53 1 53 +0 53 -0 53 -0 53 -0 53 +0 N N 0 0 53 1 53 +0 53 +0 53 +0 53 +0 53 -0 N N 0 0 53 1 53 +0 53 +0 53 +0 53 -0 53 -0 N N 0 0 53 1 53 +0 53 +0 53 -0 53 +0 53 -0 N N 0 0 53 1 53 +0 53 +0 53 -0 53 -0 53 -0 N N 0 0 53 1 53 +0 53 -0 53 +0 53 +0 53 -0 N N 0 0 53 1 53 +0 53 -0 53 +0 53 -0 53 -0 N N 0 0 53 1 53 +0 53 -0 53 -0 53 +0 53 -0 N N 0 0 53 1 53 +0 53 -0 53 -0 53 -0 53 -0 N N 0 0 53 nan 53 nan 53 +0 53 +0 53 +0 53 +1 N N 0 0 53 nan 53 nan 53 +0 53 +0 53 +0 53 -1 N N 0 0 53 0 53 0 53 +0 53 +0 53 +1 53 +0 N N 0 0 53 0 53 0 53 +0 53 +0 53 +1 53 +1 N N 0 0 53 0 53 0 53 +0 53 +0 53 +1 53 -1 N N 0 0 53 +inf 53 nan 53 +0 53 +0 53 -1 53 +0 N N 0 0 53 +inf 53 nan 53 +0 53 +0 53 -1 53 +1 N N 0 0 53 +inf 53 nan 53 +0 53 +0 53 -1 53 -1 N N 0 0 53 nan 53 nan 53 +0 53 +0 53 nan 53 +0 N N 0 0 53 nan 53 nan 53 +0 53 +0 53 nan 53 +1 N N 0 0 53 nan 53 nan 53 +0 53 +0 53 nan 53 -1 N N 0 0 53 0 53 0 53 +0 53 +0 53 +inf 53 +0 N N 0 0 53 0 53 0 53 +0 53 +0 53 +inf 53 +1 N N 0 0 53 0 53 0 53 +0 53 +0 53 +inf 53 -1 N N 0 0 53 +inf 53 nan 53 +0 53 +0 53 -inf 53 +0 N N 0 0 53 +inf 53 nan 53 +0 53 +0 53 -inf 53 +1 N N 0 0 53 +inf 53 nan 53 +0 53 +0 53 -inf 53 -1 N N # zeros with determined sign, see algorithms.tex # x^0 = +1 +sign(Im(x))*sign(Re(y))*0i when |x|=1 0 0 53 +1 53 +0 53 +0 53 +1 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 +0 53 +1 53 +0 53 +0 N D #round toward -oo 0 0 53 +1 53 +0 53 -0 53 +1 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 -1 53 +0 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 -1 53 -0 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 -0 53 -1 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 +0 53 -1 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 +0 53 +1 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 -0 53 +1 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 -1 53 +0 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 -1 53 -0 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 -0 53 -1 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +0 53 -1 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +0 53 +1 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 -0 53 +1 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 -1 53 +0 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 -1 53 -0 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 -0 53 -1 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 +0 53 -1 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 +0 53 +1 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 -0 53 +1 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 -1 53 +0 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 -1 53 -0 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 -0 53 -1 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 +0 53 -1 53 -0 53 -0 N N # x^0 = +1 +sign(Im(y))*0i when |x| > 1 0 0 53 +1 53 +0 53 +inf 53 +2 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 +inf 53 -0 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 +2 53 +inf 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 +2 53 +0 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 +0 53 +2 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 +0 53 +inf 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 -0 53 +2 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 -0 53 +inf 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 -5 53 +inf 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 -2 53 +0 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 -inf 53 +0 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 -inf 53 +3 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 +inf 53 -inf 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +inf 53 +0 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +inf 53 -2 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +2 53 -5 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +5 53 +0 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +0 53 -inf 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 -0 53 -inf 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 -5 53 -0 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +inf 53 -0 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +inf 53 -2 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 -inf 53 -inf 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 +inf 53 +0 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 +2 53 -5 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 +5 53 +0 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 +5 53 -0 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 +0 53 -2 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 -0 53 -2 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 -5 53 -0 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 -inf 53 -0 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 +inf 53 +inf 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 +2 53 +5 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 +2 53 +0 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 +2 53 -0 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 +0 53 +2 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 -0 53 +2 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 -5 53 +2 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 -5 53 +0 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 -inf 53 +inf 53 -0 53 -0 N N 0 0 53 +1 53 -0 53 -inf 53 +inf 53 -0 53 -0 N N # x^0 = +1 -sign(Im(y))*0i when 1 > |x| > 0 0 0 53 +1 53 -0 53 +0.5 53 -0.5 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 +0.5 53 +0 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 +0.5 53 -0 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 -0.5 53 -0 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 +0 53 -0.5 53 +0 53 +0 N N 0 0 53 +1 53 -0 53 -0 53 -0.5 53 +0 53 +0 N N 0 0 53 +1 53 +0 53 +0.5 53 +0.5 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 +0.5 53 +0 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 +0.5 53 -0 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 -0.5 53 +0 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 +0 53 +0.5 53 +0 53 -0 N N 0 0 53 +1 53 +0 53 -0 53 +0.5 53 +0 53 -0 N N 0 0 53 +1 53 -0 53 +0.5 53 +0.5 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 +0.5 53 +0 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 +0.5 53 -0 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 -0.5 53 -0 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 +0 53 +0.5 53 -0 53 +0 N N 0 0 53 +1 53 -0 53 -0 53 +0.5 53 -0 53 +0 N N 0 0 53 +1 53 +0 53 +0.5 53 -0.5 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 +0.5 53 +0 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 +0.5 53 -0 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 -0.5 53 -0 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 +0 53 -0.5 53 -0 53 -0 N N 0 0 53 +1 53 +0 53 -0 53 -0.5 53 -0 53 -0 N N # determined sign of imaginary part in pure real powers 0 0 53 +9 53 +0 53 +3 53 +0 53 +2 53 +0 N N 0 0 53 +9 53 -0 53 +3 53 -0 53 +2 53 -0 N N 0 0 53 0.25 53 +0 53 +2 53 -0 53 -2 53 +0 N N 0 0 53 0.25 53 -0 53 +2 53 +0 53 -2 53 -0 N N 0 0 53 +1 53 +0 53 +1 53 +0 53 +4 53 +0 N N 0 0 53 +1 53 +0 53 +1 53 +0 53 +4 53 -0 N N 0 0 53 +1 53 -0 53 +1 53 -0 53 +4 53 +0 N N 0 0 53 +1 53 -0 53 +1 53 -0 53 +4 53 -0 N N 0 0 53 +1 53 +0 53 +1 53 -0 53 -4 53 +0 N N 0 0 53 +1 53 +0 53 +1 53 -0 53 -4 53 -0 N N 0 0 53 +1 53 -0 53 +1 53 +0 53 -4 53 +0 N N 0 0 53 +1 53 -0 53 +1 53 +0 53 -4 53 -0 N N 0 0 53 0.25 53 +0 53 +0.5 53 +0 53 +2 53 -0 N N 0 0 53 0.25 53 -0 53 +0.5 53 -0 53 +2 53 +0 N N 0 0 53 +4 53 +0 53 +0.5 53 -0 53 -2 53 -0 N N 0 0 53 +4 53 -0 53 +0.5 53 +0 53 -2 53 +0 N N # pure real power with nondetermined sign in imaginary part 0 0 53 1 53 0 53 +2 53 -1 53 +0 53 +0 N N 0 0 53 1 53 0 53 -2 53 -1 53 +0 53 +0 N N 0 0 53 1 53 0 53 -2 53 -0 53 +0 53 +0 N N 0 0 53 1 53 0 53 +0.5 53 +0.5 53 +0 53 +0 N N 0 0 53 1 53 0 53 -0.5 53 +0.5 53 +0 53 +0 N N 0 0 53 1 53 0 53 -0.5 53 +0 53 +0 53 +0 N N 0 0 53 1 53 0 53 +0 53 +0.5 53 +0 53 +0 N N 0 0 53 1 53 0 53 -0 53 +0.5 53 +0 53 +0 N N 0 0 53 1 53 0 53 -0 53 -4 53 +0 53 +0 N N 0 0 53 1 53 0 53 +0 53 -4 53 +0 53 +0 N N 0 0 53 1 53 0 53 -1 53 -0 53 +0 53 +0 N N 0 0 53 1 53 0 53 -1 53 +0 53 +0 53 +0 N N 0 0 53 1 53 0 53 +2 53 -1 53 -0 53 -0 N N 0 0 53 1 53 0 53 -2 53 -1 53 -0 53 -0 N N 0 0 53 1 53 0 53 -2 53 -0 53 -0 53 -0 N N 0 0 53 1 53 0 53 +0.5 53 +0.5 53 -0 53 -0 N N 0 0 53 1 53 0 53 -0.5 53 +0.5 53 -0 53 -0 N N 0 0 53 1 53 0 53 -0.5 53 +0 53 -0 53 -0 N N 0 0 53 1 53 0 53 +0 53 +0.5 53 -0 53 -0 N N 0 0 53 1 53 0 53 -0 53 +0.5 53 -0 53 -0 N N 0 0 53 1 53 0 53 -0 53 -4 53 -0 53 -0 N N 0 0 53 1 53 0 53 +0 53 -4 53 -0 53 -0 N N 0 0 53 1 53 0 53 -1 53 -0 53 -0 53 -0 N N 0 0 53 1 53 0 53 -1 53 +0 53 -0 53 -0 N N 0 0 53 1 53 0 53 +2 53 +1 53 -0 53 +0 N N 0 0 53 1 53 0 53 -2 53 +1 53 -0 53 +0 N N 0 0 53 1 53 0 53 -2 53 +0 53 -0 53 +0 N N 0 0 53 1 53 0 53 +0.5 53 -0.5 53 -0 53 +0 N N 0 0 53 1 53 0 53 -0.5 53 -0.5 53 -0 53 +0 N N 0 0 53 1 53 0 53 -0.5 53 -0 53 -0 53 +0 N N 0 0 53 1 53 0 53 +0 53 +5 53 -0 53 +0 N N 0 0 53 1 53 0 53 -0 53 +5 53 -0 53 +0 N N 0 0 53 1 53 0 53 -0 53 -0.5 53 -0 53 +0 N N 0 0 53 1 53 0 53 +0 53 -0.5 53 -0 53 +0 N N 0 0 53 1 53 0 53 -1 53 -0 53 -0 53 +0 N N 0 0 53 1 53 0 53 -1 53 +0 53 -0 53 +0 N N 0 0 53 1 53 0 53 +2 53 +1 53 +0 53 -0 N N 0 0 53 1 53 0 53 -2 53 +1 53 +0 53 -0 N N 0 0 53 1 53 0 53 -2 53 +0 53 +0 53 -0 N N 0 0 53 1 53 0 53 +0.5 53 -0.5 53 +0 53 -0 N N 0 0 53 1 53 0 53 -0.5 53 -0.5 53 +0 53 -0 N N 0 0 53 1 53 0 53 -0.5 53 -0 53 +0 53 -0 N N 0 0 53 1 53 0 53 +0 53 +5 53 +0 53 -0 N N 0 0 53 1 53 0 53 -0 53 +5 53 +0 53 -0 N N 0 0 53 1 53 0 53 -0 53 -0.5 53 +0 53 -0 N N 0 0 53 1 53 0 53 +0 53 -0.5 53 +0 53 -0 N N 0 0 53 1 53 0 53 -1 53 -0 53 +0 53 -0 N N 0 0 53 1 53 0 53 -1 53 +0 53 +0 53 -0 N N 0 0 53 4 53 0 53 +2 53 -0 53 +2 53 +0 N N 0 0 53 1 53 0 53 +1 53 +0 53 +2 53 +0 N N 0 0 53 1 53 0 53 +1 53 +0 53 +2 53 -0 N N 0 0 53 4 53 0 53 +2 53 +0 53 +2 53 -0 N N 0 0 53 1 53 0 53 +1 53 -0 53 +2 53 +0 N N 0 0 53 1 53 0 53 +1 53 -0 53 +2 53 -0 N N 0 0 53 +.25 53 0 53 +2 53 +0 53 -2 53 +0 N N 0 0 53 1 53 0 53 +1 53 +0 53 -2 53 +0 N N 0 0 53 1 53 0 53 +1 53 +0 53 -2 53 -0 N N 0 0 53 +.25 53 0 53 +2 53 -0 53 -2 53 -0 N N 0 0 53 1 53 0 53 +1 53 -0 53 -2 53 +0 N N 0 0 53 1 53 0 53 +1 53 -0 53 -2 53 -0 N N # when (+/-1 +/-0i)^y is pure real 0 0 53 1 53 0 53 +1 53 -0 53 -2 53 +1 N N 0 0 53 1 53 0 53 +1 53 -0 53 -1 53 +2 N N 0 0 53 1 53 0 53 +1 53 -0 53 -0 53 +1 N N - 0 53 +0x10BBEEE9177E19p-43 53 0 53 -1 53 -0 53 -0 53 +2 N N + 0 53 +0x1E989F5D6DFF5Cp-62 53 0 53 -1 53 +0 53 +0 53 +2 N N 0 0 53 1 53 0 53 +1 53 +0 53 +0 53 +2 N N 0 0 53 1 53 0 53 +1 53 +0 53 +2 53 +2 N N 0 0 53 1 53 0 53 +1 53 +0 53 +0 53 +2 N N 0 0 53 1 53 0 53 +1 53 +0 53 -1 53 -1 N N 0 0 53 1 53 0 53 +1 53 +0 53 -0 53 -1 N N + 0 53 +0x1724046EB0933Ap-48 53 0 53 -1 53 +0 53 -0 53 -1 N N 0 0 53 1 53 0 53 +1 53 -0 53 +0 53 -1 N N + 0 53 +0x1620227B598EF9p-57 53 0 53 -1 53 -0 53 +0 53 -1 N N 0 0 53 1 53 0 53 +1 53 -0 53 +2 53 -3 N N + 0 53 +0x1D4102BC3F7D4Cp-71 53 0 53 -1 53 +0 53 +0 53 +4 N N + 0 53 +0x1724046EB0933Ap-48 53 0 53 -1 53 -0 53 -0 53 +1 N N # when (0 +/-i)^y is pure real + 0 53 +0x1724046EB0933Ap-48 53 0 53 -0 53 -1 53 -0 53 +2 N N - 0 53 +0x1BD4567B975381p-46 53 0 53 +0 53 -1 53 -0 53 +3 N N + 0 53 +0x1620227B598EF9p-57 53 0 53 +0 53 +1 53 +0 53 +2 N N - 0 53 +0x1265D4E92B6B9Bp-59 53 0 53 -0 53 +1 53 +0 53 +3 N N + 0 53 +0x1724046EB0933Ap-48 53 0 53 +0 53 +1 53 -0 53 -2 N N - 0 53 +0x1BD4567B975381p-46 53 0 53 -0 53 +1 53 -0 53 -3 N N - 0 53 +0x1A9BCC46F767DFp-55 53 0 53 +0 53 -1 53 +0 53 -1 N N + 0 53 +0x1620227B598EF9p-57 53 0 53 -0 53 -1 53 +0 53 -2 N N # exact cases # (-1)^(1/2) = i 0 0 2 0 2 1 2 -1 2 0 2 0x1p-1 2 0 N N # (-4)^(1/4) = 1+i 0 0 2 1 2 1 2 -4 2 0 2 0x1p-2 2 0 N N # for an odd positive integer n, a positive integer m and an integer e: # (-4 m^4 16^e)^(n/4) = (1+i)^n m^n 2^(e n) # m=3 e=5 n=7 0 0 12 0x88Bp38 12 -0x88Bp38 7 -0x51p22 7 0 3 0x7p-2 3 0 N N # (-4 16^e)^(-n/4) = (1-i)^n 2^(- (e+1) n) # e=3 n=5 0 0 2 -0x1p-18 2 0x1p-18 2 -0x1p14 2 0 3 -0x5p-2 3 0 N N # e=2 n=5 0 0 2 -0x1p-13 2 0x1p-13 2 -0x1p10 2 0 3 -0x5p-2 3 0 N N # (+2 +0)^(-3 -0) -> (-1/8 -0) # x = 2 + epsilon*i, y = -3 - delta*i # log(x) = log(2) + epsilon/2*i + O(epsilon^2) # y*log(x) = [-3*log(2) + o(1)] + [-3*epsilon/2-delta*log(2)]*i 0 0 2 0x1p-3 2 -0 2 2 2 +0 2 -3 2 -0 N N # (-2 -0)^(3 +0) -> (-8 -0) # x = -2 - epsilon*i, y = 3 + delta*i # log(x) = log(2) - [Pi-epsilon/2]*i + O(epsilon^2) # y*log(x) ~ 3*log(2) + [-3*Pi+3*epsilon/2+delta*log(2)]*i 0 0 2 -8 2 -0 2 -2 2 -0 2 3 2 +0 N N # (-2 -0)^(-3 -0) -> (-1/8 +0) # x = -2 - epsilon*i, y = -3 - delta*i # log(x) = log(2) - [Pi-epsilon/2]*i + O(epsilon^2) # y*log(x) ~ -3*log(2) + [3*Pi-3*epsilon/2-delta*log(2)]*i 0 0 2 -0x1p-3 2 +0 2 -2 2 -0 2 -3 2 -0 N N 0 0 2 +0 2 -2 2 +0 2 0x1p-1 2 -1 2 -0 N N 0 0 2 +0 2 -2 2 +0 2 0x1p-1 65 -1 2 -0 N N + + 2 -0x3p-64 2 -2 2 +0 2 0x1p-1 65 -0x10000000000000001p-64 2 -0 N N 0 - 2 +0 3 -5 2 +0 53 0xCCCCCCCCCCCCDp-54 2 -1 2 -0 N N # undefined zero sign in result - 0 5 -25 2 0 2 +0 53 0xCCCCCCCCCCCCDp-54 2 -2 2 -0 N N - - 53 -0x85649E3220691p-63 53 -0x14A25D455A9D0Dp-60 3 5 2 3 2 -3 2 +0 N N + 0 53 0xABCC77118461Dp-74 2 +0 3 5 3 5 2 -8 2 +0 N N + 0 53 -0x127DB86014739Dp-93 2 -0 2 -1 2 -0 2 1 4 -9 N N + + 24 0xC1F98Dp-21 24 0x12FF89p-2 24 -7 24 +0 24 0xCFFFF3p-21 24 +0 N N # underflow case - - 24 +0 24 +0 24 2 24 0x44CCCDp-20 24 -0x7FFFF200 24 -0x7FFFF200 N N - 0 53 0x14D55AFA6E0BB0p210433620 53 0 53 +0 53 0x44CCCCFFFFFFFp-48 53 0x5F5E100 53 +0 N N - 0 53 0x14D55B174EE67Ep210433620 53 0 53 +0 53 0x44CCCDp-20 53 0x5F5E100 53 +0 N N 0 0 24 -10 24 198 24 5 24 3 24 3 24 +0 N N + - 113 0x1731C86FF8E8C7D80C8F1C83460B7p-38951 113 0x1CE5ECB8E88C769AF45FA662568CFp-38950 113 2 113 0x11333333333333333333333333333p-110 113 -10000 113 10000 N N - - 652 0x8E0380781E0124C92903E153123260CEF2C8821EDEC1D518A270FD55720DB5114D3D72CEE0E51CCEAA532FC6DA983707E66AE0E1A5E116D72AF5F2420D8402BE3E7FF03658E7ADFE2667C67291D74877383p-651 652 -0xB5FECD07C42E7AEE5A3489729B566DB4C6284C575E281585B0BFA711859D178BD8B07352B58BF615DD2DEC68798F0D2A644D5D18149D12BC53F851C5908F1EDE1C71F2B8D4934B1CE932AB94C0B8AE54C73p-665 163 0x5E9BDCC756D1E864413EA56F2A35C6D7D58DD117Bp-158 163 -0xE6BCC7A0E6EC5F2B1CBCF2707D829C2CB1A56FCFp-164 163 0x21A13BA8E157F23649FC27B031EAA12B826FB7E9Dp-166 163 0 N N 0 0 2 0 2 1 2 -1 2 0 2 0x1p-1 2 0 N N + + 2 -0x3p-65 2 1 2 -1 2 0 65 0x10000000000000001p-65 2 0 N N 0 0 2 1 2 +0 65 0x10000000000000001p-64 2 +0 2 +0 2 +0 N N 0 0 2 1 2 -0 65 0xFFFFFFFFFFFFFFFFp-64 2 +0 2 +0 2 +0 N N 0 + 2 +0 2 0.75 2 -0.5 2 0 2 0.5 2 0 N N 0 0 2 0 2 2 2 1 2 1 2 2 2 +0 N N # I^2 = -1 0 0 2 -1 2 +0 2 +0 2 1 2 2 2 +0 N N + 0 2 -1 2 +0 2 +0 65 0x10000000000000001p-64 2 2 2 +0 N N # overflow cases - - 2 -inf 2 -inf 2 3 2 1 28 744261116 2 +0 N N - + 2 -inf 2 +inf 2 3 2 -1 28 744261116 2 +0 N N + + 2 +inf 2 +inf 2 4 2 3 28 744261116 2 +0 N N + - 2 +inf 2 -inf 2 4 2 -3 28 744261116 2 +0 N N # underflow cases + - 2 -0 2 +0 2 3 2 1 28 -744261116 2 +0 N N + + 2 -0 2 -0 2 3 2 -1 28 -744261116 2 +0 N N - + 2 +0 2 -0 2 4 2 3 28 -744261116 2 +0 N N - - 2 +0 2 +0 2 4 2 -3 28 -744261116 2 +0 N N # exact powers with non-integer exponent 0 0 2 1 2 1 2 0 2 2 2 0.5 2 0 N N 0 0 2 -2 2 2 2 0 2 2 2 1.5 2 0 N N 0 0 2 1 2 64 12 -4095 2 128 2 0.5 2 0 N N 0 0 3 5 2 3 2 16 4 30 2 0.5 2 0 N N 0 0 7 97 7 99 6 -392 14 19206 2 0.5 2 0 N N 0 0 6 63 6 61 5 248 18 7686 2 0.5 2 0 N N 0 0 6 63 6 61 24 -59013092 17 3812256 2 0.25 2 0 N N 0 + 2 0 2 0x3p-6 2 -1 2 0 2 0.5 2 1 N N + + 2 6 2 1 41 -0x2ce019e6f1e 36 0x1878418ba20 2 0.0625 2 0 N N + + 4 11 2 1 111 -0x73558286726957f922819cbeffff 109 0x1c484a8b32dbf409e966a8c00000 2 0x1p-5 2 0 N N + + 5 21 2 1 282 -0x24ea91ddba938e750d999f1075444e15d6ca0fff6a19c8cbefe6260261fd57effffffff 278 0x390aa828a3d933391ab999b0b0aa71aafbfc7b127fe30c84d107634940ba8000000000 2 0x1p-6 2 0 N N + - 53 0x7f661e2bd0db5p-51 53 0xc63ee1a1c4d19p-55 2 0x1p1000 2 0 2 0 2 0x1p1000 N N # bug reported by Joseph Myers (07 Apr 2015) + - 2 -0x3p1073741819 2 0x3p1073741819 2 1 2 2 2 0x1p1000 2 0 Z Z # bug founds and fixed on November 13, 2024 # Re((-4,eps1)^(0.5,eps2)) gives both signs depending on eps1 and eps2 # in that case we choose the + sign: 0 0 2 +0 2 +2 2 -4 2 +0 2 0.5 2 +0 N N # Re((-4,eps1)^(0.5,-eps2)) gives only + depending on eps1 and eps2: 0 0 2 +0 2 +2 2 -4 2 +0 2 0.5 2 -0 N N # Re((-4,-eps1)^(0.5,eps2)) gives only + depending on eps1 and eps2: 0 0 2 +0 2 -2 2 -4 2 -0 2 0.5 2 +0 N N # Re((-4,-eps1)^(0.5,-eps2)) gives both signs depending on eps1 and eps2: 0 0 2 +0 2 -2 2 -4 2 -0 2 0.5 2 -0 N N # Im((16,eps1)^(0.25,eps2)) gives only + depending on eps1 and eps2: 0 0 2 +2 2 +0 2 16 2 +0 2 0.25 2 +0 N N # Im((16,eps1)^(0.25,-eps2)) gives both signs depending on eps1 and eps2: 0 0 2 +2 2 +0 2 16 2 +0 2 0.25 2 -0 N N # Im((16,-eps1)^(0.25,eps2)) gives both signs depending on eps1 and eps2: 0 0 2 +2 2 +0 2 16 2 -0 2 0.25 2 +0 N N # Im((16,-eps1)^(0.25,-eps2)) gives only - depending on eps1 and eps2 # [and it should be the conjugate of (16,eps1)^(0.25,eps2)]: 0 0 2 +2 2 -0 2 16 2 -0 2 0.25 2 -0 N N ? ? 53 +0 53 -0x1.bb67ae8584caap+0 53 -3 53 -0 53 0.5 53 +0 N N ? ? 53 +0 53 +0x1.bb67ae8584caap+0 53 -3 53 +0 53 0.5 53 +0 N N