80 lines
2.3 KiB
C
80 lines
2.3 KiB
C
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/* Support routines for the intrinsic power (**) operator
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for UNSIGNED, using modulo arithmetic.
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Copyright (C) 2025 Free Software Foundation, Inc.
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Contributed by Thomas Koenig.
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This file is part of the GNU Fortran 95 runtime library (libgfortran).
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Libgfortran is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public
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License as published by the Free Software Foundation; either
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version 3 of the License, or (at your option) any later version.
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Libgfortran is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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#include "libgfortran.h"
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/* Use Binary Method to calculate the powi. This is not an optimal but
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a simple and reasonable arithmetic. See section 4.6.3, "Evaluation of
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Powers" of Donald E. Knuth, "Seminumerical Algorithms", Vol. 2, "The Art
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of Computer Programming", 3rd Edition, 1998. */
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#if defined (HAVE_GFC_UINTEGER_2) && defined (HAVE_GFC_UINTEGER_8)
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GFC_UINTEGER_2 pow_m2_m8 (GFC_UINTEGER_2 x, GFC_UINTEGER_8 n);
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export_proto(pow_m2_m8);
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inline static GFC_UINTEGER_2
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power_simple_m2_m8 (GFC_UINTEGER_2 x, GFC_UINTEGER_8 n)
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{
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GFC_UINTEGER_2 pow = 1;
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for (;;)
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{
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if (n & 1)
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pow *= x;
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n >>= 1;
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if (n)
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x *= x;
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else
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break;
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}
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return pow;
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}
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/* For odd x, Euler's theorem tells us that x**(2^(m-1)) = 1 mod 2^m.
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For even x, we use the fact that (2*x)^m = 0 mod 2^m. */
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GFC_UINTEGER_2
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pow_m2_m8 (GFC_UINTEGER_2 x, GFC_UINTEGER_8 n)
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{
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const GFC_UINTEGER_2 mask = (GFC_UINTEGER_2) (-1) / 2;
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if (n == 0)
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return 1;
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if (x == 0)
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return 0;
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if (x & 1)
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return power_simple_m2_m8 (x, n & mask);
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if (n > sizeof (x) * 8)
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return 0;
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return power_simple_m2_m8 (x, n);
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}
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#endif
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