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julius |
/* Software floating-point emulation.
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Basic four-word fraction declaration and manipulation.
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Copyright (C) 1997,1998,1999,2006,2007 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Richard Henderson (rth@cygnus.com),
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Jakub Jelinek (jj@ultra.linux.cz),
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David S. Miller (davem@redhat.com) and
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Peter Maydell (pmaydell@chiark.greenend.org.uk).
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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In addition to the permissions in the GNU Lesser General Public
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License, the Free Software Foundation gives you unlimited
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permission to link the compiled version of this file into
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combinations with other programs, and to distribute those
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combinations without any restriction coming from the use of this
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file. (The Lesser General Public License restrictions do apply in
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other respects; for example, they cover modification of the file,
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and distribution when not linked into a combine executable.)
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The GNU C Library 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 GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, write to the Free
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Software Foundation, 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#define _FP_FRAC_DECL_4(X) _FP_W_TYPE X##_f[4]
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#define _FP_FRAC_COPY_4(D,S) \
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(D##_f[0] = S##_f[0], D##_f[1] = S##_f[1], \
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D##_f[2] = S##_f[2], D##_f[3] = S##_f[3])
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#define _FP_FRAC_SET_4(X,I) __FP_FRAC_SET_4(X, I)
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#define _FP_FRAC_HIGH_4(X) (X##_f[3])
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#define _FP_FRAC_LOW_4(X) (X##_f[0])
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#define _FP_FRAC_WORD_4(X,w) (X##_f[w])
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#define _FP_FRAC_SLL_4(X,N) \
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do { \
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_FP_I_TYPE _up, _down, _skip, _i; \
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_skip = (N) / _FP_W_TYPE_SIZE; \
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_up = (N) % _FP_W_TYPE_SIZE; \
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_down = _FP_W_TYPE_SIZE - _up; \
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if (!_up) \
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for (_i = 3; _i >= _skip; --_i) \
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X##_f[_i] = X##_f[_i-_skip]; \
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else \
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{ \
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for (_i = 3; _i > _skip; --_i) \
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X##_f[_i] = X##_f[_i-_skip] << _up \
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| X##_f[_i-_skip-1] >> _down; \
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X##_f[_i--] = X##_f[0] << _up; \
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} \
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for (; _i >= 0; --_i) \
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X##_f[_i] = 0; \
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} while (0)
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/* This one was broken too */
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#define _FP_FRAC_SRL_4(X,N) \
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do { \
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_FP_I_TYPE _up, _down, _skip, _i; \
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_skip = (N) / _FP_W_TYPE_SIZE; \
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_down = (N) % _FP_W_TYPE_SIZE; \
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_up = _FP_W_TYPE_SIZE - _down; \
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if (!_down) \
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for (_i = 0; _i <= 3-_skip; ++_i) \
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X##_f[_i] = X##_f[_i+_skip]; \
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else \
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{ \
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for (_i = 0; _i < 3-_skip; ++_i) \
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X##_f[_i] = X##_f[_i+_skip] >> _down \
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| X##_f[_i+_skip+1] << _up; \
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X##_f[_i++] = X##_f[3] >> _down; \
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} \
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for (; _i < 4; ++_i) \
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X##_f[_i] = 0; \
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} while (0)
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/* Right shift with sticky-lsb.
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* What this actually means is that we do a standard right-shift,
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* but that if any of the bits that fall off the right hand side
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* were one then we always set the LSbit.
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*/
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#define _FP_FRAC_SRST_4(X,S,N,size) \
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do { \
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_FP_I_TYPE _up, _down, _skip, _i; \
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_FP_W_TYPE _s; \
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_skip = (N) / _FP_W_TYPE_SIZE; \
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_down = (N) % _FP_W_TYPE_SIZE; \
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_up = _FP_W_TYPE_SIZE - _down; \
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for (_s = _i = 0; _i < _skip; ++_i) \
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_s |= X##_f[_i]; \
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if (!_down) \
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for (_i = 0; _i <= 3-_skip; ++_i) \
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X##_f[_i] = X##_f[_i+_skip]; \
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else \
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{ \
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_s |= X##_f[_i] << _up; \
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for (_i = 0; _i < 3-_skip; ++_i) \
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X##_f[_i] = X##_f[_i+_skip] >> _down \
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| X##_f[_i+_skip+1] << _up; \
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X##_f[_i++] = X##_f[3] >> _down; \
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} \
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for (; _i < 4; ++_i) \
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X##_f[_i] = 0; \
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S = (_s != 0); \
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} while (0)
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#define _FP_FRAC_SRS_4(X,N,size) \
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do { \
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int _sticky; \
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_FP_FRAC_SRST_4(X, _sticky, N, size); \
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X##_f[0] |= _sticky; \
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} while (0)
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#define _FP_FRAC_ADD_4(R,X,Y) \
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__FP_FRAC_ADD_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
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X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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#define _FP_FRAC_SUB_4(R,X,Y) \
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__FP_FRAC_SUB_4(R##_f[3], R##_f[2], R##_f[1], R##_f[0], \
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X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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#define _FP_FRAC_DEC_4(X,Y) \
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__FP_FRAC_DEC_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
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Y##_f[3], Y##_f[2], Y##_f[1], Y##_f[0])
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#define _FP_FRAC_ADDI_4(X,I) \
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__FP_FRAC_ADDI_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], I)
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#define _FP_ZEROFRAC_4 0,0,0,0
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#define _FP_MINFRAC_4 0,0,0,1
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#define _FP_MAXFRAC_4 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
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#define _FP_FRAC_ZEROP_4(X) ((X##_f[0] | X##_f[1] | X##_f[2] | X##_f[3]) == 0)
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#define _FP_FRAC_NEGP_4(X) ((_FP_WS_TYPE)X##_f[3] < 0)
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#define _FP_FRAC_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
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#define _FP_FRAC_CLEAR_OVERP_4(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
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#define _FP_FRAC_EQ_4(X,Y) \
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(X##_f[0] == Y##_f[0] && X##_f[1] == Y##_f[1] \
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&& X##_f[2] == Y##_f[2] && X##_f[3] == Y##_f[3])
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#define _FP_FRAC_GT_4(X,Y) \
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(X##_f[3] > Y##_f[3] || \
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(X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \
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(X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \
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(X##_f[1] == Y##_f[1] && X##_f[0] > Y##_f[0]) \
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)) \
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)) \
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)
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#define _FP_FRAC_GE_4(X,Y) \
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(X##_f[3] > Y##_f[3] || \
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(X##_f[3] == Y##_f[3] && (X##_f[2] > Y##_f[2] || \
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(X##_f[2] == Y##_f[2] && (X##_f[1] > Y##_f[1] || \
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(X##_f[1] == Y##_f[1] && X##_f[0] >= Y##_f[0]) \
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)) \
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)) \
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)
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#define _FP_FRAC_CLZ_4(R,X) \
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do { \
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if (X##_f[3]) \
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{ \
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__FP_CLZ(R,X##_f[3]); \
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} \
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else if (X##_f[2]) \
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{ \
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__FP_CLZ(R,X##_f[2]); \
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R += _FP_W_TYPE_SIZE; \
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} \
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else if (X##_f[1]) \
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{ \
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__FP_CLZ(R,X##_f[1]); \
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R += _FP_W_TYPE_SIZE*2; \
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} \
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else \
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{ \
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__FP_CLZ(R,X##_f[0]); \
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R += _FP_W_TYPE_SIZE*3; \
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} \
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} while(0)
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#define _FP_UNPACK_RAW_4(fs, X, val) \
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do { \
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union _FP_UNION_##fs _flo; _flo.flt = (val); \
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X##_f[0] = _flo.bits.frac0; \
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X##_f[1] = _flo.bits.frac1; \
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X##_f[2] = _flo.bits.frac2; \
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X##_f[3] = _flo.bits.frac3; \
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X##_e = _flo.bits.exp; \
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X##_s = _flo.bits.sign; \
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} while (0)
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| 206 |
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#define _FP_UNPACK_RAW_4_P(fs, X, val) \
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do { \
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union _FP_UNION_##fs *_flo = \
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(union _FP_UNION_##fs *)(val); \
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\
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X##_f[0] = _flo->bits.frac0; \
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X##_f[1] = _flo->bits.frac1; \
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X##_f[2] = _flo->bits.frac2; \
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X##_f[3] = _flo->bits.frac3; \
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X##_e = _flo->bits.exp; \
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| 216 |
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X##_s = _flo->bits.sign; \
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| 217 |
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} while (0)
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| 218 |
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| 219 |
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#define _FP_PACK_RAW_4(fs, val, X) \
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| 220 |
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do { \
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| 221 |
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union _FP_UNION_##fs _flo; \
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| 222 |
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_flo.bits.frac0 = X##_f[0]; \
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| 223 |
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_flo.bits.frac1 = X##_f[1]; \
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| 224 |
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_flo.bits.frac2 = X##_f[2]; \
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| 225 |
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_flo.bits.frac3 = X##_f[3]; \
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| 226 |
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_flo.bits.exp = X##_e; \
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| 227 |
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_flo.bits.sign = X##_s; \
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| 228 |
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(val) = _flo.flt; \
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| 229 |
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} while (0)
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| 230 |
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| 231 |
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#define _FP_PACK_RAW_4_P(fs, val, X) \
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| 232 |
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do { \
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| 233 |
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union _FP_UNION_##fs *_flo = \
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| 234 |
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(union _FP_UNION_##fs *)(val); \
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| 235 |
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\
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| 236 |
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_flo->bits.frac0 = X##_f[0]; \
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| 237 |
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_flo->bits.frac1 = X##_f[1]; \
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| 238 |
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_flo->bits.frac2 = X##_f[2]; \
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| 239 |
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_flo->bits.frac3 = X##_f[3]; \
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| 240 |
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_flo->bits.exp = X##_e; \
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| 241 |
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_flo->bits.sign = X##_s; \
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| 242 |
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} while (0)
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| 243 |
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| 244 |
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/*
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| 245 |
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* Multiplication algorithms:
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| 246 |
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*/
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| 247 |
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| 248 |
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/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
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| 249 |
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| 250 |
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#define _FP_MUL_MEAT_4_wide(wfracbits, R, X, Y, doit) \
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| 251 |
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do { \
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| 252 |
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_FP_FRAC_DECL_8(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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| 253 |
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_FP_FRAC_DECL_2(_d); _FP_FRAC_DECL_2(_e); _FP_FRAC_DECL_2(_f); \
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| 254 |
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\
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| 255 |
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doit(_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0), X##_f[0], Y##_f[0]); \
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| 256 |
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doit(_b_f1, _b_f0, X##_f[0], Y##_f[1]); \
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| 257 |
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doit(_c_f1, _c_f0, X##_f[1], Y##_f[0]); \
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| 258 |
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doit(_d_f1, _d_f0, X##_f[1], Y##_f[1]); \
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| 259 |
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doit(_e_f1, _e_f0, X##_f[0], Y##_f[2]); \
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| 260 |
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doit(_f_f1, _f_f0, X##_f[2], Y##_f[0]); \
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| 261 |
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__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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| 262 |
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_FP_FRAC_WORD_8(_z,1), 0,_b_f1,_b_f0, \
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| 263 |
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0,0,_FP_FRAC_WORD_8(_z,1)); \
|
| 264 |
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__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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| 265 |
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_FP_FRAC_WORD_8(_z,1), 0,_c_f1,_c_f0, \
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| 266 |
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_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2), \
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| 267 |
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_FP_FRAC_WORD_8(_z,1)); \
|
| 268 |
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__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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| 269 |
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_FP_FRAC_WORD_8(_z,2), 0,_d_f1,_d_f0, \
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| 270 |
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0,_FP_FRAC_WORD_8(_z,3),_FP_FRAC_WORD_8(_z,2)); \
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| 271 |
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__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
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| 272 |
|
|
_FP_FRAC_WORD_8(_z,2), 0,_e_f1,_e_f0, \
|
| 273 |
|
|
_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
|
| 274 |
|
|
_FP_FRAC_WORD_8(_z,2)); \
|
| 275 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
|
| 276 |
|
|
_FP_FRAC_WORD_8(_z,2), 0,_f_f1,_f_f0, \
|
| 277 |
|
|
_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3), \
|
| 278 |
|
|
_FP_FRAC_WORD_8(_z,2)); \
|
| 279 |
|
|
doit(_b_f1, _b_f0, X##_f[0], Y##_f[3]); \
|
| 280 |
|
|
doit(_c_f1, _c_f0, X##_f[3], Y##_f[0]); \
|
| 281 |
|
|
doit(_d_f1, _d_f0, X##_f[1], Y##_f[2]); \
|
| 282 |
|
|
doit(_e_f1, _e_f0, X##_f[2], Y##_f[1]); \
|
| 283 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
|
| 284 |
|
|
_FP_FRAC_WORD_8(_z,3), 0,_b_f1,_b_f0, \
|
| 285 |
|
|
0,_FP_FRAC_WORD_8(_z,4),_FP_FRAC_WORD_8(_z,3)); \
|
| 286 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
|
| 287 |
|
|
_FP_FRAC_WORD_8(_z,3), 0,_c_f1,_c_f0, \
|
| 288 |
|
|
_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
|
| 289 |
|
|
_FP_FRAC_WORD_8(_z,3)); \
|
| 290 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
|
| 291 |
|
|
_FP_FRAC_WORD_8(_z,3), 0,_d_f1,_d_f0, \
|
| 292 |
|
|
_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
|
| 293 |
|
|
_FP_FRAC_WORD_8(_z,3)); \
|
| 294 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
|
| 295 |
|
|
_FP_FRAC_WORD_8(_z,3), 0,_e_f1,_e_f0, \
|
| 296 |
|
|
_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4), \
|
| 297 |
|
|
_FP_FRAC_WORD_8(_z,3)); \
|
| 298 |
|
|
doit(_b_f1, _b_f0, X##_f[2], Y##_f[2]); \
|
| 299 |
|
|
doit(_c_f1, _c_f0, X##_f[1], Y##_f[3]); \
|
| 300 |
|
|
doit(_d_f1, _d_f0, X##_f[3], Y##_f[1]); \
|
| 301 |
|
|
doit(_e_f1, _e_f0, X##_f[2], Y##_f[3]); \
|
| 302 |
|
|
doit(_f_f1, _f_f0, X##_f[3], Y##_f[2]); \
|
| 303 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
| 304 |
|
|
_FP_FRAC_WORD_8(_z,4), 0,_b_f1,_b_f0, \
|
| 305 |
|
|
0,_FP_FRAC_WORD_8(_z,5),_FP_FRAC_WORD_8(_z,4)); \
|
| 306 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
| 307 |
|
|
_FP_FRAC_WORD_8(_z,4), 0,_c_f1,_c_f0, \
|
| 308 |
|
|
_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
| 309 |
|
|
_FP_FRAC_WORD_8(_z,4)); \
|
| 310 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
| 311 |
|
|
_FP_FRAC_WORD_8(_z,4), 0,_d_f1,_d_f0, \
|
| 312 |
|
|
_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5), \
|
| 313 |
|
|
_FP_FRAC_WORD_8(_z,4)); \
|
| 314 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
| 315 |
|
|
_FP_FRAC_WORD_8(_z,5), 0,_e_f1,_e_f0, \
|
| 316 |
|
|
0,_FP_FRAC_WORD_8(_z,6),_FP_FRAC_WORD_8(_z,5)); \
|
| 317 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
| 318 |
|
|
_FP_FRAC_WORD_8(_z,5), 0,_f_f1,_f_f0, \
|
| 319 |
|
|
_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
| 320 |
|
|
_FP_FRAC_WORD_8(_z,5)); \
|
| 321 |
|
|
doit(_b_f1, _b_f0, X##_f[3], Y##_f[3]); \
|
| 322 |
|
|
__FP_FRAC_ADD_2(_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6), \
|
| 323 |
|
|
_b_f1,_b_f0, \
|
| 324 |
|
|
_FP_FRAC_WORD_8(_z,7),_FP_FRAC_WORD_8(_z,6)); \
|
| 325 |
|
|
\
|
| 326 |
|
|
/* Normalize since we know where the msb of the multiplicands \
|
| 327 |
|
|
were (bit B), we know that the msb of the of the product is \
|
| 328 |
|
|
at either 2B or 2B-1. */ \
|
| 329 |
|
|
_FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \
|
| 330 |
|
|
__FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \
|
| 331 |
|
|
_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \
|
| 332 |
|
|
} while (0)
|
| 333 |
|
|
|
| 334 |
|
|
#define _FP_MUL_MEAT_4_gmp(wfracbits, R, X, Y) \
|
| 335 |
|
|
do { \
|
| 336 |
|
|
_FP_FRAC_DECL_8(_z); \
|
| 337 |
|
|
\
|
| 338 |
|
|
mpn_mul_n(_z_f, _x_f, _y_f, 4); \
|
| 339 |
|
|
\
|
| 340 |
|
|
/* Normalize since we know where the msb of the multiplicands \
|
| 341 |
|
|
were (bit B), we know that the msb of the of the product is \
|
| 342 |
|
|
at either 2B or 2B-1. */ \
|
| 343 |
|
|
_FP_FRAC_SRS_8(_z, wfracbits-1, 2*wfracbits); \
|
| 344 |
|
|
__FP_FRAC_SET_4(R, _FP_FRAC_WORD_8(_z,3), _FP_FRAC_WORD_8(_z,2), \
|
| 345 |
|
|
_FP_FRAC_WORD_8(_z,1), _FP_FRAC_WORD_8(_z,0)); \
|
| 346 |
|
|
} while (0)
|
| 347 |
|
|
|
| 348 |
|
|
/*
|
| 349 |
|
|
* Helper utility for _FP_DIV_MEAT_4_udiv:
|
| 350 |
|
|
* pppp = m * nnn
|
| 351 |
|
|
*/
|
| 352 |
|
|
#define umul_ppppmnnn(p3,p2,p1,p0,m,n2,n1,n0) \
|
| 353 |
|
|
do { \
|
| 354 |
|
|
UWtype _t; \
|
| 355 |
|
|
umul_ppmm(p1,p0,m,n0); \
|
| 356 |
|
|
umul_ppmm(p2,_t,m,n1); \
|
| 357 |
|
|
__FP_FRAC_ADDI_2(p2,p1,_t); \
|
| 358 |
|
|
umul_ppmm(p3,_t,m,n2); \
|
| 359 |
|
|
__FP_FRAC_ADDI_2(p3,p2,_t); \
|
| 360 |
|
|
} while (0)
|
| 361 |
|
|
|
| 362 |
|
|
/*
|
| 363 |
|
|
* Division algorithms:
|
| 364 |
|
|
*/
|
| 365 |
|
|
|
| 366 |
|
|
#define _FP_DIV_MEAT_4_udiv(fs, R, X, Y) \
|
| 367 |
|
|
do { \
|
| 368 |
|
|
int _i; \
|
| 369 |
|
|
_FP_FRAC_DECL_4(_n); _FP_FRAC_DECL_4(_m); \
|
| 370 |
|
|
_FP_FRAC_SET_4(_n, _FP_ZEROFRAC_4); \
|
| 371 |
|
|
if (_FP_FRAC_GT_4(X, Y)) \
|
| 372 |
|
|
{ \
|
| 373 |
|
|
_n_f[3] = X##_f[0] << (_FP_W_TYPE_SIZE - 1); \
|
| 374 |
|
|
_FP_FRAC_SRL_4(X, 1); \
|
| 375 |
|
|
} \
|
| 376 |
|
|
else \
|
| 377 |
|
|
R##_e--; \
|
| 378 |
|
|
\
|
| 379 |
|
|
/* Normalize, i.e. make the most significant bit of the \
|
| 380 |
|
|
denominator set. */ \
|
| 381 |
|
|
_FP_FRAC_SLL_4(Y, _FP_WFRACXBITS_##fs); \
|
| 382 |
|
|
\
|
| 383 |
|
|
for (_i = 3; ; _i--) \
|
| 384 |
|
|
{ \
|
| 385 |
|
|
if (X##_f[3] == Y##_f[3]) \
|
| 386 |
|
|
{ \
|
| 387 |
|
|
/* This is a special case, not an optimization \
|
| 388 |
|
|
(X##_f[3]/Y##_f[3] would not fit into UWtype). \
|
| 389 |
|
|
As X## is guaranteed to be < Y, R##_f[_i] can be either \
|
| 390 |
|
|
(UWtype)-1 or (UWtype)-2. */ \
|
| 391 |
|
|
R##_f[_i] = -1; \
|
| 392 |
|
|
if (!_i) \
|
| 393 |
|
|
break; \
|
| 394 |
|
|
__FP_FRAC_SUB_4(X##_f[3], X##_f[2], X##_f[1], X##_f[0], \
|
| 395 |
|
|
Y##_f[2], Y##_f[1], Y##_f[0], 0, \
|
| 396 |
|
|
X##_f[2], X##_f[1], X##_f[0], _n_f[_i]); \
|
| 397 |
|
|
_FP_FRAC_SUB_4(X, Y, X); \
|
| 398 |
|
|
if (X##_f[3] > Y##_f[3]) \
|
| 399 |
|
|
{ \
|
| 400 |
|
|
R##_f[_i] = -2; \
|
| 401 |
|
|
_FP_FRAC_ADD_4(X, Y, X); \
|
| 402 |
|
|
} \
|
| 403 |
|
|
} \
|
| 404 |
|
|
else \
|
| 405 |
|
|
{ \
|
| 406 |
|
|
udiv_qrnnd(R##_f[_i], X##_f[3], X##_f[3], X##_f[2], Y##_f[3]); \
|
| 407 |
|
|
umul_ppppmnnn(_m_f[3], _m_f[2], _m_f[1], _m_f[0], \
|
| 408 |
|
|
R##_f[_i], Y##_f[2], Y##_f[1], Y##_f[0]); \
|
| 409 |
|
|
X##_f[2] = X##_f[1]; \
|
| 410 |
|
|
X##_f[1] = X##_f[0]; \
|
| 411 |
|
|
X##_f[0] = _n_f[_i]; \
|
| 412 |
|
|
if (_FP_FRAC_GT_4(_m, X)) \
|
| 413 |
|
|
{ \
|
| 414 |
|
|
R##_f[_i]--; \
|
| 415 |
|
|
_FP_FRAC_ADD_4(X, Y, X); \
|
| 416 |
|
|
if (_FP_FRAC_GE_4(X, Y) && _FP_FRAC_GT_4(_m, X)) \
|
| 417 |
|
|
{ \
|
| 418 |
|
|
R##_f[_i]--; \
|
| 419 |
|
|
_FP_FRAC_ADD_4(X, Y, X); \
|
| 420 |
|
|
} \
|
| 421 |
|
|
} \
|
| 422 |
|
|
_FP_FRAC_DEC_4(X, _m); \
|
| 423 |
|
|
if (!_i) \
|
| 424 |
|
|
{ \
|
| 425 |
|
|
if (!_FP_FRAC_EQ_4(X, _m)) \
|
| 426 |
|
|
R##_f[0] |= _FP_WORK_STICKY; \
|
| 427 |
|
|
break; \
|
| 428 |
|
|
} \
|
| 429 |
|
|
} \
|
| 430 |
|
|
} \
|
| 431 |
|
|
} while (0)
|
| 432 |
|
|
|
| 433 |
|
|
|
| 434 |
|
|
/*
|
| 435 |
|
|
* Square root algorithms:
|
| 436 |
|
|
* We have just one right now, maybe Newton approximation
|
| 437 |
|
|
* should be added for those machines where division is fast.
|
| 438 |
|
|
*/
|
| 439 |
|
|
|
| 440 |
|
|
#define _FP_SQRT_MEAT_4(R, S, T, X, q) \
|
| 441 |
|
|
do { \
|
| 442 |
|
|
while (q) \
|
| 443 |
|
|
{ \
|
| 444 |
|
|
T##_f[3] = S##_f[3] + q; \
|
| 445 |
|
|
if (T##_f[3] <= X##_f[3]) \
|
| 446 |
|
|
{ \
|
| 447 |
|
|
S##_f[3] = T##_f[3] + q; \
|
| 448 |
|
|
X##_f[3] -= T##_f[3]; \
|
| 449 |
|
|
R##_f[3] += q; \
|
| 450 |
|
|
} \
|
| 451 |
|
|
_FP_FRAC_SLL_4(X, 1); \
|
| 452 |
|
|
q >>= 1; \
|
| 453 |
|
|
} \
|
| 454 |
|
|
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 455 |
|
|
while (q) \
|
| 456 |
|
|
{ \
|
| 457 |
|
|
T##_f[2] = S##_f[2] + q; \
|
| 458 |
|
|
T##_f[3] = S##_f[3]; \
|
| 459 |
|
|
if (T##_f[3] < X##_f[3] || \
|
| 460 |
|
|
(T##_f[3] == X##_f[3] && T##_f[2] <= X##_f[2])) \
|
| 461 |
|
|
{ \
|
| 462 |
|
|
S##_f[2] = T##_f[2] + q; \
|
| 463 |
|
|
S##_f[3] += (T##_f[2] > S##_f[2]); \
|
| 464 |
|
|
__FP_FRAC_DEC_2(X##_f[3], X##_f[2], \
|
| 465 |
|
|
T##_f[3], T##_f[2]); \
|
| 466 |
|
|
R##_f[2] += q; \
|
| 467 |
|
|
} \
|
| 468 |
|
|
_FP_FRAC_SLL_4(X, 1); \
|
| 469 |
|
|
q >>= 1; \
|
| 470 |
|
|
} \
|
| 471 |
|
|
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 472 |
|
|
while (q) \
|
| 473 |
|
|
{ \
|
| 474 |
|
|
T##_f[1] = S##_f[1] + q; \
|
| 475 |
|
|
T##_f[2] = S##_f[2]; \
|
| 476 |
|
|
T##_f[3] = S##_f[3]; \
|
| 477 |
|
|
if (T##_f[3] < X##_f[3] || \
|
| 478 |
|
|
(T##_f[3] == X##_f[3] && (T##_f[2] < X##_f[2] || \
|
| 479 |
|
|
(T##_f[2] == X##_f[2] && T##_f[1] <= X##_f[1])))) \
|
| 480 |
|
|
{ \
|
| 481 |
|
|
S##_f[1] = T##_f[1] + q; \
|
| 482 |
|
|
S##_f[2] += (T##_f[1] > S##_f[1]); \
|
| 483 |
|
|
S##_f[3] += (T##_f[2] > S##_f[2]); \
|
| 484 |
|
|
__FP_FRAC_DEC_3(X##_f[3], X##_f[2], X##_f[1], \
|
| 485 |
|
|
T##_f[3], T##_f[2], T##_f[1]); \
|
| 486 |
|
|
R##_f[1] += q; \
|
| 487 |
|
|
} \
|
| 488 |
|
|
_FP_FRAC_SLL_4(X, 1); \
|
| 489 |
|
|
q >>= 1; \
|
| 490 |
|
|
} \
|
| 491 |
|
|
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 492 |
|
|
while (q != _FP_WORK_ROUND) \
|
| 493 |
|
|
{ \
|
| 494 |
|
|
T##_f[0] = S##_f[0] + q; \
|
| 495 |
|
|
T##_f[1] = S##_f[1]; \
|
| 496 |
|
|
T##_f[2] = S##_f[2]; \
|
| 497 |
|
|
T##_f[3] = S##_f[3]; \
|
| 498 |
|
|
if (_FP_FRAC_GE_4(X,T)) \
|
| 499 |
|
|
{ \
|
| 500 |
|
|
S##_f[0] = T##_f[0] + q; \
|
| 501 |
|
|
S##_f[1] += (T##_f[0] > S##_f[0]); \
|
| 502 |
|
|
S##_f[2] += (T##_f[1] > S##_f[1]); \
|
| 503 |
|
|
S##_f[3] += (T##_f[2] > S##_f[2]); \
|
| 504 |
|
|
_FP_FRAC_DEC_4(X, T); \
|
| 505 |
|
|
R##_f[0] += q; \
|
| 506 |
|
|
} \
|
| 507 |
|
|
_FP_FRAC_SLL_4(X, 1); \
|
| 508 |
|
|
q >>= 1; \
|
| 509 |
|
|
} \
|
| 510 |
|
|
if (!_FP_FRAC_ZEROP_4(X)) \
|
| 511 |
|
|
{ \
|
| 512 |
|
|
if (_FP_FRAC_GT_4(X,S)) \
|
| 513 |
|
|
R##_f[0] |= _FP_WORK_ROUND; \
|
| 514 |
|
|
R##_f[0] |= _FP_WORK_STICKY; \
|
| 515 |
|
|
} \
|
| 516 |
|
|
} while (0)
|
| 517 |
|
|
|
| 518 |
|
|
|
| 519 |
|
|
/*
|
| 520 |
|
|
* Internals
|
| 521 |
|
|
*/
|
| 522 |
|
|
|
| 523 |
|
|
#define __FP_FRAC_SET_4(X,I3,I2,I1,I0) \
|
| 524 |
|
|
(X##_f[3] = I3, X##_f[2] = I2, X##_f[1] = I1, X##_f[0] = I0)
|
| 525 |
|
|
|
| 526 |
|
|
#ifndef __FP_FRAC_ADD_3
|
| 527 |
|
|
#define __FP_FRAC_ADD_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \
|
| 528 |
|
|
do { \
|
| 529 |
|
|
_FP_W_TYPE _c1, _c2; \
|
| 530 |
|
|
r0 = x0 + y0; \
|
| 531 |
|
|
_c1 = r0 < x0; \
|
| 532 |
|
|
r1 = x1 + y1; \
|
| 533 |
|
|
_c2 = r1 < x1; \
|
| 534 |
|
|
r1 += _c1; \
|
| 535 |
|
|
_c2 |= r1 < _c1; \
|
| 536 |
|
|
r2 = x2 + y2 + _c2; \
|
| 537 |
|
|
} while (0)
|
| 538 |
|
|
#endif
|
| 539 |
|
|
|
| 540 |
|
|
#ifndef __FP_FRAC_ADD_4
|
| 541 |
|
|
#define __FP_FRAC_ADD_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \
|
| 542 |
|
|
do { \
|
| 543 |
|
|
_FP_W_TYPE _c1, _c2, _c3; \
|
| 544 |
|
|
r0 = x0 + y0; \
|
| 545 |
|
|
_c1 = r0 < x0; \
|
| 546 |
|
|
r1 = x1 + y1; \
|
| 547 |
|
|
_c2 = r1 < x1; \
|
| 548 |
|
|
r1 += _c1; \
|
| 549 |
|
|
_c2 |= r1 < _c1; \
|
| 550 |
|
|
r2 = x2 + y2; \
|
| 551 |
|
|
_c3 = r2 < x2; \
|
| 552 |
|
|
r2 += _c2; \
|
| 553 |
|
|
_c3 |= r2 < _c2; \
|
| 554 |
|
|
r3 = x3 + y3 + _c3; \
|
| 555 |
|
|
} while (0)
|
| 556 |
|
|
#endif
|
| 557 |
|
|
|
| 558 |
|
|
#ifndef __FP_FRAC_SUB_3
|
| 559 |
|
|
#define __FP_FRAC_SUB_3(r2,r1,r0,x2,x1,x0,y2,y1,y0) \
|
| 560 |
|
|
do { \
|
| 561 |
|
|
_FP_W_TYPE _c1, _c2; \
|
| 562 |
|
|
r0 = x0 - y0; \
|
| 563 |
|
|
_c1 = r0 > x0; \
|
| 564 |
|
|
r1 = x1 - y1; \
|
| 565 |
|
|
_c2 = r1 > x1; \
|
| 566 |
|
|
r1 -= _c1; \
|
| 567 |
|
|
_c2 |= _c1 && (y1 == x1); \
|
| 568 |
|
|
r2 = x2 - y2 - _c2; \
|
| 569 |
|
|
} while (0)
|
| 570 |
|
|
#endif
|
| 571 |
|
|
|
| 572 |
|
|
#ifndef __FP_FRAC_SUB_4
|
| 573 |
|
|
#define __FP_FRAC_SUB_4(r3,r2,r1,r0,x3,x2,x1,x0,y3,y2,y1,y0) \
|
| 574 |
|
|
do { \
|
| 575 |
|
|
_FP_W_TYPE _c1, _c2, _c3; \
|
| 576 |
|
|
r0 = x0 - y0; \
|
| 577 |
|
|
_c1 = r0 > x0; \
|
| 578 |
|
|
r1 = x1 - y1; \
|
| 579 |
|
|
_c2 = r1 > x1; \
|
| 580 |
|
|
r1 -= _c1; \
|
| 581 |
|
|
_c2 |= _c1 && (y1 == x1); \
|
| 582 |
|
|
r2 = x2 - y2; \
|
| 583 |
|
|
_c3 = r2 > x2; \
|
| 584 |
|
|
r2 -= _c2; \
|
| 585 |
|
|
_c3 |= _c2 && (y2 == x2); \
|
| 586 |
|
|
r3 = x3 - y3 - _c3; \
|
| 587 |
|
|
} while (0)
|
| 588 |
|
|
#endif
|
| 589 |
|
|
|
| 590 |
|
|
#ifndef __FP_FRAC_DEC_3
|
| 591 |
|
|
#define __FP_FRAC_DEC_3(x2,x1,x0,y2,y1,y0) \
|
| 592 |
|
|
do { \
|
| 593 |
|
|
UWtype _t0, _t1, _t2; \
|
| 594 |
|
|
_t0 = x0, _t1 = x1, _t2 = x2; \
|
| 595 |
|
|
__FP_FRAC_SUB_3 (x2, x1, x0, _t2, _t1, _t0, y2, y1, y0); \
|
| 596 |
|
|
} while (0)
|
| 597 |
|
|
#endif
|
| 598 |
|
|
|
| 599 |
|
|
#ifndef __FP_FRAC_DEC_4
|
| 600 |
|
|
#define __FP_FRAC_DEC_4(x3,x2,x1,x0,y3,y2,y1,y0) \
|
| 601 |
|
|
do { \
|
| 602 |
|
|
UWtype _t0, _t1, _t2, _t3; \
|
| 603 |
|
|
_t0 = x0, _t1 = x1, _t2 = x2, _t3 = x3; \
|
| 604 |
|
|
__FP_FRAC_SUB_4 (x3,x2,x1,x0,_t3,_t2,_t1,_t0, y3,y2,y1,y0); \
|
| 605 |
|
|
} while (0)
|
| 606 |
|
|
#endif
|
| 607 |
|
|
|
| 608 |
|
|
#ifndef __FP_FRAC_ADDI_4
|
| 609 |
|
|
#define __FP_FRAC_ADDI_4(x3,x2,x1,x0,i) \
|
| 610 |
|
|
do { \
|
| 611 |
|
|
UWtype _t; \
|
| 612 |
|
|
_t = ((x0 += i) < i); \
|
| 613 |
|
|
x1 += _t; _t = (x1 < _t); \
|
| 614 |
|
|
x2 += _t; _t = (x2 < _t); \
|
| 615 |
|
|
x3 += _t; \
|
| 616 |
|
|
} while (0)
|
| 617 |
|
|
#endif
|
| 618 |
|
|
|
| 619 |
|
|
/* Convert FP values between word sizes. This appears to be more
|
| 620 |
|
|
* complicated than I'd have expected it to be, so these might be
|
| 621 |
|
|
* wrong... These macros are in any case somewhat bogus because they
|
| 622 |
|
|
* use information about what various FRAC_n variables look like
|
| 623 |
|
|
* internally [eg, that 2 word vars are X_f0 and x_f1]. But so do
|
| 624 |
|
|
* the ones in op-2.h and op-1.h.
|
| 625 |
|
|
*/
|
| 626 |
|
|
#define _FP_FRAC_COPY_1_4(D, S) (D##_f = S##_f[0])
|
| 627 |
|
|
|
| 628 |
|
|
#define _FP_FRAC_COPY_2_4(D, S) \
|
| 629 |
|
|
do { \
|
| 630 |
|
|
D##_f0 = S##_f[0]; \
|
| 631 |
|
|
D##_f1 = S##_f[1]; \
|
| 632 |
|
|
} while (0)
|
| 633 |
|
|
|
| 634 |
|
|
/* Assembly/disassembly for converting to/from integral types.
|
| 635 |
|
|
* No shifting or overflow handled here.
|
| 636 |
|
|
*/
|
| 637 |
|
|
/* Put the FP value X into r, which is an integer of size rsize. */
|
| 638 |
|
|
#define _FP_FRAC_ASSEMBLE_4(r, X, rsize) \
|
| 639 |
|
|
do { \
|
| 640 |
|
|
if (rsize <= _FP_W_TYPE_SIZE) \
|
| 641 |
|
|
r = X##_f[0]; \
|
| 642 |
|
|
else if (rsize <= 2*_FP_W_TYPE_SIZE) \
|
| 643 |
|
|
{ \
|
| 644 |
|
|
r = X##_f[1]; \
|
| 645 |
|
|
r <<= _FP_W_TYPE_SIZE; \
|
| 646 |
|
|
r += X##_f[0]; \
|
| 647 |
|
|
} \
|
| 648 |
|
|
else \
|
| 649 |
|
|
{ \
|
| 650 |
|
|
/* I'm feeling lazy so we deal with int == 3words (implausible)*/ \
|
| 651 |
|
|
/* and int == 4words as a single case. */ \
|
| 652 |
|
|
r = X##_f[3]; \
|
| 653 |
|
|
r <<= _FP_W_TYPE_SIZE; \
|
| 654 |
|
|
r += X##_f[2]; \
|
| 655 |
|
|
r <<= _FP_W_TYPE_SIZE; \
|
| 656 |
|
|
r += X##_f[1]; \
|
| 657 |
|
|
r <<= _FP_W_TYPE_SIZE; \
|
| 658 |
|
|
r += X##_f[0]; \
|
| 659 |
|
|
} \
|
| 660 |
|
|
} while (0)
|
| 661 |
|
|
|
| 662 |
|
|
/* "No disassemble Number Five!" */
|
| 663 |
|
|
/* move an integer of size rsize into X's fractional part. We rely on
|
| 664 |
|
|
* the _f[] array consisting of words of size _FP_W_TYPE_SIZE to avoid
|
| 665 |
|
|
* having to mask the values we store into it.
|
| 666 |
|
|
*/
|
| 667 |
|
|
#define _FP_FRAC_DISASSEMBLE_4(X, r, rsize) \
|
| 668 |
|
|
do { \
|
| 669 |
|
|
X##_f[0] = r; \
|
| 670 |
|
|
X##_f[1] = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
|
| 671 |
|
|
X##_f[2] = (rsize <= 2*_FP_W_TYPE_SIZE ? 0 : r >> 2*_FP_W_TYPE_SIZE); \
|
| 672 |
|
|
X##_f[3] = (rsize <= 3*_FP_W_TYPE_SIZE ? 0 : r >> 3*_FP_W_TYPE_SIZE); \
|
| 673 |
|
|
} while (0);
|
| 674 |
|
|
|
| 675 |
|
|
#define _FP_FRAC_COPY_4_1(D, S) \
|
| 676 |
|
|
do { \
|
| 677 |
|
|
D##_f[0] = S##_f; \
|
| 678 |
|
|
D##_f[1] = D##_f[2] = D##_f[3] = 0; \
|
| 679 |
|
|
} while (0)
|
| 680 |
|
|
|
| 681 |
|
|
#define _FP_FRAC_COPY_4_2(D, S) \
|
| 682 |
|
|
do { \
|
| 683 |
|
|
D##_f[0] = S##_f0; \
|
| 684 |
|
|
D##_f[1] = S##_f1; \
|
| 685 |
|
|
D##_f[2] = D##_f[3] = 0; \
|
| 686 |
|
|
} while (0)
|
| 687 |
|
|
|
| 688 |
|
|
#define _FP_FRAC_COPY_4_4(D,S) _FP_FRAC_COPY_4(D,S)
|
