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julius |
/* Software floating-point emulation.
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Basic two-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_2(X) _FP_W_TYPE X##_f0, X##_f1
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#define _FP_FRAC_COPY_2(D,S) (D##_f0 = S##_f0, D##_f1 = S##_f1)
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#define _FP_FRAC_SET_2(X,I) __FP_FRAC_SET_2(X, I)
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#define _FP_FRAC_HIGH_2(X) (X##_f1)
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#define _FP_FRAC_LOW_2(X) (X##_f0)
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#define _FP_FRAC_WORD_2(X,w) (X##_f##w)
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#define _FP_FRAC_SLL_2(X,N) \
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(void)(((N) < _FP_W_TYPE_SIZE) \
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? ({ \
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if (__builtin_constant_p(N) && (N) == 1) \
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{ \
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X##_f1 = X##_f1 + X##_f1 + (((_FP_WS_TYPE)(X##_f0)) < 0); \
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X##_f0 += X##_f0; \
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} \
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else \
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{ \
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X##_f1 = X##_f1 << (N) | X##_f0 >> (_FP_W_TYPE_SIZE - (N)); \
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X##_f0 <<= (N); \
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} \
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0; \
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}) \
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: ({ \
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X##_f1 = X##_f0 << ((N) - _FP_W_TYPE_SIZE); \
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X##_f0 = 0; \
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}))
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#define _FP_FRAC_SRL_2(X,N) \
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(void)(((N) < _FP_W_TYPE_SIZE) \
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? ({ \
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X##_f0 = X##_f0 >> (N) | X##_f1 << (_FP_W_TYPE_SIZE - (N)); \
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X##_f1 >>= (N); \
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}) \
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: ({ \
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X##_f0 = X##_f1 >> ((N) - _FP_W_TYPE_SIZE); \
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X##_f1 = 0; \
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}))
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/* Right shift with sticky-lsb. */
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#define _FP_FRAC_SRST_2(X,S, N,sz) \
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(void)(((N) < _FP_W_TYPE_SIZE) \
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? ({ \
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S = (__builtin_constant_p(N) && (N) == 1 \
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? X##_f0 & 1 \
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: (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0); \
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X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N)); \
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X##_f1 >>= (N); \
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}) \
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: ({ \
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S = ((((N) == _FP_W_TYPE_SIZE \
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? 0 \
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: (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \
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| X##_f0) != 0); \
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X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE)); \
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X##_f1 = 0; \
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}))
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#define _FP_FRAC_SRS_2(X,N,sz) \
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(void)(((N) < _FP_W_TYPE_SIZE) \
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? ({ \
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X##_f0 = (X##_f1 << (_FP_W_TYPE_SIZE - (N)) | X##_f0 >> (N) | \
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(__builtin_constant_p(N) && (N) == 1 \
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? X##_f0 & 1 \
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: (X##_f0 << (_FP_W_TYPE_SIZE - (N))) != 0)); \
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X##_f1 >>= (N); \
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}) \
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: ({ \
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X##_f0 = (X##_f1 >> ((N) - _FP_W_TYPE_SIZE) | \
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((((N) == _FP_W_TYPE_SIZE \
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? 0 \
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: (X##_f1 << (2*_FP_W_TYPE_SIZE - (N)))) \
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| X##_f0) != 0)); \
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X##_f1 = 0; \
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}))
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#define _FP_FRAC_ADDI_2(X,I) \
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__FP_FRAC_ADDI_2(X##_f1, X##_f0, I)
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#define _FP_FRAC_ADD_2(R,X,Y) \
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__FP_FRAC_ADD_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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#define _FP_FRAC_SUB_2(R,X,Y) \
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__FP_FRAC_SUB_2(R##_f1, R##_f0, X##_f1, X##_f0, Y##_f1, Y##_f0)
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#define _FP_FRAC_DEC_2(X,Y) \
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__FP_FRAC_DEC_2(X##_f1, X##_f0, Y##_f1, Y##_f0)
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#define _FP_FRAC_CLZ_2(R,X) \
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do { \
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if (X##_f1) \
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__FP_CLZ(R,X##_f1); \
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else \
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{ \
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__FP_CLZ(R,X##_f0); \
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R += _FP_W_TYPE_SIZE; \
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} \
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} while(0)
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/* Predicates */
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#define _FP_FRAC_NEGP_2(X) ((_FP_WS_TYPE)X##_f1 < 0)
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#define _FP_FRAC_ZEROP_2(X) ((X##_f1 | X##_f0) == 0)
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#define _FP_FRAC_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) & _FP_OVERFLOW_##fs)
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#define _FP_FRAC_CLEAR_OVERP_2(fs,X) (_FP_FRAC_HIGH_##fs(X) &= ~_FP_OVERFLOW_##fs)
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#define _FP_FRAC_EQ_2(X, Y) (X##_f1 == Y##_f1 && X##_f0 == Y##_f0)
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#define _FP_FRAC_GT_2(X, Y) \
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(X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 > Y##_f0))
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#define _FP_FRAC_GE_2(X, Y) \
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(X##_f1 > Y##_f1 || (X##_f1 == Y##_f1 && X##_f0 >= Y##_f0))
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#define _FP_ZEROFRAC_2 0, 0
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#define _FP_MINFRAC_2 0, 1
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#define _FP_MAXFRAC_2 (~(_FP_WS_TYPE)0), (~(_FP_WS_TYPE)0)
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/*
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* Internals
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*/
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#define __FP_FRAC_SET_2(X,I1,I0) (X##_f0 = I0, X##_f1 = I1)
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#define __FP_CLZ_2(R, xh, xl) \
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do { \
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if (xh) \
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__FP_CLZ(R,xh); \
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else \
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{ \
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__FP_CLZ(R,xl); \
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R += _FP_W_TYPE_SIZE; \
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} \
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} while(0)
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#if 0
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#ifndef __FP_FRAC_ADDI_2
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#define __FP_FRAC_ADDI_2(xh, xl, i) \
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(xh += ((xl += i) < i))
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#endif
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#ifndef __FP_FRAC_ADD_2
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#define __FP_FRAC_ADD_2(rh, rl, xh, xl, yh, yl) \
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(rh = xh + yh + ((rl = xl + yl) < xl))
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#endif
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#ifndef __FP_FRAC_SUB_2
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#define __FP_FRAC_SUB_2(rh, rl, xh, xl, yh, yl) \
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(rh = xh - yh - ((rl = xl - yl) > xl))
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#endif
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#ifndef __FP_FRAC_DEC_2
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#define __FP_FRAC_DEC_2(xh, xl, yh, yl) \
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do { \
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UWtype _t = xl; \
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xh -= yh + ((xl -= yl) > _t); \
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} while (0)
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#endif
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#else
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#undef __FP_FRAC_ADDI_2
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#define __FP_FRAC_ADDI_2(xh, xl, i) add_ssaaaa(xh, xl, xh, xl, 0, i)
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#undef __FP_FRAC_ADD_2
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#define __FP_FRAC_ADD_2 add_ssaaaa
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#undef __FP_FRAC_SUB_2
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#define __FP_FRAC_SUB_2 sub_ddmmss
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#undef __FP_FRAC_DEC_2
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#define __FP_FRAC_DEC_2(xh, xl, yh, yl) sub_ddmmss(xh, xl, xh, xl, yh, yl)
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| 198 |
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#endif
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/*
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* Unpack the raw bits of a native fp value. Do not classify or
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| 202 |
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* normalize the data.
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*/
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#define _FP_UNPACK_RAW_2(fs, X, val) \
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do { \
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union _FP_UNION_##fs _flo; _flo.flt = (val); \
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\
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X##_f0 = _flo.bits.frac0; \
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X##_f1 = _flo.bits.frac1; \
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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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| 215 |
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#define _FP_UNPACK_RAW_2_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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| 219 |
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\
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| 220 |
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X##_f0 = _flo->bits.frac0; \
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X##_f1 = _flo->bits.frac1; \
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X##_e = _flo->bits.exp; \
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| 223 |
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X##_s = _flo->bits.sign; \
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| 224 |
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} while (0)
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| 225 |
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| 226 |
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| 227 |
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/*
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| 228 |
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* Repack the raw bits of a native fp value.
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| 229 |
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*/
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| 230 |
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| 231 |
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#define _FP_PACK_RAW_2(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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\
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| 235 |
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_flo.bits.frac0 = X##_f0; \
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| 236 |
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_flo.bits.frac1 = X##_f1; \
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| 237 |
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_flo.bits.exp = X##_e; \
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| 238 |
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_flo.bits.sign = X##_s; \
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| 239 |
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\
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| 240 |
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(val) = _flo.flt; \
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| 241 |
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} while (0)
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| 242 |
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| 243 |
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#define _FP_PACK_RAW_2_P(fs, val, X) \
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| 244 |
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do { \
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| 245 |
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union _FP_UNION_##fs *_flo = \
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| 246 |
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(union _FP_UNION_##fs *)(val); \
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| 247 |
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\
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| 248 |
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_flo->bits.frac0 = X##_f0; \
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| 249 |
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_flo->bits.frac1 = X##_f1; \
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| 250 |
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_flo->bits.exp = X##_e; \
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| 251 |
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_flo->bits.sign = X##_s; \
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| 252 |
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} while (0)
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| 253 |
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| 254 |
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| 255 |
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/*
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| 256 |
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* Multiplication algorithms:
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| 257 |
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*/
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| 258 |
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| 259 |
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/* Given a 1W * 1W => 2W primitive, do the extended multiplication. */
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| 260 |
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| 261 |
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#define _FP_MUL_MEAT_2_wide(wfracbits, R, X, Y, doit) \
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| 262 |
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do { \
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| 263 |
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_FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
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| 264 |
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\
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| 265 |
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doit(_FP_FRAC_WORD_4(_z,1), _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
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| 266 |
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doit(_b_f1, _b_f0, X##_f0, Y##_f1); \
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| 267 |
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doit(_c_f1, _c_f0, X##_f1, Y##_f0); \
|
| 268 |
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doit(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), X##_f1, Y##_f1); \
|
| 269 |
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\
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| 270 |
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__FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 271 |
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_FP_FRAC_WORD_4(_z,1), 0, _b_f1, _b_f0, \
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| 272 |
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_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 273 |
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_FP_FRAC_WORD_4(_z,1)); \
|
| 274 |
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__FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 275 |
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_FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0, \
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| 276 |
|
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_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
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| 277 |
|
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_FP_FRAC_WORD_4(_z,1)); \
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| 278 |
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\
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| 279 |
|
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/* Normalize since we know where the msb of the multiplicands \
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| 280 |
|
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were (bit B), we know that the msb of the of the product is \
|
| 281 |
|
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at either 2B or 2B-1. */ \
|
| 282 |
|
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_FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
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| 283 |
|
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R##_f0 = _FP_FRAC_WORD_4(_z,0); \
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| 284 |
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R##_f1 = _FP_FRAC_WORD_4(_z,1); \
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| 285 |
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} while (0)
|
| 286 |
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| 287 |
|
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/* Given a 1W * 1W => 2W primitive, do the extended multiplication.
|
| 288 |
|
|
Do only 3 multiplications instead of four. This one is for machines
|
| 289 |
|
|
where multiplication is much more expensive than subtraction. */
|
| 290 |
|
|
|
| 291 |
|
|
#define _FP_MUL_MEAT_2_wide_3mul(wfracbits, R, X, Y, doit) \
|
| 292 |
|
|
do { \
|
| 293 |
|
|
_FP_FRAC_DECL_4(_z); _FP_FRAC_DECL_2(_b); _FP_FRAC_DECL_2(_c); \
|
| 294 |
|
|
_FP_W_TYPE _d; \
|
| 295 |
|
|
int _c1, _c2; \
|
| 296 |
|
|
\
|
| 297 |
|
|
_b_f0 = X##_f0 + X##_f1; \
|
| 298 |
|
|
_c1 = _b_f0 < X##_f0; \
|
| 299 |
|
|
_b_f1 = Y##_f0 + Y##_f1; \
|
| 300 |
|
|
_c2 = _b_f1 < Y##_f0; \
|
| 301 |
|
|
doit(_d, _FP_FRAC_WORD_4(_z,0), X##_f0, Y##_f0); \
|
| 302 |
|
|
doit(_FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1), _b_f0, _b_f1); \
|
| 303 |
|
|
doit(_c_f1, _c_f0, X##_f1, Y##_f1); \
|
| 304 |
|
|
\
|
| 305 |
|
|
_b_f0 &= -_c2; \
|
| 306 |
|
|
_b_f1 &= -_c1; \
|
| 307 |
|
|
__FP_FRAC_ADD_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
|
| 308 |
|
|
_FP_FRAC_WORD_4(_z,1), (_c1 & _c2), 0, _d, \
|
| 309 |
|
|
0, _FP_FRAC_WORD_4(_z,2), _FP_FRAC_WORD_4(_z,1)); \
|
| 310 |
|
|
__FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
|
| 311 |
|
|
_b_f0); \
|
| 312 |
|
|
__FP_FRAC_ADDI_2(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
|
| 313 |
|
|
_b_f1); \
|
| 314 |
|
|
__FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
|
| 315 |
|
|
_FP_FRAC_WORD_4(_z,1), \
|
| 316 |
|
|
0, _d, _FP_FRAC_WORD_4(_z,0)); \
|
| 317 |
|
|
__FP_FRAC_DEC_3(_FP_FRAC_WORD_4(_z,3),_FP_FRAC_WORD_4(_z,2), \
|
| 318 |
|
|
_FP_FRAC_WORD_4(_z,1), 0, _c_f1, _c_f0); \
|
| 319 |
|
|
__FP_FRAC_ADD_2(_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2), \
|
| 320 |
|
|
_c_f1, _c_f0, \
|
| 321 |
|
|
_FP_FRAC_WORD_4(_z,3), _FP_FRAC_WORD_4(_z,2)); \
|
| 322 |
|
|
\
|
| 323 |
|
|
/* Normalize since we know where the msb of the multiplicands \
|
| 324 |
|
|
were (bit B), we know that the msb of the of the product is \
|
| 325 |
|
|
at either 2B or 2B-1. */ \
|
| 326 |
|
|
_FP_FRAC_SRS_4(_z, wfracbits-1, 2*wfracbits); \
|
| 327 |
|
|
R##_f0 = _FP_FRAC_WORD_4(_z,0); \
|
| 328 |
|
|
R##_f1 = _FP_FRAC_WORD_4(_z,1); \
|
| 329 |
|
|
} while (0)
|
| 330 |
|
|
|
| 331 |
|
|
#define _FP_MUL_MEAT_2_gmp(wfracbits, R, X, Y) \
|
| 332 |
|
|
do { \
|
| 333 |
|
|
_FP_FRAC_DECL_4(_z); \
|
| 334 |
|
|
_FP_W_TYPE _x[2], _y[2]; \
|
| 335 |
|
|
_x[0] = X##_f0; _x[1] = X##_f1; \
|
| 336 |
|
|
_y[0] = Y##_f0; _y[1] = Y##_f1; \
|
| 337 |
|
|
\
|
| 338 |
|
|
mpn_mul_n(_z_f, _x, _y, 2); \
|
| 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_4(_z, wfracbits-1, 2*wfracbits); \
|
| 344 |
|
|
R##_f0 = _z_f[0]; \
|
| 345 |
|
|
R##_f1 = _z_f[1]; \
|
| 346 |
|
|
} while (0)
|
| 347 |
|
|
|
| 348 |
|
|
/* Do at most 120x120=240 bits multiplication using double floating
|
| 349 |
|
|
point multiplication. This is useful if floating point
|
| 350 |
|
|
multiplication has much bigger throughput than integer multiply.
|
| 351 |
|
|
It is supposed to work for _FP_W_TYPE_SIZE 64 and wfracbits
|
| 352 |
|
|
between 106 and 120 only.
|
| 353 |
|
|
Caller guarantees that X and Y has (1LLL << (wfracbits - 1)) set.
|
| 354 |
|
|
SETFETZ is a macro which will disable all FPU exceptions and set rounding
|
| 355 |
|
|
towards zero, RESETFE should optionally reset it back. */
|
| 356 |
|
|
|
| 357 |
|
|
#define _FP_MUL_MEAT_2_120_240_double(wfracbits, R, X, Y, setfetz, resetfe) \
|
| 358 |
|
|
do { \
|
| 359 |
|
|
static const double _const[] = { \
|
| 360 |
|
|
/* 2^-24 */ 5.9604644775390625e-08, \
|
| 361 |
|
|
/* 2^-48 */ 3.5527136788005009e-15, \
|
| 362 |
|
|
/* 2^-72 */ 2.1175823681357508e-22, \
|
| 363 |
|
|
/* 2^-96 */ 1.2621774483536189e-29, \
|
| 364 |
|
|
/* 2^28 */ 2.68435456e+08, \
|
| 365 |
|
|
/* 2^4 */ 1.600000e+01, \
|
| 366 |
|
|
/* 2^-20 */ 9.5367431640625e-07, \
|
| 367 |
|
|
/* 2^-44 */ 5.6843418860808015e-14, \
|
| 368 |
|
|
/* 2^-68 */ 3.3881317890172014e-21, \
|
| 369 |
|
|
/* 2^-92 */ 2.0194839173657902e-28, \
|
| 370 |
|
|
/* 2^-116 */ 1.2037062152420224e-35}; \
|
| 371 |
|
|
double _a240, _b240, _c240, _d240, _e240, _f240, \
|
| 372 |
|
|
_g240, _h240, _i240, _j240, _k240; \
|
| 373 |
|
|
union { double d; UDItype i; } _l240, _m240, _n240, _o240, \
|
| 374 |
|
|
_p240, _q240, _r240, _s240; \
|
| 375 |
|
|
UDItype _t240, _u240, _v240, _w240, _x240, _y240 = 0; \
|
| 376 |
|
|
\
|
| 377 |
|
|
if (wfracbits < 106 || wfracbits > 120) \
|
| 378 |
|
|
abort(); \
|
| 379 |
|
|
\
|
| 380 |
|
|
setfetz; \
|
| 381 |
|
|
\
|
| 382 |
|
|
_e240 = (double)(long)(X##_f0 & 0xffffff); \
|
| 383 |
|
|
_j240 = (double)(long)(Y##_f0 & 0xffffff); \
|
| 384 |
|
|
_d240 = (double)(long)((X##_f0 >> 24) & 0xffffff); \
|
| 385 |
|
|
_i240 = (double)(long)((Y##_f0 >> 24) & 0xffffff); \
|
| 386 |
|
|
_c240 = (double)(long)(((X##_f1 << 16) & 0xffffff) | (X##_f0 >> 48)); \
|
| 387 |
|
|
_h240 = (double)(long)(((Y##_f1 << 16) & 0xffffff) | (Y##_f0 >> 48)); \
|
| 388 |
|
|
_b240 = (double)(long)((X##_f1 >> 8) & 0xffffff); \
|
| 389 |
|
|
_g240 = (double)(long)((Y##_f1 >> 8) & 0xffffff); \
|
| 390 |
|
|
_a240 = (double)(long)(X##_f1 >> 32); \
|
| 391 |
|
|
_f240 = (double)(long)(Y##_f1 >> 32); \
|
| 392 |
|
|
_e240 *= _const[3]; \
|
| 393 |
|
|
_j240 *= _const[3]; \
|
| 394 |
|
|
_d240 *= _const[2]; \
|
| 395 |
|
|
_i240 *= _const[2]; \
|
| 396 |
|
|
_c240 *= _const[1]; \
|
| 397 |
|
|
_h240 *= _const[1]; \
|
| 398 |
|
|
_b240 *= _const[0]; \
|
| 399 |
|
|
_g240 *= _const[0]; \
|
| 400 |
|
|
_s240.d = _e240*_j240;\
|
| 401 |
|
|
_r240.d = _d240*_j240 + _e240*_i240;\
|
| 402 |
|
|
_q240.d = _c240*_j240 + _d240*_i240 + _e240*_h240;\
|
| 403 |
|
|
_p240.d = _b240*_j240 + _c240*_i240 + _d240*_h240 + _e240*_g240;\
|
| 404 |
|
|
_o240.d = _a240*_j240 + _b240*_i240 + _c240*_h240 + _d240*_g240 + _e240*_f240;\
|
| 405 |
|
|
_n240.d = _a240*_i240 + _b240*_h240 + _c240*_g240 + _d240*_f240; \
|
| 406 |
|
|
_m240.d = _a240*_h240 + _b240*_g240 + _c240*_f240; \
|
| 407 |
|
|
_l240.d = _a240*_g240 + _b240*_f240; \
|
| 408 |
|
|
_k240 = _a240*_f240; \
|
| 409 |
|
|
_r240.d += _s240.d; \
|
| 410 |
|
|
_q240.d += _r240.d; \
|
| 411 |
|
|
_p240.d += _q240.d; \
|
| 412 |
|
|
_o240.d += _p240.d; \
|
| 413 |
|
|
_n240.d += _o240.d; \
|
| 414 |
|
|
_m240.d += _n240.d; \
|
| 415 |
|
|
_l240.d += _m240.d; \
|
| 416 |
|
|
_k240 += _l240.d; \
|
| 417 |
|
|
_s240.d -= ((_const[10]+_s240.d)-_const[10]); \
|
| 418 |
|
|
_r240.d -= ((_const[9]+_r240.d)-_const[9]); \
|
| 419 |
|
|
_q240.d -= ((_const[8]+_q240.d)-_const[8]); \
|
| 420 |
|
|
_p240.d -= ((_const[7]+_p240.d)-_const[7]); \
|
| 421 |
|
|
_o240.d += _const[7]; \
|
| 422 |
|
|
_n240.d += _const[6]; \
|
| 423 |
|
|
_m240.d += _const[5]; \
|
| 424 |
|
|
_l240.d += _const[4]; \
|
| 425 |
|
|
if (_s240.d != 0.0) _y240 = 1; \
|
| 426 |
|
|
if (_r240.d != 0.0) _y240 = 1; \
|
| 427 |
|
|
if (_q240.d != 0.0) _y240 = 1; \
|
| 428 |
|
|
if (_p240.d != 0.0) _y240 = 1; \
|
| 429 |
|
|
_t240 = (DItype)_k240; \
|
| 430 |
|
|
_u240 = _l240.i; \
|
| 431 |
|
|
_v240 = _m240.i; \
|
| 432 |
|
|
_w240 = _n240.i; \
|
| 433 |
|
|
_x240 = _o240.i; \
|
| 434 |
|
|
R##_f1 = (_t240 << (128 - (wfracbits - 1))) \
|
| 435 |
|
|
| ((_u240 & 0xffffff) >> ((wfracbits - 1) - 104)); \
|
| 436 |
|
|
R##_f0 = ((_u240 & 0xffffff) << (168 - (wfracbits - 1))) \
|
| 437 |
|
|
| ((_v240 & 0xffffff) << (144 - (wfracbits - 1))) \
|
| 438 |
|
|
| ((_w240 & 0xffffff) << (120 - (wfracbits - 1))) \
|
| 439 |
|
|
| ((_x240 & 0xffffff) >> ((wfracbits - 1) - 96)) \
|
| 440 |
|
|
| _y240; \
|
| 441 |
|
|
resetfe; \
|
| 442 |
|
|
} while (0)
|
| 443 |
|
|
|
| 444 |
|
|
/*
|
| 445 |
|
|
* Division algorithms:
|
| 446 |
|
|
*/
|
| 447 |
|
|
|
| 448 |
|
|
#define _FP_DIV_MEAT_2_udiv(fs, R, X, Y) \
|
| 449 |
|
|
do { \
|
| 450 |
|
|
_FP_W_TYPE _n_f2, _n_f1, _n_f0, _r_f1, _r_f0, _m_f1, _m_f0; \
|
| 451 |
|
|
if (_FP_FRAC_GT_2(X, Y)) \
|
| 452 |
|
|
{ \
|
| 453 |
|
|
_n_f2 = X##_f1 >> 1; \
|
| 454 |
|
|
_n_f1 = X##_f1 << (_FP_W_TYPE_SIZE - 1) | X##_f0 >> 1; \
|
| 455 |
|
|
_n_f0 = X##_f0 << (_FP_W_TYPE_SIZE - 1); \
|
| 456 |
|
|
} \
|
| 457 |
|
|
else \
|
| 458 |
|
|
{ \
|
| 459 |
|
|
R##_e--; \
|
| 460 |
|
|
_n_f2 = X##_f1; \
|
| 461 |
|
|
_n_f1 = X##_f0; \
|
| 462 |
|
|
_n_f0 = 0; \
|
| 463 |
|
|
} \
|
| 464 |
|
|
\
|
| 465 |
|
|
/* Normalize, i.e. make the most significant bit of the \
|
| 466 |
|
|
denominator set. */ \
|
| 467 |
|
|
_FP_FRAC_SLL_2(Y, _FP_WFRACXBITS_##fs); \
|
| 468 |
|
|
\
|
| 469 |
|
|
udiv_qrnnd(R##_f1, _r_f1, _n_f2, _n_f1, Y##_f1); \
|
| 470 |
|
|
umul_ppmm(_m_f1, _m_f0, R##_f1, Y##_f0); \
|
| 471 |
|
|
_r_f0 = _n_f0; \
|
| 472 |
|
|
if (_FP_FRAC_GT_2(_m, _r)) \
|
| 473 |
|
|
{ \
|
| 474 |
|
|
R##_f1--; \
|
| 475 |
|
|
_FP_FRAC_ADD_2(_r, Y, _r); \
|
| 476 |
|
|
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
| 477 |
|
|
{ \
|
| 478 |
|
|
R##_f1--; \
|
| 479 |
|
|
_FP_FRAC_ADD_2(_r, Y, _r); \
|
| 480 |
|
|
} \
|
| 481 |
|
|
} \
|
| 482 |
|
|
_FP_FRAC_DEC_2(_r, _m); \
|
| 483 |
|
|
\
|
| 484 |
|
|
if (_r_f1 == Y##_f1) \
|
| 485 |
|
|
{ \
|
| 486 |
|
|
/* This is a special case, not an optimization \
|
| 487 |
|
|
(_r/Y##_f1 would not fit into UWtype). \
|
| 488 |
|
|
As _r is guaranteed to be < Y, R##_f0 can be either \
|
| 489 |
|
|
(UWtype)-1 or (UWtype)-2. But as we know what kind \
|
| 490 |
|
|
of bits it is (sticky, guard, round), we don't care. \
|
| 491 |
|
|
We also don't care what the reminder is, because the \
|
| 492 |
|
|
guard bit will be set anyway. -jj */ \
|
| 493 |
|
|
R##_f0 = -1; \
|
| 494 |
|
|
} \
|
| 495 |
|
|
else \
|
| 496 |
|
|
{ \
|
| 497 |
|
|
udiv_qrnnd(R##_f0, _r_f1, _r_f1, _r_f0, Y##_f1); \
|
| 498 |
|
|
umul_ppmm(_m_f1, _m_f0, R##_f0, Y##_f0); \
|
| 499 |
|
|
_r_f0 = 0; \
|
| 500 |
|
|
if (_FP_FRAC_GT_2(_m, _r)) \
|
| 501 |
|
|
{ \
|
| 502 |
|
|
R##_f0--; \
|
| 503 |
|
|
_FP_FRAC_ADD_2(_r, Y, _r); \
|
| 504 |
|
|
if (_FP_FRAC_GE_2(_r, Y) && _FP_FRAC_GT_2(_m, _r)) \
|
| 505 |
|
|
{ \
|
| 506 |
|
|
R##_f0--; \
|
| 507 |
|
|
_FP_FRAC_ADD_2(_r, Y, _r); \
|
| 508 |
|
|
} \
|
| 509 |
|
|
} \
|
| 510 |
|
|
if (!_FP_FRAC_EQ_2(_r, _m)) \
|
| 511 |
|
|
R##_f0 |= _FP_WORK_STICKY; \
|
| 512 |
|
|
} \
|
| 513 |
|
|
} while (0)
|
| 514 |
|
|
|
| 515 |
|
|
|
| 516 |
|
|
#define _FP_DIV_MEAT_2_gmp(fs, R, X, Y) \
|
| 517 |
|
|
do { \
|
| 518 |
|
|
_FP_W_TYPE _x[4], _y[2], _z[4]; \
|
| 519 |
|
|
_y[0] = Y##_f0; _y[1] = Y##_f1; \
|
| 520 |
|
|
_x[0] = _x[3] = 0; \
|
| 521 |
|
|
if (_FP_FRAC_GT_2(X, Y)) \
|
| 522 |
|
|
{ \
|
| 523 |
|
|
R##_e++; \
|
| 524 |
|
|
_x[1] = (X##_f0 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE) | \
|
| 525 |
|
|
X##_f1 >> (_FP_W_TYPE_SIZE - \
|
| 526 |
|
|
(_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE))); \
|
| 527 |
|
|
_x[2] = X##_f1 << (_FP_WFRACBITS_##fs-1 - _FP_W_TYPE_SIZE); \
|
| 528 |
|
|
} \
|
| 529 |
|
|
else \
|
| 530 |
|
|
{ \
|
| 531 |
|
|
_x[1] = (X##_f0 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE) | \
|
| 532 |
|
|
X##_f1 >> (_FP_W_TYPE_SIZE - \
|
| 533 |
|
|
(_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE))); \
|
| 534 |
|
|
_x[2] = X##_f1 << (_FP_WFRACBITS_##fs - _FP_W_TYPE_SIZE); \
|
| 535 |
|
|
} \
|
| 536 |
|
|
\
|
| 537 |
|
|
(void) mpn_divrem (_z, 0, _x, 4, _y, 2); \
|
| 538 |
|
|
R##_f1 = _z[1]; \
|
| 539 |
|
|
R##_f0 = _z[0] | ((_x[0] | _x[1]) != 0); \
|
| 540 |
|
|
} while (0)
|
| 541 |
|
|
|
| 542 |
|
|
|
| 543 |
|
|
/*
|
| 544 |
|
|
* Square root algorithms:
|
| 545 |
|
|
* We have just one right now, maybe Newton approximation
|
| 546 |
|
|
* should be added for those machines where division is fast.
|
| 547 |
|
|
*/
|
| 548 |
|
|
|
| 549 |
|
|
#define _FP_SQRT_MEAT_2(R, S, T, X, q) \
|
| 550 |
|
|
do { \
|
| 551 |
|
|
while (q) \
|
| 552 |
|
|
{ \
|
| 553 |
|
|
T##_f1 = S##_f1 + q; \
|
| 554 |
|
|
if (T##_f1 <= X##_f1) \
|
| 555 |
|
|
{ \
|
| 556 |
|
|
S##_f1 = T##_f1 + q; \
|
| 557 |
|
|
X##_f1 -= T##_f1; \
|
| 558 |
|
|
R##_f1 += q; \
|
| 559 |
|
|
} \
|
| 560 |
|
|
_FP_FRAC_SLL_2(X, 1); \
|
| 561 |
|
|
q >>= 1; \
|
| 562 |
|
|
} \
|
| 563 |
|
|
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 564 |
|
|
while (q != _FP_WORK_ROUND) \
|
| 565 |
|
|
{ \
|
| 566 |
|
|
T##_f0 = S##_f0 + q; \
|
| 567 |
|
|
T##_f1 = S##_f1; \
|
| 568 |
|
|
if (T##_f1 < X##_f1 || \
|
| 569 |
|
|
(T##_f1 == X##_f1 && T##_f0 <= X##_f0)) \
|
| 570 |
|
|
{ \
|
| 571 |
|
|
S##_f0 = T##_f0 + q; \
|
| 572 |
|
|
S##_f1 += (T##_f0 > S##_f0); \
|
| 573 |
|
|
_FP_FRAC_DEC_2(X, T); \
|
| 574 |
|
|
R##_f0 += q; \
|
| 575 |
|
|
} \
|
| 576 |
|
|
_FP_FRAC_SLL_2(X, 1); \
|
| 577 |
|
|
q >>= 1; \
|
| 578 |
|
|
} \
|
| 579 |
|
|
if (X##_f0 | X##_f1) \
|
| 580 |
|
|
{ \
|
| 581 |
|
|
if (S##_f1 < X##_f1 || \
|
| 582 |
|
|
(S##_f1 == X##_f1 && S##_f0 < X##_f0)) \
|
| 583 |
|
|
R##_f0 |= _FP_WORK_ROUND; \
|
| 584 |
|
|
R##_f0 |= _FP_WORK_STICKY; \
|
| 585 |
|
|
} \
|
| 586 |
|
|
} while (0)
|
| 587 |
|
|
|
| 588 |
|
|
|
| 589 |
|
|
/*
|
| 590 |
|
|
* Assembly/disassembly for converting to/from integral types.
|
| 591 |
|
|
* No shifting or overflow handled here.
|
| 592 |
|
|
*/
|
| 593 |
|
|
|
| 594 |
|
|
#define _FP_FRAC_ASSEMBLE_2(r, X, rsize) \
|
| 595 |
|
|
(void)((rsize <= _FP_W_TYPE_SIZE) \
|
| 596 |
|
|
? ({ r = X##_f0; }) \
|
| 597 |
|
|
: ({ \
|
| 598 |
|
|
r = X##_f1; \
|
| 599 |
|
|
r <<= _FP_W_TYPE_SIZE; \
|
| 600 |
|
|
r += X##_f0; \
|
| 601 |
|
|
}))
|
| 602 |
|
|
|
| 603 |
|
|
#define _FP_FRAC_DISASSEMBLE_2(X, r, rsize) \
|
| 604 |
|
|
do { \
|
| 605 |
|
|
X##_f0 = r; \
|
| 606 |
|
|
X##_f1 = (rsize <= _FP_W_TYPE_SIZE ? 0 : r >> _FP_W_TYPE_SIZE); \
|
| 607 |
|
|
} while (0)
|
| 608 |
|
|
|
| 609 |
|
|
/*
|
| 610 |
|
|
* Convert FP values between word sizes
|
| 611 |
|
|
*/
|
| 612 |
|
|
|
| 613 |
|
|
#define _FP_FRAC_COPY_1_2(D, S) (D##_f = S##_f0)
|
| 614 |
|
|
|
| 615 |
|
|
#define _FP_FRAC_COPY_2_1(D, S) ((D##_f0 = S##_f), (D##_f1 = 0))
|
| 616 |
|
|
|
| 617 |
|
|
#define _FP_FRAC_COPY_2_2(D,S) _FP_FRAC_COPY_2(D,S)
|
