2005-04-17 02:20:36 +04:00
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/* Software floating-point emulation. Common operations.
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Copyright (C) 1997,1998,1999 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 Library General Public License as
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published by the Free Software Foundation; either version 2 of the
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License, or (at your option) any later version.
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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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Library General Public License for more details.
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You should have received a copy of the GNU Library General Public
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License along with the GNU C Library; see the file COPYING.LIB. If
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not, write to the Free Software Foundation, Inc.,
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59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */
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#ifndef __MATH_EMU_OP_COMMON_H__
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#define __MATH_EMU_OP_COMMON_H__
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#define _FP_DECL(wc, X) \
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_FP_I_TYPE X##_c=0, X##_s=0, X##_e=0; \
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_FP_FRAC_DECL_##wc(X)
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/*
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* Finish truely unpacking a native fp value by classifying the kind
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* of fp value and normalizing both the exponent and the fraction.
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*/
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#define _FP_UNPACK_CANONICAL(fs, wc, X) \
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do { \
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switch (X##_e) \
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{ \
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default: \
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_FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \
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_FP_FRAC_SLL_##wc(X, _FP_WORKBITS); \
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X##_e -= _FP_EXPBIAS_##fs; \
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X##_c = FP_CLS_NORMAL; \
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break; \
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\
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case 0: \
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if (_FP_FRAC_ZEROP_##wc(X)) \
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X##_c = FP_CLS_ZERO; \
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else \
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{ \
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/* a denormalized number */ \
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_FP_I_TYPE _shift; \
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_FP_FRAC_CLZ_##wc(_shift, X); \
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_shift -= _FP_FRACXBITS_##fs; \
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_FP_FRAC_SLL_##wc(X, (_shift+_FP_WORKBITS)); \
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X##_e -= _FP_EXPBIAS_##fs - 1 + _shift; \
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X##_c = FP_CLS_NORMAL; \
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FP_SET_EXCEPTION(FP_EX_DENORM); \
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if (FP_DENORM_ZERO) \
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{ \
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FP_SET_EXCEPTION(FP_EX_INEXACT); \
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X##_c = FP_CLS_ZERO; \
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} \
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} \
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break; \
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\
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case _FP_EXPMAX_##fs: \
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if (_FP_FRAC_ZEROP_##wc(X)) \
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X##_c = FP_CLS_INF; \
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else \
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{ \
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X##_c = FP_CLS_NAN; \
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/* Check for signaling NaN */ \
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if (!(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs)) \
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FP_SET_EXCEPTION(FP_EX_INVALID); \
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} \
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break; \
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} \
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} while (0)
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/*
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* Before packing the bits back into the native fp result, take care
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* of such mundane things as rounding and overflow. Also, for some
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* kinds of fp values, the original parts may not have been fully
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* extracted -- but that is ok, we can regenerate them now.
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*/
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#define _FP_PACK_CANONICAL(fs, wc, X) \
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do { \
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switch (X##_c) \
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{ \
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case FP_CLS_NORMAL: \
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X##_e += _FP_EXPBIAS_##fs; \
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if (X##_e > 0) \
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{ \
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_FP_ROUND(wc, X); \
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if (_FP_FRAC_OVERP_##wc(fs, X)) \
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{ \
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_FP_FRAC_CLEAR_OVERP_##wc(fs, X); \
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X##_e++; \
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} \
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_FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
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if (X##_e >= _FP_EXPMAX_##fs) \
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{ \
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/* overflow */ \
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switch (FP_ROUNDMODE) \
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{ \
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case FP_RND_NEAREST: \
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X##_c = FP_CLS_INF; \
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break; \
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case FP_RND_PINF: \
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if (!X##_s) X##_c = FP_CLS_INF; \
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break; \
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case FP_RND_MINF: \
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if (X##_s) X##_c = FP_CLS_INF; \
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break; \
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} \
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if (X##_c == FP_CLS_INF) \
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{ \
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/* Overflow to infinity */ \
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X##_e = _FP_EXPMAX_##fs; \
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_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
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} \
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else \
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{ \
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/* Overflow to maximum normal */ \
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X##_e = _FP_EXPMAX_##fs - 1; \
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_FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \
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} \
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FP_SET_EXCEPTION(FP_EX_OVERFLOW); \
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FP_SET_EXCEPTION(FP_EX_INEXACT); \
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} \
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} \
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else \
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{ \
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/* we've got a denormalized number */ \
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X##_e = -X##_e + 1; \
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if (X##_e <= _FP_WFRACBITS_##fs) \
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{ \
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_FP_FRAC_SRS_##wc(X, X##_e, _FP_WFRACBITS_##fs); \
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_FP_ROUND(wc, X); \
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if (_FP_FRAC_HIGH_##fs(X) \
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& (_FP_OVERFLOW_##fs >> 1)) \
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{ \
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X##_e = 1; \
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_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
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2007-08-17 09:59:49 +04:00
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FP_SET_EXCEPTION(FP_EX_INEXACT); \
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2005-04-17 02:20:36 +04:00
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} \
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else \
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{ \
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X##_e = 0; \
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_FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
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} \
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2007-08-17 09:59:49 +04:00
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if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) || \
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(FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \
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FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
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2005-04-17 02:20:36 +04:00
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} \
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else \
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{ \
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/* underflow to zero */ \
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X##_e = 0; \
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if (!_FP_FRAC_ZEROP_##wc(X)) \
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{ \
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_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
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_FP_ROUND(wc, X); \
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_FP_FRAC_LOW_##wc(X) >>= (_FP_WORKBITS); \
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} \
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FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
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} \
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} \
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break; \
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\
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case FP_CLS_ZERO: \
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X##_e = 0; \
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_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
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break; \
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\
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case FP_CLS_INF: \
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X##_e = _FP_EXPMAX_##fs; \
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_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
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break; \
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\
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case FP_CLS_NAN: \
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X##_e = _FP_EXPMAX_##fs; \
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if (!_FP_KEEPNANFRACP) \
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{ \
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_FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \
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X##_s = _FP_NANSIGN_##fs; \
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} \
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else \
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_FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \
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break; \
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} \
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} while (0)
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/* This one accepts raw argument and not cooked, returns
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* 1 if X is a signaling NaN.
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*/
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#define _FP_ISSIGNAN(fs, wc, X) \
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({ \
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int __ret = 0; \
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if (X##_e == _FP_EXPMAX_##fs) \
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{ \
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if (!_FP_FRAC_ZEROP_##wc(X) \
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&& !(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs)) \
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__ret = 1; \
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} \
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__ret; \
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})
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/*
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* Main addition routine. The input values should be cooked.
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*/
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#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
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do { \
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switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
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{ \
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case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
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{ \
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/* shift the smaller number so that its exponent matches the larger */ \
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_FP_I_TYPE diff = X##_e - Y##_e; \
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\
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if (diff < 0) \
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{ \
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diff = -diff; \
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if (diff <= _FP_WFRACBITS_##fs) \
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_FP_FRAC_SRS_##wc(X, diff, _FP_WFRACBITS_##fs); \
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else if (!_FP_FRAC_ZEROP_##wc(X)) \
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_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
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R##_e = Y##_e; \
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} \
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else \
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{ \
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if (diff > 0) \
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{ \
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if (diff <= _FP_WFRACBITS_##fs) \
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_FP_FRAC_SRS_##wc(Y, diff, _FP_WFRACBITS_##fs); \
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else if (!_FP_FRAC_ZEROP_##wc(Y)) \
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_FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \
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} \
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R##_e = X##_e; \
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} \
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\
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R##_c = FP_CLS_NORMAL; \
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\
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if (X##_s == Y##_s) \
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{ \
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R##_s = X##_s; \
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_FP_FRAC_ADD_##wc(R, X, Y); \
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if (_FP_FRAC_OVERP_##wc(fs, R)) \
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{ \
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_FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
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R##_e++; \
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} \
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} \
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else \
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{ \
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R##_s = X##_s; \
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_FP_FRAC_SUB_##wc(R, X, Y); \
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if (_FP_FRAC_ZEROP_##wc(R)) \
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{ \
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/* return an exact zero */ \
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if (FP_ROUNDMODE == FP_RND_MINF) \
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R##_s |= Y##_s; \
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else \
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R##_s &= Y##_s; \
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R##_c = FP_CLS_ZERO; \
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} \
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else \
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{ \
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if (_FP_FRAC_NEGP_##wc(R)) \
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{ \
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_FP_FRAC_SUB_##wc(R, Y, X); \
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R##_s = Y##_s; \
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} \
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\
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/* renormalize after subtraction */ \
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_FP_FRAC_CLZ_##wc(diff, R); \
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diff -= _FP_WFRACXBITS_##fs; \
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if (diff) \
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{ \
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R##_e -= diff; \
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_FP_FRAC_SLL_##wc(R, diff); \
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} \
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} \
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} \
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break; \
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} \
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\
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case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
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_FP_CHOOSENAN(fs, wc, R, X, Y, OP); \
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break; \
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\
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case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
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R##_e = X##_e; \
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case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
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case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
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case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
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|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
|
|
|
R##_s = X##_s; \
|
|
|
|
|
R##_c = X##_c; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
|
|
|
|
|
R##_e = Y##_e; \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
|
|
|
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
|
|
|
R##_s = Y##_s; \
|
|
|
|
|
R##_c = Y##_c; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
|
|
|
|
|
if (X##_s != Y##_s) \
|
|
|
|
|
{ \
|
|
|
|
|
/* +INF + -INF => NAN */ \
|
|
|
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
|
|
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
|
|
|
R##_c = FP_CLS_NAN; \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
|
|
|
break; \
|
|
|
|
|
} \
|
|
|
|
|
/* FALLTHRU */ \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
|
|
|
|
|
R##_s = X##_s; \
|
|
|
|
|
R##_c = FP_CLS_INF; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
|
|
|
|
|
R##_s = Y##_s; \
|
|
|
|
|
R##_c = FP_CLS_INF; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
|
|
|
|
|
/* make sure the sign is correct */ \
|
|
|
|
|
if (FP_ROUNDMODE == FP_RND_MINF) \
|
|
|
|
|
R##_s = X##_s | Y##_s; \
|
|
|
|
|
else \
|
|
|
|
|
R##_s = X##_s & Y##_s; \
|
|
|
|
|
R##_c = FP_CLS_ZERO; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
default: \
|
|
|
|
|
abort(); \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
#define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+')
|
|
|
|
|
#define _FP_SUB(fs, wc, R, X, Y) \
|
|
|
|
|
do { \
|
|
|
|
|
if (Y##_c != FP_CLS_NAN) Y##_s ^= 1; \
|
|
|
|
|
_FP_ADD_INTERNAL(fs, wc, R, X, Y, '-'); \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Main negation routine. FIXME -- when we care about setting exception
|
|
|
|
|
* bits reliably, this will not do. We should examine all of the fp classes.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
#define _FP_NEG(fs, wc, R, X) \
|
|
|
|
|
do { \
|
|
|
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
|
|
|
R##_c = X##_c; \
|
|
|
|
|
R##_e = X##_e; \
|
|
|
|
|
R##_s = 1 ^ X##_s; \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Main multiplication routine. The input values should be cooked.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
#define _FP_MUL(fs, wc, R, X, Y) \
|
|
|
|
|
do { \
|
|
|
|
|
R##_s = X##_s ^ Y##_s; \
|
|
|
|
|
switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
|
|
|
|
|
{ \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
|
|
|
|
|
R##_c = FP_CLS_NORMAL; \
|
|
|
|
|
R##_e = X##_e + Y##_e + 1; \
|
|
|
|
|
\
|
|
|
|
|
_FP_MUL_MEAT_##fs(R,X,Y); \
|
|
|
|
|
\
|
|
|
|
|
if (_FP_FRAC_OVERP_##wc(fs, R)) \
|
|
|
|
|
_FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
|
|
|
|
|
else \
|
|
|
|
|
R##_e--; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
|
|
|
|
|
_FP_CHOOSENAN(fs, wc, R, X, Y, '*'); \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
|
|
|
|
|
R##_s = X##_s; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
|
|
|
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
|
|
|
R##_c = X##_c; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
|
|
|
|
|
R##_s = Y##_s; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
|
|
|
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
|
|
|
R##_c = Y##_c; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
|
|
|
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
|
|
|
R##_c = FP_CLS_NAN; \
|
|
|
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
default: \
|
|
|
|
|
abort(); \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Main division routine. The input values should be cooked.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
#define _FP_DIV(fs, wc, R, X, Y) \
|
|
|
|
|
do { \
|
|
|
|
|
R##_s = X##_s ^ Y##_s; \
|
|
|
|
|
switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
|
|
|
|
|
{ \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
|
|
|
|
|
R##_c = FP_CLS_NORMAL; \
|
|
|
|
|
R##_e = X##_e - Y##_e; \
|
|
|
|
|
\
|
|
|
|
|
_FP_DIV_MEAT_##fs(R,X,Y); \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
|
|
|
|
|
_FP_CHOOSENAN(fs, wc, R, X, Y, '/'); \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
|
|
|
|
|
R##_s = X##_s; \
|
|
|
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
|
|
|
R##_c = X##_c; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
|
|
|
|
|
R##_s = Y##_s; \
|
|
|
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
|
|
|
R##_c = Y##_c; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
|
|
|
|
|
R##_c = FP_CLS_ZERO; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_DIVZERO); \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
|
|
|
|
|
R##_c = FP_CLS_INF; \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
|
|
|
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
|
|
|
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
|
|
|
R##_c = FP_CLS_NAN; \
|
|
|
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
|
|
|
break; \
|
|
|
|
|
\
|
|
|
|
|
default: \
|
|
|
|
|
abort(); \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Main differential comparison routine. The inputs should be raw not
|
|
|
|
|
* cooked. The return is -1,0,1 for normal values, 2 otherwise.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
#define _FP_CMP(fs, wc, ret, X, Y, un) \
|
|
|
|
|
do { \
|
|
|
|
|
/* NANs are unordered */ \
|
|
|
|
|
if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
|
|
|
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \
|
|
|
|
|
{ \
|
|
|
|
|
ret = un; \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
int __is_zero_x; \
|
|
|
|
|
int __is_zero_y; \
|
|
|
|
|
\
|
|
|
|
|
__is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0; \
|
|
|
|
|
__is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0; \
|
|
|
|
|
\
|
|
|
|
|
if (__is_zero_x && __is_zero_y) \
|
|
|
|
|
ret = 0; \
|
|
|
|
|
else if (__is_zero_x) \
|
|
|
|
|
ret = Y##_s ? 1 : -1; \
|
|
|
|
|
else if (__is_zero_y) \
|
|
|
|
|
ret = X##_s ? -1 : 1; \
|
|
|
|
|
else if (X##_s != Y##_s) \
|
|
|
|
|
ret = X##_s ? -1 : 1; \
|
|
|
|
|
else if (X##_e > Y##_e) \
|
|
|
|
|
ret = X##_s ? -1 : 1; \
|
|
|
|
|
else if (X##_e < Y##_e) \
|
|
|
|
|
ret = X##_s ? 1 : -1; \
|
|
|
|
|
else if (_FP_FRAC_GT_##wc(X, Y)) \
|
|
|
|
|
ret = X##_s ? -1 : 1; \
|
|
|
|
|
else if (_FP_FRAC_GT_##wc(Y, X)) \
|
|
|
|
|
ret = X##_s ? 1 : -1; \
|
|
|
|
|
else \
|
|
|
|
|
ret = 0; \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
/* Simplification for strict equality. */
|
|
|
|
|
|
|
|
|
|
#define _FP_CMP_EQ(fs, wc, ret, X, Y) \
|
|
|
|
|
do { \
|
|
|
|
|
/* NANs are unordered */ \
|
|
|
|
|
if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
|
|
|
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \
|
|
|
|
|
{ \
|
|
|
|
|
ret = 1; \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
ret = !(X##_e == Y##_e \
|
|
|
|
|
&& _FP_FRAC_EQ_##wc(X, Y) \
|
|
|
|
|
&& (X##_s == Y##_s || !X##_e && _FP_FRAC_ZEROP_##wc(X))); \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Main square root routine. The input value should be cooked.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
#define _FP_SQRT(fs, wc, R, X) \
|
|
|
|
|
do { \
|
|
|
|
|
_FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S); \
|
|
|
|
|
_FP_W_TYPE q; \
|
|
|
|
|
switch (X##_c) \
|
|
|
|
|
{ \
|
|
|
|
|
case FP_CLS_NAN: \
|
|
|
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
|
|
|
R##_s = X##_s; \
|
|
|
|
|
R##_c = FP_CLS_NAN; \
|
|
|
|
|
break; \
|
|
|
|
|
case FP_CLS_INF: \
|
|
|
|
|
if (X##_s) \
|
|
|
|
|
{ \
|
|
|
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
|
|
|
R##_c = FP_CLS_NAN; /* NAN */ \
|
|
|
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
R##_s = 0; \
|
|
|
|
|
R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \
|
|
|
|
|
} \
|
|
|
|
|
break; \
|
|
|
|
|
case FP_CLS_ZERO: \
|
|
|
|
|
R##_s = X##_s; \
|
|
|
|
|
R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \
|
|
|
|
|
break; \
|
|
|
|
|
case FP_CLS_NORMAL: \
|
|
|
|
|
R##_s = 0; \
|
|
|
|
|
if (X##_s) \
|
|
|
|
|
{ \
|
|
|
|
|
R##_c = FP_CLS_NAN; /* sNAN */ \
|
|
|
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
|
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
|
|
|
break; \
|
|
|
|
|
} \
|
|
|
|
|
R##_c = FP_CLS_NORMAL; \
|
|
|
|
|
if (X##_e & 1) \
|
|
|
|
|
_FP_FRAC_SLL_##wc(X, 1); \
|
|
|
|
|
R##_e = X##_e >> 1; \
|
|
|
|
|
_FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc); \
|
|
|
|
|
_FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc); \
|
|
|
|
|
q = _FP_OVERFLOW_##fs >> 1; \
|
|
|
|
|
_FP_SQRT_MEAT_##wc(R, S, T, X, q); \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Convert from FP to integer
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* RSIGNED can have following values:
|
|
|
|
|
* 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus
|
|
|
|
|
* the result is either 0 or (2^rsize)-1 depending on the sign in such case.
|
|
|
|
|
* 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
|
|
|
|
|
* set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
|
|
|
|
|
* on the sign in such case.
|
|
|
|
|
* 2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not, NV is
|
|
|
|
|
* set plus the result is truncated to fit into destination.
|
|
|
|
|
* -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
|
|
|
|
|
* set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1 depending
|
|
|
|
|
* on the sign in such case.
|
|
|
|
|
*/
|
|
|
|
|
#define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \
|
|
|
|
|
do { \
|
|
|
|
|
switch (X##_c) \
|
|
|
|
|
{ \
|
|
|
|
|
case FP_CLS_NORMAL: \
|
|
|
|
|
if (X##_e < 0) \
|
|
|
|
|
{ \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
|
|
|
|
case FP_CLS_ZERO: \
|
|
|
|
|
r = 0; \
|
|
|
|
|
} \
|
|
|
|
|
else if (X##_e >= rsize - (rsigned > 0 || X##_s) \
|
|
|
|
|
|| (!rsigned && X##_s)) \
|
|
|
|
|
{ /* overflow */ \
|
|
|
|
|
case FP_CLS_NAN: \
|
|
|
|
|
case FP_CLS_INF: \
|
|
|
|
|
if (rsigned == 2) \
|
|
|
|
|
{ \
|
|
|
|
|
if (X##_c != FP_CLS_NORMAL \
|
|
|
|
|
|| X##_e >= rsize - 1 + _FP_WFRACBITS_##fs) \
|
|
|
|
|
r = 0; \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
_FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1)); \
|
|
|
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
|
|
|
} \
|
|
|
|
|
} \
|
|
|
|
|
else if (rsigned) \
|
|
|
|
|
{ \
|
|
|
|
|
r = 1; \
|
|
|
|
|
r <<= rsize - 1; \
|
|
|
|
|
r -= 1 - X##_s; \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
r = 0; \
|
|
|
|
|
if (X##_s) \
|
|
|
|
|
r = ~r; \
|
|
|
|
|
} \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
if (_FP_W_TYPE_SIZE*wc < rsize) \
|
|
|
|
|
{ \
|
|
|
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
|
|
|
r <<= X##_e - _FP_WFRACBITS_##fs; \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
if (X##_e >= _FP_WFRACBITS_##fs) \
|
|
|
|
|
_FP_FRAC_SLL_##wc(X, (X##_e - _FP_WFRACBITS_##fs + 1)); \
|
|
|
|
|
else if (X##_e < _FP_WFRACBITS_##fs - 1) \
|
|
|
|
|
{ \
|
|
|
|
|
_FP_FRAC_SRS_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 2), \
|
|
|
|
|
_FP_WFRACBITS_##fs); \
|
|
|
|
|
if (_FP_FRAC_LOW_##wc(X) & 1) \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
|
|
|
|
_FP_FRAC_SRL_##wc(X, 1); \
|
|
|
|
|
} \
|
|
|
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
|
|
|
} \
|
|
|
|
|
if (rsigned && X##_s) \
|
|
|
|
|
r = -r; \
|
|
|
|
|
} \
|
|
|
|
|
break; \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
#define _FP_TO_INT_ROUND(fs, wc, r, X, rsize, rsigned) \
|
|
|
|
|
do { \
|
|
|
|
|
r = 0; \
|
|
|
|
|
switch (X##_c) \
|
|
|
|
|
{ \
|
|
|
|
|
case FP_CLS_NORMAL: \
|
|
|
|
|
if (X##_e >= _FP_FRACBITS_##fs - 1) \
|
|
|
|
|
{ \
|
|
|
|
|
if (X##_e < rsize - 1 + _FP_WFRACBITS_##fs) \
|
|
|
|
|
{ \
|
|
|
|
|
if (X##_e >= _FP_WFRACBITS_##fs - 1) \
|
|
|
|
|
{ \
|
|
|
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
|
|
|
r <<= X##_e - _FP_WFRACBITS_##fs + 1; \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
_FP_FRAC_SRL_##wc(X, _FP_WORKBITS - X##_e \
|
|
|
|
|
+ _FP_FRACBITS_##fs - 1); \
|
|
|
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
|
|
|
} \
|
|
|
|
|
} \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
if (X##_e <= -_FP_WORKBITS - 1) \
|
|
|
|
|
_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
|
|
|
|
|
else \
|
|
|
|
|
_FP_FRAC_SRS_##wc(X, _FP_FRACBITS_##fs - 1 - X##_e, \
|
|
|
|
|
_FP_WFRACBITS_##fs); \
|
|
|
|
|
_FP_ROUND(wc, X); \
|
|
|
|
|
_FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
|
|
|
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
|
|
|
} \
|
|
|
|
|
if (rsigned && X##_s) \
|
|
|
|
|
r = -r; \
|
|
|
|
|
if (X##_e >= rsize - (rsigned > 0 || X##_s) \
|
|
|
|
|
|| (!rsigned && X##_s)) \
|
|
|
|
|
{ /* overflow */ \
|
|
|
|
|
case FP_CLS_NAN: \
|
|
|
|
|
case FP_CLS_INF: \
|
|
|
|
|
if (!rsigned) \
|
|
|
|
|
{ \
|
|
|
|
|
r = 0; \
|
|
|
|
|
if (X##_s) \
|
|
|
|
|
r = ~r; \
|
|
|
|
|
} \
|
|
|
|
|
else if (rsigned != 2) \
|
|
|
|
|
{ \
|
|
|
|
|
r = 1; \
|
|
|
|
|
r <<= rsize - 1; \
|
|
|
|
|
r -= 1 - X##_s; \
|
|
|
|
|
} \
|
|
|
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
|
|
|
} \
|
|
|
|
|
break; \
|
|
|
|
|
case FP_CLS_ZERO: \
|
|
|
|
|
break; \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
|
|
|
|
|
do { \
|
|
|
|
|
if (r) \
|
|
|
|
|
{ \
|
|
|
|
|
unsigned rtype ur_; \
|
|
|
|
|
X##_c = FP_CLS_NORMAL; \
|
|
|
|
|
\
|
|
|
|
|
if ((X##_s = (r < 0))) \
|
|
|
|
|
ur_ = (unsigned rtype) -r; \
|
|
|
|
|
else \
|
|
|
|
|
ur_ = (unsigned rtype) r; \
|
|
|
|
|
if (rsize <= _FP_W_TYPE_SIZE) \
|
|
|
|
|
__FP_CLZ(X##_e, ur_); \
|
|
|
|
|
else \
|
|
|
|
|
__FP_CLZ_2(X##_e, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE), \
|
|
|
|
|
(_FP_W_TYPE)ur_); \
|
|
|
|
|
if (rsize < _FP_W_TYPE_SIZE) \
|
|
|
|
|
X##_e -= (_FP_W_TYPE_SIZE - rsize); \
|
|
|
|
|
X##_e = rsize - X##_e - 1; \
|
|
|
|
|
\
|
|
|
|
|
if (_FP_FRACBITS_##fs < rsize && _FP_WFRACBITS_##fs < X##_e) \
|
|
|
|
|
__FP_FRAC_SRS_1(ur_, (X##_e - _FP_WFRACBITS_##fs + 1), rsize);\
|
|
|
|
|
_FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \
|
|
|
|
|
if ((_FP_WFRACBITS_##fs - X##_e - 1) > 0) \
|
|
|
|
|
_FP_FRAC_SLL_##wc(X, (_FP_WFRACBITS_##fs - X##_e - 1)); \
|
|
|
|
|
} \
|
|
|
|
|
else \
|
|
|
|
|
{ \
|
|
|
|
|
X##_c = FP_CLS_ZERO, X##_s = 0; \
|
|
|
|
|
} \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define FP_CONV(dfs,sfs,dwc,swc,D,S) \
|
|
|
|
|
do { \
|
|
|
|
|
_FP_FRAC_CONV_##dwc##_##swc(dfs, sfs, D, S); \
|
|
|
|
|
D##_e = S##_e; \
|
|
|
|
|
D##_c = S##_c; \
|
|
|
|
|
D##_s = S##_s; \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* Helper primitives.
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
/* Count leading zeros in a word. */
|
|
|
|
|
|
|
|
|
|
#ifndef __FP_CLZ
|
|
|
|
|
#if _FP_W_TYPE_SIZE < 64
|
|
|
|
|
/* this is just to shut the compiler up about shifts > word length -- PMM 02/1998 */
|
|
|
|
|
#define __FP_CLZ(r, x) \
|
|
|
|
|
do { \
|
|
|
|
|
_FP_W_TYPE _t = (x); \
|
|
|
|
|
r = _FP_W_TYPE_SIZE - 1; \
|
|
|
|
|
if (_t > 0xffff) r -= 16; \
|
|
|
|
|
if (_t > 0xffff) _t >>= 16; \
|
|
|
|
|
if (_t > 0xff) r -= 8; \
|
|
|
|
|
if (_t > 0xff) _t >>= 8; \
|
|
|
|
|
if (_t & 0xf0) r -= 4; \
|
|
|
|
|
if (_t & 0xf0) _t >>= 4; \
|
|
|
|
|
if (_t & 0xc) r -= 2; \
|
|
|
|
|
if (_t & 0xc) _t >>= 2; \
|
|
|
|
|
if (_t & 0x2) r -= 1; \
|
|
|
|
|
} while (0)
|
|
|
|
|
#else /* not _FP_W_TYPE_SIZE < 64 */
|
|
|
|
|
#define __FP_CLZ(r, x) \
|
|
|
|
|
do { \
|
|
|
|
|
_FP_W_TYPE _t = (x); \
|
|
|
|
|
r = _FP_W_TYPE_SIZE - 1; \
|
|
|
|
|
if (_t > 0xffffffff) r -= 32; \
|
|
|
|
|
if (_t > 0xffffffff) _t >>= 32; \
|
|
|
|
|
if (_t > 0xffff) r -= 16; \
|
|
|
|
|
if (_t > 0xffff) _t >>= 16; \
|
|
|
|
|
if (_t > 0xff) r -= 8; \
|
|
|
|
|
if (_t > 0xff) _t >>= 8; \
|
|
|
|
|
if (_t & 0xf0) r -= 4; \
|
|
|
|
|
if (_t & 0xf0) _t >>= 4; \
|
|
|
|
|
if (_t & 0xc) r -= 2; \
|
|
|
|
|
if (_t & 0xc) _t >>= 2; \
|
|
|
|
|
if (_t & 0x2) r -= 1; \
|
|
|
|
|
} while (0)
|
|
|
|
|
#endif /* not _FP_W_TYPE_SIZE < 64 */
|
|
|
|
|
#endif /* ndef __FP_CLZ */
|
|
|
|
|
|
|
|
|
|
#define _FP_DIV_HELP_imm(q, r, n, d) \
|
|
|
|
|
do { \
|
|
|
|
|
q = n / d, r = n % d; \
|
|
|
|
|
} while (0)
|
|
|
|
|
|
|
|
|
|
#endif /* __MATH_EMU_OP_COMMON_H__ */
|
