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734 |
jeremybenn |
/* Software floating-point emulation. Common operations.
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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_DECL(wc, X) \
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_FP_I_TYPE X##_c __attribute__((unused)), X##_s, X##_e; \
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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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} \
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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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/* Finish unpacking an fp value in semi-raw mode: the mantissa is
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shifted by _FP_WORKBITS but the implicit MSB is not inserted and
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other classification is not done. */
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#define _FP_UNPACK_SEMIRAW(fs, wc, X) _FP_FRAC_SLL_##wc(X, _FP_WORKBITS)
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/* A semi-raw value has overflowed to infinity. Adjust the mantissa
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and exponent appropriately. */
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#define _FP_OVERFLOW_SEMIRAW(fs, wc, X) \
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do { \
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if (FP_ROUNDMODE == FP_RND_NEAREST \
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|| (FP_ROUNDMODE == FP_RND_PINF && !X##_s) \
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|| (FP_ROUNDMODE == FP_RND_MINF && X##_s)) \
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{ \
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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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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_INEXACT); \
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FP_SET_EXCEPTION(FP_EX_OVERFLOW); \
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} while (0)
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/* Check for a semi-raw value being a signaling NaN and raise the
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invalid exception if so. */
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#define _FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X) \
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do { \
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if (X##_e == _FP_EXPMAX_##fs \
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&& !_FP_FRAC_ZEROP_##wc(X) \
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&& !(_FP_FRAC_HIGH_##fs(X) & _FP_QNANBIT_SH_##fs)) \
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FP_SET_EXCEPTION(FP_EX_INVALID); \
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} while (0)
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/* Choose a NaN result from an operation on two semi-raw NaN
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values. */
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#define _FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP) \
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do { \
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/* _FP_CHOOSENAN expects raw values, so shift as required. */ \
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_FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
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_FP_FRAC_SRL_##wc(Y, _FP_WORKBITS); \
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_FP_CHOOSENAN(fs, wc, R, X, Y, OP); \
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_FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \
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} while (0)
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/* Test whether a biased exponent is normal (not zero or maximum). */
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#define _FP_EXP_NORMAL(fs, wc, X) (((X##_e + 1) & _FP_EXPMAX_##fs) > 1)
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/* Prepare to pack an fp value in semi-raw mode: the mantissa is
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rounded and shifted right, with the rounding possibly increasing
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the exponent (including changing a finite value to infinity). */
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#define _FP_PACK_SEMIRAW(fs, wc, X) \
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do { \
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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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_FP_FRAC_HIGH_##fs(X) &= ~(_FP_OVERFLOW_##fs >> 1); \
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X##_e++; \
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if (X##_e == _FP_EXPMAX_##fs) \
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_FP_OVERFLOW_SEMIRAW(fs, wc, X); \
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} \
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_FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
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if (!_FP_EXP_NORMAL(fs, wc, X) && !_FP_FRAC_ZEROP_##wc(X)) \
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{ \
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if (X##_e == 0) \
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FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
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else \
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{ \
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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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} \
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} \
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} while (0)
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| 163 |
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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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| 180 |
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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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| 186 |
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if (X##_e >= _FP_EXPMAX_##fs) \
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{ \
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/* overflow */ \
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| 189 |
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switch (FP_ROUNDMODE) \
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{ \
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| 191 |
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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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| 197 |
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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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| 200 |
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} \
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| 201 |
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if (X##_c == FP_CLS_INF) \
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| 202 |
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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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| 207 |
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else \
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| 208 |
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{ \
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| 209 |
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/* Overflow to maximum normal */ \
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| 210 |
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X##_e = _FP_EXPMAX_##fs - 1; \
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| 211 |
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_FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \
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| 212 |
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} \
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| 213 |
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FP_SET_EXCEPTION(FP_EX_OVERFLOW); \
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| 214 |
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FP_SET_EXCEPTION(FP_EX_INEXACT); \
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| 215 |
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} \
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| 216 |
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} \
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| 217 |
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else \
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| 218 |
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{ \
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| 219 |
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/* we've got a denormalized number */ \
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| 220 |
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X##_e = -X##_e + 1; \
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| 221 |
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if (X##_e <= _FP_WFRACBITS_##fs) \
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| 222 |
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{ \
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| 223 |
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_FP_FRAC_SRS_##wc(X, X##_e, _FP_WFRACBITS_##fs); \
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| 224 |
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_FP_ROUND(wc, X); \
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| 225 |
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if (_FP_FRAC_HIGH_##fs(X) \
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| 226 |
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& (_FP_OVERFLOW_##fs >> 1)) \
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| 227 |
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{ \
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| 228 |
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X##_e = 1; \
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| 229 |
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_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
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| 230 |
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} \
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| 231 |
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else \
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| 232 |
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{ \
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| 233 |
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X##_e = 0; \
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| 234 |
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_FP_FRAC_SRL_##wc(X, _FP_WORKBITS); \
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| 235 |
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FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
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| 236 |
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} \
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| 237 |
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} \
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| 238 |
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else \
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| 239 |
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{ \
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| 240 |
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/* underflow to zero */ \
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| 241 |
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X##_e = 0; \
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| 242 |
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if (!_FP_FRAC_ZEROP_##wc(X)) \
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| 243 |
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{ \
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| 244 |
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_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
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| 245 |
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_FP_ROUND(wc, X); \
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| 246 |
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_FP_FRAC_LOW_##wc(X) >>= (_FP_WORKBITS); \
|
| 247 |
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} \
|
| 248 |
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FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
|
| 249 |
|
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} \
|
| 250 |
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} \
|
| 251 |
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break; \
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| 252 |
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\
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| 253 |
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case FP_CLS_ZERO: \
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| 254 |
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X##_e = 0; \
|
| 255 |
|
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_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
|
| 256 |
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break; \
|
| 257 |
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\
|
| 258 |
|
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case FP_CLS_INF: \
|
| 259 |
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X##_e = _FP_EXPMAX_##fs; \
|
| 260 |
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_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
|
| 261 |
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break; \
|
| 262 |
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\
|
| 263 |
|
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case FP_CLS_NAN: \
|
| 264 |
|
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X##_e = _FP_EXPMAX_##fs; \
|
| 265 |
|
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if (!_FP_KEEPNANFRACP) \
|
| 266 |
|
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{ \
|
| 267 |
|
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_FP_FRAC_SET_##wc(X, _FP_NANFRAC_##fs); \
|
| 268 |
|
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X##_s = _FP_NANSIGN_##fs; \
|
| 269 |
|
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} \
|
| 270 |
|
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else \
|
| 271 |
|
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_FP_FRAC_HIGH_RAW_##fs(X) |= _FP_QNANBIT_##fs; \
|
| 272 |
|
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break; \
|
| 273 |
|
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} \
|
| 274 |
|
|
} while (0)
|
| 275 |
|
|
|
| 276 |
|
|
/* This one accepts raw argument and not cooked, returns
|
| 277 |
|
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* 1 if X is a signaling NaN.
|
| 278 |
|
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*/
|
| 279 |
|
|
#define _FP_ISSIGNAN(fs, wc, X) \
|
| 280 |
|
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({ \
|
| 281 |
|
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int __ret = 0; \
|
| 282 |
|
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if (X##_e == _FP_EXPMAX_##fs) \
|
| 283 |
|
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{ \
|
| 284 |
|
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if (!_FP_FRAC_ZEROP_##wc(X) \
|
| 285 |
|
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&& !(_FP_FRAC_HIGH_RAW_##fs(X) & _FP_QNANBIT_##fs)) \
|
| 286 |
|
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__ret = 1; \
|
| 287 |
|
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} \
|
| 288 |
|
|
__ret; \
|
| 289 |
|
|
})
|
| 290 |
|
|
|
| 291 |
|
|
|
| 292 |
|
|
|
| 293 |
|
|
|
| 294 |
|
|
|
| 295 |
|
|
/* Addition on semi-raw values. */
|
| 296 |
|
|
#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
|
| 297 |
|
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do { \
|
| 298 |
|
|
if (X##_s == Y##_s) \
|
| 299 |
|
|
{ \
|
| 300 |
|
|
/* Addition. */ \
|
| 301 |
|
|
R##_s = X##_s; \
|
| 302 |
|
|
int ediff = X##_e - Y##_e; \
|
| 303 |
|
|
if (ediff > 0) \
|
| 304 |
|
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{ \
|
| 305 |
|
|
R##_e = X##_e; \
|
| 306 |
|
|
if (Y##_e == 0) \
|
| 307 |
|
|
{ \
|
| 308 |
|
|
/* Y is zero or denormalized. */ \
|
| 309 |
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 310 |
|
|
{ \
|
| 311 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 312 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 313 |
|
|
goto add_done; \
|
| 314 |
|
|
} \
|
| 315 |
|
|
else \
|
| 316 |
|
|
{ \
|
| 317 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 318 |
|
|
ediff--; \
|
| 319 |
|
|
if (ediff == 0) \
|
| 320 |
|
|
{ \
|
| 321 |
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
|
| 322 |
|
|
goto add3; \
|
| 323 |
|
|
} \
|
| 324 |
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
| 325 |
|
|
{ \
|
| 326 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 327 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 328 |
|
|
goto add_done; \
|
| 329 |
|
|
} \
|
| 330 |
|
|
goto add1; \
|
| 331 |
|
|
} \
|
| 332 |
|
|
} \
|
| 333 |
|
|
else if (X##_e == _FP_EXPMAX_##fs) \
|
| 334 |
|
|
{ \
|
| 335 |
|
|
/* X is NaN or Inf, Y is normal. */ \
|
| 336 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 337 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 338 |
|
|
goto add_done; \
|
| 339 |
|
|
} \
|
| 340 |
|
|
\
|
| 341 |
|
|
/* Insert implicit MSB of Y. */ \
|
| 342 |
|
|
_FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \
|
| 343 |
|
|
\
|
| 344 |
|
|
add1: \
|
| 345 |
|
|
/* Shift the mantissa of Y to the right EDIFF steps; \
|
| 346 |
|
|
remember to account later for the implicit MSB of X. */ \
|
| 347 |
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
| 348 |
|
|
_FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \
|
| 349 |
|
|
else if (!_FP_FRAC_ZEROP_##wc(Y)) \
|
| 350 |
|
|
_FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \
|
| 351 |
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
|
| 352 |
|
|
} \
|
| 353 |
|
|
else if (ediff < 0) \
|
| 354 |
|
|
{ \
|
| 355 |
|
|
ediff = -ediff; \
|
| 356 |
|
|
R##_e = Y##_e; \
|
| 357 |
|
|
if (X##_e == 0) \
|
| 358 |
|
|
{ \
|
| 359 |
|
|
/* X is zero or denormalized. */ \
|
| 360 |
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
| 361 |
|
|
{ \
|
| 362 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 363 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 364 |
|
|
goto add_done; \
|
| 365 |
|
|
} \
|
| 366 |
|
|
else \
|
| 367 |
|
|
{ \
|
| 368 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 369 |
|
|
ediff--; \
|
| 370 |
|
|
if (ediff == 0) \
|
| 371 |
|
|
{ \
|
| 372 |
|
|
_FP_FRAC_ADD_##wc(R, Y, X); \
|
| 373 |
|
|
goto add3; \
|
| 374 |
|
|
} \
|
| 375 |
|
|
if (Y##_e == _FP_EXPMAX_##fs) \
|
| 376 |
|
|
{ \
|
| 377 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 378 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 379 |
|
|
goto add_done; \
|
| 380 |
|
|
} \
|
| 381 |
|
|
goto add2; \
|
| 382 |
|
|
} \
|
| 383 |
|
|
} \
|
| 384 |
|
|
else if (Y##_e == _FP_EXPMAX_##fs) \
|
| 385 |
|
|
{ \
|
| 386 |
|
|
/* Y is NaN or Inf, X is normal. */ \
|
| 387 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 388 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 389 |
|
|
goto add_done; \
|
| 390 |
|
|
} \
|
| 391 |
|
|
\
|
| 392 |
|
|
/* Insert implicit MSB of X. */ \
|
| 393 |
|
|
_FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \
|
| 394 |
|
|
\
|
| 395 |
|
|
add2: \
|
| 396 |
|
|
/* Shift the mantissa of X to the right EDIFF steps; \
|
| 397 |
|
|
remember to account later for the implicit MSB of Y. */ \
|
| 398 |
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
| 399 |
|
|
_FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \
|
| 400 |
|
|
else if (!_FP_FRAC_ZEROP_##wc(X)) \
|
| 401 |
|
|
_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
|
| 402 |
|
|
_FP_FRAC_ADD_##wc(R, Y, X); \
|
| 403 |
|
|
} \
|
| 404 |
|
|
else \
|
| 405 |
|
|
{ \
|
| 406 |
|
|
/* ediff == 0. */ \
|
| 407 |
|
|
if (!_FP_EXP_NORMAL(fs, wc, X)) \
|
| 408 |
|
|
{ \
|
| 409 |
|
|
if (X##_e == 0) \
|
| 410 |
|
|
{ \
|
| 411 |
|
|
/* X and Y are zero or denormalized. */ \
|
| 412 |
|
|
R##_e = 0; \
|
| 413 |
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
| 414 |
|
|
{ \
|
| 415 |
|
|
if (!_FP_FRAC_ZEROP_##wc(Y)) \
|
| 416 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 417 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 418 |
|
|
goto add_done; \
|
| 419 |
|
|
} \
|
| 420 |
|
|
else if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 421 |
|
|
{ \
|
| 422 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 423 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 424 |
|
|
goto add_done; \
|
| 425 |
|
|
} \
|
| 426 |
|
|
else \
|
| 427 |
|
|
{ \
|
| 428 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 429 |
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
|
| 430 |
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
| 431 |
|
|
{ \
|
| 432 |
|
|
/* Normalized result. */ \
|
| 433 |
|
|
_FP_FRAC_HIGH_##fs(R) \
|
| 434 |
|
|
&= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
| 435 |
|
|
R##_e = 1; \
|
| 436 |
|
|
} \
|
| 437 |
|
|
goto add_done; \
|
| 438 |
|
|
} \
|
| 439 |
|
|
} \
|
| 440 |
|
|
else \
|
| 441 |
|
|
{ \
|
| 442 |
|
|
/* X and Y are NaN or Inf. */ \
|
| 443 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 444 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 445 |
|
|
R##_e = _FP_EXPMAX_##fs; \
|
| 446 |
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
| 447 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 448 |
|
|
else if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 449 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 450 |
|
|
else \
|
| 451 |
|
|
_FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \
|
| 452 |
|
|
goto add_done; \
|
| 453 |
|
|
} \
|
| 454 |
|
|
} \
|
| 455 |
|
|
/* The exponents of X and Y, both normal, are equal. The \
|
| 456 |
|
|
implicit MSBs will always add to increase the \
|
| 457 |
|
|
exponent. */ \
|
| 458 |
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
|
| 459 |
|
|
R##_e = X##_e + 1; \
|
| 460 |
|
|
_FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
|
| 461 |
|
|
if (R##_e == _FP_EXPMAX_##fs) \
|
| 462 |
|
|
/* Overflow to infinity (depending on rounding mode). */ \
|
| 463 |
|
|
_FP_OVERFLOW_SEMIRAW(fs, wc, R); \
|
| 464 |
|
|
goto add_done; \
|
| 465 |
|
|
} \
|
| 466 |
|
|
add3: \
|
| 467 |
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
| 468 |
|
|
{ \
|
| 469 |
|
|
/* Overflow. */ \
|
| 470 |
|
|
_FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
| 471 |
|
|
R##_e++; \
|
| 472 |
|
|
_FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
|
| 473 |
|
|
if (R##_e == _FP_EXPMAX_##fs) \
|
| 474 |
|
|
/* Overflow to infinity (depending on rounding mode). */ \
|
| 475 |
|
|
_FP_OVERFLOW_SEMIRAW(fs, wc, R); \
|
| 476 |
|
|
} \
|
| 477 |
|
|
add_done: ; \
|
| 478 |
|
|
} \
|
| 479 |
|
|
else \
|
| 480 |
|
|
{ \
|
| 481 |
|
|
/* Subtraction. */ \
|
| 482 |
|
|
int ediff = X##_e - Y##_e; \
|
| 483 |
|
|
if (ediff > 0) \
|
| 484 |
|
|
{ \
|
| 485 |
|
|
R##_e = X##_e; \
|
| 486 |
|
|
R##_s = X##_s; \
|
| 487 |
|
|
if (Y##_e == 0) \
|
| 488 |
|
|
{ \
|
| 489 |
|
|
/* Y is zero or denormalized. */ \
|
| 490 |
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 491 |
|
|
{ \
|
| 492 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 493 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 494 |
|
|
goto sub_done; \
|
| 495 |
|
|
} \
|
| 496 |
|
|
else \
|
| 497 |
|
|
{ \
|
| 498 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 499 |
|
|
ediff--; \
|
| 500 |
|
|
if (ediff == 0) \
|
| 501 |
|
|
{ \
|
| 502 |
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
| 503 |
|
|
goto sub3; \
|
| 504 |
|
|
} \
|
| 505 |
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
| 506 |
|
|
{ \
|
| 507 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 508 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 509 |
|
|
goto sub_done; \
|
| 510 |
|
|
} \
|
| 511 |
|
|
goto sub1; \
|
| 512 |
|
|
} \
|
| 513 |
|
|
} \
|
| 514 |
|
|
else if (X##_e == _FP_EXPMAX_##fs) \
|
| 515 |
|
|
{ \
|
| 516 |
|
|
/* X is NaN or Inf, Y is normal. */ \
|
| 517 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 518 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 519 |
|
|
goto sub_done; \
|
| 520 |
|
|
} \
|
| 521 |
|
|
\
|
| 522 |
|
|
/* Insert implicit MSB of Y. */ \
|
| 523 |
|
|
_FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \
|
| 524 |
|
|
\
|
| 525 |
|
|
sub1: \
|
| 526 |
|
|
/* Shift the mantissa of Y to the right EDIFF steps; \
|
| 527 |
|
|
remember to account later for the implicit MSB of X. */ \
|
| 528 |
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
| 529 |
|
|
_FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \
|
| 530 |
|
|
else if (!_FP_FRAC_ZEROP_##wc(Y)) \
|
| 531 |
|
|
_FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \
|
| 532 |
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
| 533 |
|
|
} \
|
| 534 |
|
|
else if (ediff < 0) \
|
| 535 |
|
|
{ \
|
| 536 |
|
|
ediff = -ediff; \
|
| 537 |
|
|
R##_e = Y##_e; \
|
| 538 |
|
|
R##_s = Y##_s; \
|
| 539 |
|
|
if (X##_e == 0) \
|
| 540 |
|
|
{ \
|
| 541 |
|
|
/* X is zero or denormalized. */ \
|
| 542 |
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
| 543 |
|
|
{ \
|
| 544 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 545 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 546 |
|
|
goto sub_done; \
|
| 547 |
|
|
} \
|
| 548 |
|
|
else \
|
| 549 |
|
|
{ \
|
| 550 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 551 |
|
|
ediff--; \
|
| 552 |
|
|
if (ediff == 0) \
|
| 553 |
|
|
{ \
|
| 554 |
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
| 555 |
|
|
goto sub3; \
|
| 556 |
|
|
} \
|
| 557 |
|
|
if (Y##_e == _FP_EXPMAX_##fs) \
|
| 558 |
|
|
{ \
|
| 559 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 560 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 561 |
|
|
goto sub_done; \
|
| 562 |
|
|
} \
|
| 563 |
|
|
goto sub2; \
|
| 564 |
|
|
} \
|
| 565 |
|
|
} \
|
| 566 |
|
|
else if (Y##_e == _FP_EXPMAX_##fs) \
|
| 567 |
|
|
{ \
|
| 568 |
|
|
/* Y is NaN or Inf, X is normal. */ \
|
| 569 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 570 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 571 |
|
|
goto sub_done; \
|
| 572 |
|
|
} \
|
| 573 |
|
|
\
|
| 574 |
|
|
/* Insert implicit MSB of X. */ \
|
| 575 |
|
|
_FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \
|
| 576 |
|
|
\
|
| 577 |
|
|
sub2: \
|
| 578 |
|
|
/* Shift the mantissa of X to the right EDIFF steps; \
|
| 579 |
|
|
remember to account later for the implicit MSB of Y. */ \
|
| 580 |
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
| 581 |
|
|
_FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \
|
| 582 |
|
|
else if (!_FP_FRAC_ZEROP_##wc(X)) \
|
| 583 |
|
|
_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
|
| 584 |
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
| 585 |
|
|
} \
|
| 586 |
|
|
else \
|
| 587 |
|
|
{ \
|
| 588 |
|
|
/* ediff == 0. */ \
|
| 589 |
|
|
if (!_FP_EXP_NORMAL(fs, wc, X)) \
|
| 590 |
|
|
{ \
|
| 591 |
|
|
if (X##_e == 0) \
|
| 592 |
|
|
{ \
|
| 593 |
|
|
/* X and Y are zero or denormalized. */ \
|
| 594 |
|
|
R##_e = 0; \
|
| 595 |
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
| 596 |
|
|
{ \
|
| 597 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 598 |
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 599 |
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
| 600 |
|
|
else \
|
| 601 |
|
|
{ \
|
| 602 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 603 |
|
|
R##_s = Y##_s; \
|
| 604 |
|
|
} \
|
| 605 |
|
|
goto sub_done; \
|
| 606 |
|
|
} \
|
| 607 |
|
|
else if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 608 |
|
|
{ \
|
| 609 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 610 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 611 |
|
|
R##_s = X##_s; \
|
| 612 |
|
|
goto sub_done; \
|
| 613 |
|
|
} \
|
| 614 |
|
|
else \
|
| 615 |
|
|
{ \
|
| 616 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 617 |
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
| 618 |
|
|
R##_s = X##_s; \
|
| 619 |
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
| 620 |
|
|
{ \
|
| 621 |
|
|
/* |X| < |Y|, negate result. */ \
|
| 622 |
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
| 623 |
|
|
R##_s = Y##_s; \
|
| 624 |
|
|
} \
|
| 625 |
|
|
else if (_FP_FRAC_ZEROP_##wc(R)) \
|
| 626 |
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
| 627 |
|
|
goto sub_done; \
|
| 628 |
|
|
} \
|
| 629 |
|
|
} \
|
| 630 |
|
|
else \
|
| 631 |
|
|
{ \
|
| 632 |
|
|
/* X and Y are NaN or Inf, of opposite signs. */ \
|
| 633 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
| 634 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
| 635 |
|
|
R##_e = _FP_EXPMAX_##fs; \
|
| 636 |
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
| 637 |
|
|
{ \
|
| 638 |
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 639 |
|
|
{ \
|
| 640 |
|
|
/* Inf - Inf. */ \
|
| 641 |
|
|
R##_s = _FP_NANSIGN_##fs; \
|
| 642 |
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
| 643 |
|
|
_FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \
|
| 644 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 645 |
|
|
} \
|
| 646 |
|
|
else \
|
| 647 |
|
|
{ \
|
| 648 |
|
|
/* Inf - NaN. */ \
|
| 649 |
|
|
R##_s = Y##_s; \
|
| 650 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 651 |
|
|
} \
|
| 652 |
|
|
} \
|
| 653 |
|
|
else \
|
| 654 |
|
|
{ \
|
| 655 |
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
| 656 |
|
|
{ \
|
| 657 |
|
|
/* NaN - Inf. */ \
|
| 658 |
|
|
R##_s = X##_s; \
|
| 659 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 660 |
|
|
} \
|
| 661 |
|
|
else \
|
| 662 |
|
|
{ \
|
| 663 |
|
|
/* NaN - NaN. */ \
|
| 664 |
|
|
_FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \
|
| 665 |
|
|
} \
|
| 666 |
|
|
} \
|
| 667 |
|
|
goto sub_done; \
|
| 668 |
|
|
} \
|
| 669 |
|
|
} \
|
| 670 |
|
|
/* The exponents of X and Y, both normal, are equal. The \
|
| 671 |
|
|
implicit MSBs cancel. */ \
|
| 672 |
|
|
R##_e = X##_e; \
|
| 673 |
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
| 674 |
|
|
R##_s = X##_s; \
|
| 675 |
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
| 676 |
|
|
{ \
|
| 677 |
|
|
/* |X| < |Y|, negate result. */ \
|
| 678 |
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
| 679 |
|
|
R##_s = Y##_s; \
|
| 680 |
|
|
} \
|
| 681 |
|
|
else if (_FP_FRAC_ZEROP_##wc(R)) \
|
| 682 |
|
|
{ \
|
| 683 |
|
|
R##_e = 0; \
|
| 684 |
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
| 685 |
|
|
goto sub_done; \
|
| 686 |
|
|
} \
|
| 687 |
|
|
goto norm; \
|
| 688 |
|
|
} \
|
| 689 |
|
|
sub3: \
|
| 690 |
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
| 691 |
|
|
{ \
|
| 692 |
|
|
int diff; \
|
| 693 |
|
|
/* Carry into most significant bit of larger one of X and Y, \
|
| 694 |
|
|
canceling it; renormalize. */ \
|
| 695 |
|
|
_FP_FRAC_HIGH_##fs(R) &= _FP_IMPLBIT_SH_##fs - 1; \
|
| 696 |
|
|
norm: \
|
| 697 |
|
|
_FP_FRAC_CLZ_##wc(diff, R); \
|
| 698 |
|
|
diff -= _FP_WFRACXBITS_##fs; \
|
| 699 |
|
|
_FP_FRAC_SLL_##wc(R, diff); \
|
| 700 |
|
|
if (R##_e <= diff) \
|
| 701 |
|
|
{ \
|
| 702 |
|
|
/* R is denormalized. */ \
|
| 703 |
|
|
diff = diff - R##_e + 1; \
|
| 704 |
|
|
_FP_FRAC_SRS_##wc(R, diff, _FP_WFRACBITS_##fs); \
|
| 705 |
|
|
R##_e = 0; \
|
| 706 |
|
|
} \
|
| 707 |
|
|
else \
|
| 708 |
|
|
{ \
|
| 709 |
|
|
R##_e -= diff; \
|
| 710 |
|
|
_FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
| 711 |
|
|
} \
|
| 712 |
|
|
} \
|
| 713 |
|
|
sub_done: ; \
|
| 714 |
|
|
} \
|
| 715 |
|
|
} while (0)
|
| 716 |
|
|
|
| 717 |
|
|
#define _FP_ADD(fs, wc, R, X, Y) _FP_ADD_INTERNAL(fs, wc, R, X, Y, '+')
|
| 718 |
|
|
#define _FP_SUB(fs, wc, R, X, Y) \
|
| 719 |
|
|
do { \
|
| 720 |
|
|
if (!(Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) Y##_s ^= 1; \
|
| 721 |
|
|
_FP_ADD_INTERNAL(fs, wc, R, X, Y, '-'); \
|
| 722 |
|
|
} while (0)
|
| 723 |
|
|
|
| 724 |
|
|
|
| 725 |
|
|
/*
|
| 726 |
|
|
* Main negation routine. FIXME -- when we care about setting exception
|
| 727 |
|
|
* bits reliably, this will not do. We should examine all of the fp classes.
|
| 728 |
|
|
*/
|
| 729 |
|
|
|
| 730 |
|
|
#define _FP_NEG(fs, wc, R, X) \
|
| 731 |
|
|
do { \
|
| 732 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 733 |
|
|
R##_c = X##_c; \
|
| 734 |
|
|
R##_e = X##_e; \
|
| 735 |
|
|
R##_s = 1 ^ X##_s; \
|
| 736 |
|
|
} while (0)
|
| 737 |
|
|
|
| 738 |
|
|
|
| 739 |
|
|
/*
|
| 740 |
|
|
* Main multiplication routine. The input values should be cooked.
|
| 741 |
|
|
*/
|
| 742 |
|
|
|
| 743 |
|
|
#define _FP_MUL(fs, wc, R, X, Y) \
|
| 744 |
|
|
do { \
|
| 745 |
|
|
R##_s = X##_s ^ Y##_s; \
|
| 746 |
|
|
switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
|
| 747 |
|
|
{ \
|
| 748 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
|
| 749 |
|
|
R##_c = FP_CLS_NORMAL; \
|
| 750 |
|
|
R##_e = X##_e + Y##_e + 1; \
|
| 751 |
|
|
\
|
| 752 |
|
|
_FP_MUL_MEAT_##fs(R,X,Y); \
|
| 753 |
|
|
\
|
| 754 |
|
|
if (_FP_FRAC_OVERP_##wc(fs, R)) \
|
| 755 |
|
|
_FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
|
| 756 |
|
|
else \
|
| 757 |
|
|
R##_e--; \
|
| 758 |
|
|
break; \
|
| 759 |
|
|
\
|
| 760 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
|
| 761 |
|
|
_FP_CHOOSENAN(fs, wc, R, X, Y, '*'); \
|
| 762 |
|
|
break; \
|
| 763 |
|
|
\
|
| 764 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
|
| 765 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
|
| 766 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
|
| 767 |
|
|
R##_s = X##_s; \
|
| 768 |
|
|
\
|
| 769 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
|
| 770 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
|
| 771 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
|
| 772 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
|
| 773 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 774 |
|
|
R##_c = X##_c; \
|
| 775 |
|
|
break; \
|
| 776 |
|
|
\
|
| 777 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
|
| 778 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
|
| 779 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
|
| 780 |
|
|
R##_s = Y##_s; \
|
| 781 |
|
|
\
|
| 782 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
|
| 783 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
|
| 784 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 785 |
|
|
R##_c = Y##_c; \
|
| 786 |
|
|
break; \
|
| 787 |
|
|
\
|
| 788 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
|
| 789 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
|
| 790 |
|
|
R##_s = _FP_NANSIGN_##fs; \
|
| 791 |
|
|
R##_c = FP_CLS_NAN; \
|
| 792 |
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
| 793 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 794 |
|
|
break; \
|
| 795 |
|
|
\
|
| 796 |
|
|
default: \
|
| 797 |
|
|
abort(); \
|
| 798 |
|
|
} \
|
| 799 |
|
|
} while (0)
|
| 800 |
|
|
|
| 801 |
|
|
|
| 802 |
|
|
/*
|
| 803 |
|
|
* Main division routine. The input values should be cooked.
|
| 804 |
|
|
*/
|
| 805 |
|
|
|
| 806 |
|
|
#define _FP_DIV(fs, wc, R, X, Y) \
|
| 807 |
|
|
do { \
|
| 808 |
|
|
R##_s = X##_s ^ Y##_s; \
|
| 809 |
|
|
switch (_FP_CLS_COMBINE(X##_c, Y##_c)) \
|
| 810 |
|
|
{ \
|
| 811 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NORMAL): \
|
| 812 |
|
|
R##_c = FP_CLS_NORMAL; \
|
| 813 |
|
|
R##_e = X##_e - Y##_e; \
|
| 814 |
|
|
\
|
| 815 |
|
|
_FP_DIV_MEAT_##fs(R,X,Y); \
|
| 816 |
|
|
break; \
|
| 817 |
|
|
\
|
| 818 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NAN): \
|
| 819 |
|
|
_FP_CHOOSENAN(fs, wc, R, X, Y, '/'); \
|
| 820 |
|
|
break; \
|
| 821 |
|
|
\
|
| 822 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_NORMAL): \
|
| 823 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_INF): \
|
| 824 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NAN,FP_CLS_ZERO): \
|
| 825 |
|
|
R##_s = X##_s; \
|
| 826 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 827 |
|
|
R##_c = X##_c; \
|
| 828 |
|
|
break; \
|
| 829 |
|
|
\
|
| 830 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_NAN): \
|
| 831 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NAN): \
|
| 832 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NAN): \
|
| 833 |
|
|
R##_s = Y##_s; \
|
| 834 |
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
| 835 |
|
|
R##_c = Y##_c; \
|
| 836 |
|
|
break; \
|
| 837 |
|
|
\
|
| 838 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_INF): \
|
| 839 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_INF): \
|
| 840 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_NORMAL): \
|
| 841 |
|
|
R##_c = FP_CLS_ZERO; \
|
| 842 |
|
|
break; \
|
| 843 |
|
|
\
|
| 844 |
|
|
case _FP_CLS_COMBINE(FP_CLS_NORMAL,FP_CLS_ZERO): \
|
| 845 |
|
|
FP_SET_EXCEPTION(FP_EX_DIVZERO); \
|
| 846 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_ZERO): \
|
| 847 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_NORMAL): \
|
| 848 |
|
|
R##_c = FP_CLS_INF; \
|
| 849 |
|
|
break; \
|
| 850 |
|
|
\
|
| 851 |
|
|
case _FP_CLS_COMBINE(FP_CLS_INF,FP_CLS_INF): \
|
| 852 |
|
|
case _FP_CLS_COMBINE(FP_CLS_ZERO,FP_CLS_ZERO): \
|
| 853 |
|
|
R##_s = _FP_NANSIGN_##fs; \
|
| 854 |
|
|
R##_c = FP_CLS_NAN; \
|
| 855 |
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
| 856 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 857 |
|
|
break; \
|
| 858 |
|
|
\
|
| 859 |
|
|
default: \
|
| 860 |
|
|
abort(); \
|
| 861 |
|
|
} \
|
| 862 |
|
|
} while (0)
|
| 863 |
|
|
|
| 864 |
|
|
|
| 865 |
|
|
/*
|
| 866 |
|
|
* Main differential comparison routine. The inputs should be raw not
|
| 867 |
|
|
* cooked. The return is -1,0,1 for normal values, 2 otherwise.
|
| 868 |
|
|
*/
|
| 869 |
|
|
|
| 870 |
|
|
#define _FP_CMP(fs, wc, ret, X, Y, un) \
|
| 871 |
|
|
do { \
|
| 872 |
|
|
/* NANs are unordered */ \
|
| 873 |
|
|
if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
|
| 874 |
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \
|
| 875 |
|
|
{ \
|
| 876 |
|
|
ret = un; \
|
| 877 |
|
|
} \
|
| 878 |
|
|
else \
|
| 879 |
|
|
{ \
|
| 880 |
|
|
int __is_zero_x; \
|
| 881 |
|
|
int __is_zero_y; \
|
| 882 |
|
|
\
|
| 883 |
|
|
__is_zero_x = (!X##_e && _FP_FRAC_ZEROP_##wc(X)) ? 1 : 0; \
|
| 884 |
|
|
__is_zero_y = (!Y##_e && _FP_FRAC_ZEROP_##wc(Y)) ? 1 : 0; \
|
| 885 |
|
|
\
|
| 886 |
|
|
if (__is_zero_x && __is_zero_y) \
|
| 887 |
|
|
ret = 0; \
|
| 888 |
|
|
else if (__is_zero_x) \
|
| 889 |
|
|
ret = Y##_s ? 1 : -1; \
|
| 890 |
|
|
else if (__is_zero_y) \
|
| 891 |
|
|
ret = X##_s ? -1 : 1; \
|
| 892 |
|
|
else if (X##_s != Y##_s) \
|
| 893 |
|
|
ret = X##_s ? -1 : 1; \
|
| 894 |
|
|
else if (X##_e > Y##_e) \
|
| 895 |
|
|
ret = X##_s ? -1 : 1; \
|
| 896 |
|
|
else if (X##_e < Y##_e) \
|
| 897 |
|
|
ret = X##_s ? 1 : -1; \
|
| 898 |
|
|
else if (_FP_FRAC_GT_##wc(X, Y)) \
|
| 899 |
|
|
ret = X##_s ? -1 : 1; \
|
| 900 |
|
|
else if (_FP_FRAC_GT_##wc(Y, X)) \
|
| 901 |
|
|
ret = X##_s ? 1 : -1; \
|
| 902 |
|
|
else \
|
| 903 |
|
|
ret = 0; \
|
| 904 |
|
|
} \
|
| 905 |
|
|
} while (0)
|
| 906 |
|
|
|
| 907 |
|
|
|
| 908 |
|
|
/* Simplification for strict equality. */
|
| 909 |
|
|
|
| 910 |
|
|
#define _FP_CMP_EQ(fs, wc, ret, X, Y) \
|
| 911 |
|
|
do { \
|
| 912 |
|
|
/* NANs are unordered */ \
|
| 913 |
|
|
if ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
|
| 914 |
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) \
|
| 915 |
|
|
{ \
|
| 916 |
|
|
ret = 1; \
|
| 917 |
|
|
} \
|
| 918 |
|
|
else \
|
| 919 |
|
|
{ \
|
| 920 |
|
|
ret = !(X##_e == Y##_e \
|
| 921 |
|
|
&& _FP_FRAC_EQ_##wc(X, Y) \
|
| 922 |
|
|
&& (X##_s == Y##_s || (!X##_e && _FP_FRAC_ZEROP_##wc(X)))); \
|
| 923 |
|
|
} \
|
| 924 |
|
|
} while (0)
|
| 925 |
|
|
|
| 926 |
|
|
/* Version to test unordered. */
|
| 927 |
|
|
|
| 928 |
|
|
#define _FP_CMP_UNORD(fs, wc, ret, X, Y) \
|
| 929 |
|
|
do { \
|
| 930 |
|
|
ret = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
|
| 931 |
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))); \
|
| 932 |
|
|
} while (0)
|
| 933 |
|
|
|
| 934 |
|
|
/*
|
| 935 |
|
|
* Main square root routine. The input value should be cooked.
|
| 936 |
|
|
*/
|
| 937 |
|
|
|
| 938 |
|
|
#define _FP_SQRT(fs, wc, R, X) \
|
| 939 |
|
|
do { \
|
| 940 |
|
|
_FP_FRAC_DECL_##wc(T); _FP_FRAC_DECL_##wc(S); \
|
| 941 |
|
|
_FP_W_TYPE q; \
|
| 942 |
|
|
switch (X##_c) \
|
| 943 |
|
|
{ \
|
| 944 |
|
|
case FP_CLS_NAN: \
|
| 945 |
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
| 946 |
|
|
R##_s = X##_s; \
|
| 947 |
|
|
R##_c = FP_CLS_NAN; \
|
| 948 |
|
|
break; \
|
| 949 |
|
|
case FP_CLS_INF: \
|
| 950 |
|
|
if (X##_s) \
|
| 951 |
|
|
{ \
|
| 952 |
|
|
R##_s = _FP_NANSIGN_##fs; \
|
| 953 |
|
|
R##_c = FP_CLS_NAN; /* NAN */ \
|
| 954 |
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
| 955 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 956 |
|
|
} \
|
| 957 |
|
|
else \
|
| 958 |
|
|
{ \
|
| 959 |
|
|
R##_s = 0; \
|
| 960 |
|
|
R##_c = FP_CLS_INF; /* sqrt(+inf) = +inf */ \
|
| 961 |
|
|
} \
|
| 962 |
|
|
break; \
|
| 963 |
|
|
case FP_CLS_ZERO: \
|
| 964 |
|
|
R##_s = X##_s; \
|
| 965 |
|
|
R##_c = FP_CLS_ZERO; /* sqrt(+-0) = +-0 */ \
|
| 966 |
|
|
break; \
|
| 967 |
|
|
case FP_CLS_NORMAL: \
|
| 968 |
|
|
R##_s = 0; \
|
| 969 |
|
|
if (X##_s) \
|
| 970 |
|
|
{ \
|
| 971 |
|
|
R##_c = FP_CLS_NAN; /* sNAN */ \
|
| 972 |
|
|
R##_s = _FP_NANSIGN_##fs; \
|
| 973 |
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
| 974 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 975 |
|
|
break; \
|
| 976 |
|
|
} \
|
| 977 |
|
|
R##_c = FP_CLS_NORMAL; \
|
| 978 |
|
|
if (X##_e & 1) \
|
| 979 |
|
|
_FP_FRAC_SLL_##wc(X, 1); \
|
| 980 |
|
|
R##_e = X##_e >> 1; \
|
| 981 |
|
|
_FP_FRAC_SET_##wc(S, _FP_ZEROFRAC_##wc); \
|
| 982 |
|
|
_FP_FRAC_SET_##wc(R, _FP_ZEROFRAC_##wc); \
|
| 983 |
|
|
q = _FP_OVERFLOW_##fs >> 1; \
|
| 984 |
|
|
_FP_SQRT_MEAT_##wc(R, S, T, X, q); \
|
| 985 |
|
|
} \
|
| 986 |
|
|
} while (0)
|
| 987 |
|
|
|
| 988 |
|
|
/*
|
| 989 |
|
|
* Convert from FP to integer. Input is raw.
|
| 990 |
|
|
*/
|
| 991 |
|
|
|
| 992 |
|
|
/* RSIGNED can have following values:
|
| 993 |
|
|
* 0: the number is required to be 0..(2^rsize)-1, if not, NV is set plus
|
| 994 |
|
|
* the result is either 0 or (2^rsize)-1 depending on the sign in such
|
| 995 |
|
|
* case.
|
| 996 |
|
|
* 1: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
|
| 997 |
|
|
* NV is set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
|
| 998 |
|
|
* depending on the sign in such case.
|
| 999 |
|
|
* -1: the number is required to be -(2^(rsize-1))..(2^rsize)-1, if not, NV is
|
| 1000 |
|
|
* set plus the result is either -(2^(rsize-1)) or (2^(rsize-1))-1
|
| 1001 |
|
|
* depending on the sign in such case.
|
| 1002 |
|
|
*/
|
| 1003 |
|
|
#define _FP_TO_INT(fs, wc, r, X, rsize, rsigned) \
|
| 1004 |
|
|
do { \
|
| 1005 |
|
|
if (X##_e < _FP_EXPBIAS_##fs) \
|
| 1006 |
|
|
{ \
|
| 1007 |
|
|
r = 0; \
|
| 1008 |
|
|
if (X##_e == 0) \
|
| 1009 |
|
|
{ \
|
| 1010 |
|
|
if (!_FP_FRAC_ZEROP_##wc(X)) \
|
| 1011 |
|
|
{ \
|
| 1012 |
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
| 1013 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 1014 |
|
|
} \
|
| 1015 |
|
|
} \
|
| 1016 |
|
|
else \
|
| 1017 |
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
| 1018 |
|
|
} \
|
| 1019 |
|
|
else if (X##_e >= _FP_EXPBIAS_##fs + rsize - (rsigned > 0 || X##_s) \
|
| 1020 |
|
|
|| (!rsigned && X##_s)) \
|
| 1021 |
|
|
{ \
|
| 1022 |
|
|
/* Overflow or converting to the most negative integer. */ \
|
| 1023 |
|
|
if (rsigned) \
|
| 1024 |
|
|
{ \
|
| 1025 |
|
|
r = 1; \
|
| 1026 |
|
|
r <<= rsize - 1; \
|
| 1027 |
|
|
r -= 1 - X##_s; \
|
| 1028 |
|
|
} else { \
|
| 1029 |
|
|
r = 0; \
|
| 1030 |
|
|
if (X##_s) \
|
| 1031 |
|
|
r = ~r; \
|
| 1032 |
|
|
} \
|
| 1033 |
|
|
\
|
| 1034 |
|
|
if (rsigned && X##_s && X##_e == _FP_EXPBIAS_##fs + rsize - 1) \
|
| 1035 |
|
|
{ \
|
| 1036 |
|
|
/* Possibly converting to most negative integer; check the \
|
| 1037 |
|
|
mantissa. */ \
|
| 1038 |
|
|
int inexact = 0; \
|
| 1039 |
|
|
(void)((_FP_FRACBITS_##fs > rsize) \
|
| 1040 |
|
|
? ({ _FP_FRAC_SRST_##wc(X, inexact, \
|
| 1041 |
|
|
_FP_FRACBITS_##fs - rsize, \
|
| 1042 |
|
|
_FP_FRACBITS_##fs); 0; }) \
|
| 1043 |
|
|
: 0); \
|
| 1044 |
|
|
if (!_FP_FRAC_ZEROP_##wc(X)) \
|
| 1045 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 1046 |
|
|
else if (inexact) \
|
| 1047 |
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
| 1048 |
|
|
} \
|
| 1049 |
|
|
else \
|
| 1050 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 1051 |
|
|
} \
|
| 1052 |
|
|
else \
|
| 1053 |
|
|
{ \
|
| 1054 |
|
|
_FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \
|
| 1055 |
|
|
if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
|
| 1056 |
|
|
{ \
|
| 1057 |
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
| 1058 |
|
|
r <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
|
| 1059 |
|
|
} \
|
| 1060 |
|
|
else \
|
| 1061 |
|
|
{ \
|
| 1062 |
|
|
int inexact; \
|
| 1063 |
|
|
_FP_FRAC_SRST_##wc(X, inexact, \
|
| 1064 |
|
|
(_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
|
| 1065 |
|
|
- X##_e), \
|
| 1066 |
|
|
_FP_FRACBITS_##fs); \
|
| 1067 |
|
|
if (inexact) \
|
| 1068 |
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
| 1069 |
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
| 1070 |
|
|
} \
|
| 1071 |
|
|
if (rsigned && X##_s) \
|
| 1072 |
|
|
r = -r; \
|
| 1073 |
|
|
} \
|
| 1074 |
|
|
} while (0)
|
| 1075 |
|
|
|
| 1076 |
|
|
/* Convert integer to fp. Output is raw. RTYPE is unsigned even if
|
| 1077 |
|
|
input is signed. */
|
| 1078 |
|
|
#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
|
| 1079 |
|
|
do { \
|
| 1080 |
|
|
if (r) \
|
| 1081 |
|
|
{ \
|
| 1082 |
|
|
rtype ur_; \
|
| 1083 |
|
|
\
|
| 1084 |
|
|
if ((X##_s = (r < 0))) \
|
| 1085 |
|
|
r = -(rtype)r; \
|
| 1086 |
|
|
\
|
| 1087 |
|
|
ur_ = (rtype) r; \
|
| 1088 |
|
|
(void)((rsize <= _FP_W_TYPE_SIZE) \
|
| 1089 |
|
|
? ({ \
|
| 1090 |
|
|
int lz_; \
|
| 1091 |
|
|
__FP_CLZ(lz_, (_FP_W_TYPE)ur_); \
|
| 1092 |
|
|
X##_e = _FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 - lz_; \
|
| 1093 |
|
|
}) \
|
| 1094 |
|
|
: ((rsize <= 2 * _FP_W_TYPE_SIZE) \
|
| 1095 |
|
|
? ({ \
|
| 1096 |
|
|
int lz_; \
|
| 1097 |
|
|
__FP_CLZ_2(lz_, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE), \
|
| 1098 |
|
|
(_FP_W_TYPE)ur_); \
|
| 1099 |
|
|
X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
|
| 1100 |
|
|
- lz_); \
|
| 1101 |
|
|
}) \
|
| 1102 |
|
|
: (abort(), 0))); \
|
| 1103 |
|
|
\
|
| 1104 |
|
|
if (rsize - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \
|
| 1105 |
|
|
&& X##_e >= _FP_EXPMAX_##fs) \
|
| 1106 |
|
|
{ \
|
| 1107 |
|
|
/* Exponent too big; overflow to infinity. (May also \
|
| 1108 |
|
|
happen after rounding below.) */ \
|
| 1109 |
|
|
_FP_OVERFLOW_SEMIRAW(fs, wc, X); \
|
| 1110 |
|
|
goto pack_semiraw; \
|
| 1111 |
|
|
} \
|
| 1112 |
|
|
\
|
| 1113 |
|
|
if (rsize <= _FP_FRACBITS_##fs \
|
| 1114 |
|
|
|| X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \
|
| 1115 |
|
|
{ \
|
| 1116 |
|
|
/* Exactly representable; shift left. */ \
|
| 1117 |
|
|
_FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \
|
| 1118 |
|
|
_FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \
|
| 1119 |
|
|
+ _FP_FRACBITS_##fs - 1 - X##_e)); \
|
| 1120 |
|
|
} \
|
| 1121 |
|
|
else \
|
| 1122 |
|
|
{ \
|
| 1123 |
|
|
/* More bits in integer than in floating type; need to \
|
| 1124 |
|
|
round. */ \
|
| 1125 |
|
|
if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \
|
| 1126 |
|
|
ur_ = ((ur_ >> (X##_e - _FP_EXPBIAS_##fs \
|
| 1127 |
|
|
- _FP_WFRACBITS_##fs + 1)) \
|
| 1128 |
|
|
| ((ur_ << (rsize - (X##_e - _FP_EXPBIAS_##fs \
|
| 1129 |
|
|
- _FP_WFRACBITS_##fs + 1))) \
|
| 1130 |
|
|
!= 0)); \
|
| 1131 |
|
|
_FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \
|
| 1132 |
|
|
if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \
|
| 1133 |
|
|
_FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \
|
| 1134 |
|
|
+ _FP_WFRACBITS_##fs - 1 - X##_e)); \
|
| 1135 |
|
|
_FP_FRAC_HIGH_##fs(X) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
| 1136 |
|
|
pack_semiraw: \
|
| 1137 |
|
|
_FP_PACK_SEMIRAW(fs, wc, X); \
|
| 1138 |
|
|
} \
|
| 1139 |
|
|
} \
|
| 1140 |
|
|
else \
|
| 1141 |
|
|
{ \
|
| 1142 |
|
|
X##_s = 0; \
|
| 1143 |
|
|
X##_e = 0; \
|
| 1144 |
|
|
_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
|
| 1145 |
|
|
} \
|
| 1146 |
|
|
} while (0)
|
| 1147 |
|
|
|
| 1148 |
|
|
|
| 1149 |
|
|
/* Extend from a narrower floating-point format to a wider one. Input
|
| 1150 |
|
|
and output are raw. */
|
| 1151 |
|
|
#define FP_EXTEND(dfs,sfs,dwc,swc,D,S) \
|
| 1152 |
|
|
do { \
|
| 1153 |
|
|
if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \
|
| 1154 |
|
|
|| (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \
|
| 1155 |
|
|
< _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \
|
| 1156 |
|
|
|| (_FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1 \
|
| 1157 |
|
|
&& _FP_EXPBIAS_##dfs != _FP_EXPBIAS_##sfs)) \
|
| 1158 |
|
|
abort(); \
|
| 1159 |
|
|
D##_s = S##_s; \
|
| 1160 |
|
|
_FP_FRAC_COPY_##dwc##_##swc(D, S); \
|
| 1161 |
|
|
if (_FP_EXP_NORMAL(sfs, swc, S)) \
|
| 1162 |
|
|
{ \
|
| 1163 |
|
|
D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
|
| 1164 |
|
|
_FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \
|
| 1165 |
|
|
} \
|
| 1166 |
|
|
else \
|
| 1167 |
|
|
{ \
|
| 1168 |
|
|
if (S##_e == 0) \
|
| 1169 |
|
|
{ \
|
| 1170 |
|
|
if (_FP_FRAC_ZEROP_##swc(S)) \
|
| 1171 |
|
|
D##_e = 0; \
|
| 1172 |
|
|
else if (_FP_EXPBIAS_##dfs \
|
| 1173 |
|
|
< _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \
|
| 1174 |
|
|
{ \
|
| 1175 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 1176 |
|
|
_FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs \
|
| 1177 |
|
|
- _FP_FRACBITS_##sfs)); \
|
| 1178 |
|
|
D##_e = 0; \
|
| 1179 |
|
|
} \
|
| 1180 |
|
|
else \
|
| 1181 |
|
|
{ \
|
| 1182 |
|
|
int _lz; \
|
| 1183 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 1184 |
|
|
_FP_FRAC_CLZ_##swc(_lz, S); \
|
| 1185 |
|
|
_FP_FRAC_SLL_##dwc(D, \
|
| 1186 |
|
|
_lz + _FP_FRACBITS_##dfs \
|
| 1187 |
|
|
- _FP_FRACTBITS_##sfs); \
|
| 1188 |
|
|
D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
|
| 1189 |
|
|
+ _FP_FRACXBITS_##sfs - _lz); \
|
| 1190 |
|
|
} \
|
| 1191 |
|
|
} \
|
| 1192 |
|
|
else \
|
| 1193 |
|
|
{ \
|
| 1194 |
|
|
D##_e = _FP_EXPMAX_##dfs; \
|
| 1195 |
|
|
if (!_FP_FRAC_ZEROP_##swc(S)) \
|
| 1196 |
|
|
{ \
|
| 1197 |
|
|
if (!(_FP_FRAC_HIGH_RAW_##sfs(S) & _FP_QNANBIT_##sfs)) \
|
| 1198 |
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
| 1199 |
|
|
_FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs \
|
| 1200 |
|
|
- _FP_FRACBITS_##sfs)); \
|
| 1201 |
|
|
} \
|
| 1202 |
|
|
} \
|
| 1203 |
|
|
} \
|
| 1204 |
|
|
} while (0)
|
| 1205 |
|
|
|
| 1206 |
|
|
/* Truncate from a wider floating-point format to a narrower one.
|
| 1207 |
|
|
Input and output are semi-raw. */
|
| 1208 |
|
|
#define FP_TRUNC(dfs,sfs,dwc,swc,D,S) \
|
| 1209 |
|
|
do { \
|
| 1210 |
|
|
if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \
|
| 1211 |
|
|
|| (_FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1 \
|
| 1212 |
|
|
&& _FP_EXPBIAS_##sfs != _FP_EXPBIAS_##dfs)) \
|
| 1213 |
|
|
abort(); \
|
| 1214 |
|
|
D##_s = S##_s; \
|
| 1215 |
|
|
if (_FP_EXP_NORMAL(sfs, swc, S)) \
|
| 1216 |
|
|
{ \
|
| 1217 |
|
|
D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
|
| 1218 |
|
|
if (D##_e >= _FP_EXPMAX_##dfs) \
|
| 1219 |
|
|
_FP_OVERFLOW_SEMIRAW(dfs, dwc, D); \
|
| 1220 |
|
|
else \
|
| 1221 |
|
|
{ \
|
| 1222 |
|
|
if (D##_e <= 0) \
|
| 1223 |
|
|
{ \
|
| 1224 |
|
|
if (D##_e < 1 - _FP_FRACBITS_##dfs) \
|
| 1225 |
|
|
{ \
|
| 1226 |
|
|
_FP_FRAC_SET_##swc(S, _FP_ZEROFRAC_##swc); \
|
| 1227 |
|
|
_FP_FRAC_LOW_##swc(S) |= 1; \
|
| 1228 |
|
|
} \
|
| 1229 |
|
|
else \
|
| 1230 |
|
|
{ \
|
| 1231 |
|
|
_FP_FRAC_HIGH_##sfs(S) |= _FP_IMPLBIT_SH_##sfs; \
|
| 1232 |
|
|
_FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
|
| 1233 |
|
|
- _FP_WFRACBITS_##dfs + 1 - D##_e), \
|
| 1234 |
|
|
_FP_WFRACBITS_##sfs); \
|
| 1235 |
|
|
} \
|
| 1236 |
|
|
D##_e = 0; \
|
| 1237 |
|
|
} \
|
| 1238 |
|
|
else \
|
| 1239 |
|
|
_FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
|
| 1240 |
|
|
- _FP_WFRACBITS_##dfs), \
|
| 1241 |
|
|
_FP_WFRACBITS_##sfs); \
|
| 1242 |
|
|
_FP_FRAC_COPY_##dwc##_##swc(D, S); \
|
| 1243 |
|
|
} \
|
| 1244 |
|
|
} \
|
| 1245 |
|
|
else \
|
| 1246 |
|
|
{ \
|
| 1247 |
|
|
if (S##_e == 0) \
|
| 1248 |
|
|
{ \
|
| 1249 |
|
|
D##_e = 0; \
|
| 1250 |
|
|
if (_FP_FRAC_ZEROP_##swc(S)) \
|
| 1251 |
|
|
_FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
|
| 1252 |
|
|
else \
|
| 1253 |
|
|
{ \
|
| 1254 |
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
| 1255 |
|
|
if (_FP_EXPBIAS_##sfs \
|
| 1256 |
|
|
< _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \
|
| 1257 |
|
|
{ \
|
| 1258 |
|
|
_FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
|
| 1259 |
|
|
- _FP_WFRACBITS_##dfs), \
|
| 1260 |
|
|
_FP_WFRACBITS_##sfs); \
|
| 1261 |
|
|
_FP_FRAC_COPY_##dwc##_##swc(D, S); \
|
| 1262 |
|
|
} \
|
| 1263 |
|
|
else \
|
| 1264 |
|
|
{ \
|
| 1265 |
|
|
_FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
|
| 1266 |
|
|
_FP_FRAC_LOW_##dwc(D) |= 1; \
|
| 1267 |
|
|
} \
|
| 1268 |
|
|
} \
|
| 1269 |
|
|
} \
|
| 1270 |
|
|
else \
|
| 1271 |
|
|
{ \
|
| 1272 |
|
|
D##_e = _FP_EXPMAX_##dfs; \
|
| 1273 |
|
|
if (_FP_FRAC_ZEROP_##swc(S)) \
|
| 1274 |
|
|
_FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
|
| 1275 |
|
|
else \
|
| 1276 |
|
|
{ \
|
| 1277 |
|
|
_FP_CHECK_SIGNAN_SEMIRAW(sfs, swc, S); \
|
| 1278 |
|
|
_FP_FRAC_SRL_##swc(S, (_FP_WFRACBITS_##sfs \
|
| 1279 |
|
|
- _FP_WFRACBITS_##dfs)); \
|
| 1280 |
|
|
_FP_FRAC_COPY_##dwc##_##swc(D, S); \
|
| 1281 |
|
|
/* Semi-raw NaN must have all workbits cleared. */ \
|
| 1282 |
|
|
_FP_FRAC_LOW_##dwc(D) \
|
| 1283 |
|
|
&= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \
|
| 1284 |
|
|
_FP_FRAC_HIGH_##dfs(D) |= _FP_QNANBIT_SH_##dfs; \
|
| 1285 |
|
|
} \
|
| 1286 |
|
|
} \
|
| 1287 |
|
|
} \
|
| 1288 |
|
|
} while (0)
|
| 1289 |
|
|
|
| 1290 |
|
|
/*
|
| 1291 |
|
|
* Helper primitives.
|
| 1292 |
|
|
*/
|
| 1293 |
|
|
|
| 1294 |
|
|
/* Count leading zeros in a word. */
|
| 1295 |
|
|
|
| 1296 |
|
|
#ifndef __FP_CLZ
|
| 1297 |
|
|
/* GCC 3.4 and later provide the builtins for us. */
|
| 1298 |
|
|
#define __FP_CLZ(r, x) \
|
| 1299 |
|
|
do { \
|
| 1300 |
|
|
if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \
|
| 1301 |
|
|
r = __builtin_clz (x); \
|
| 1302 |
|
|
else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \
|
| 1303 |
|
|
r = __builtin_clzl (x); \
|
| 1304 |
|
|
else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \
|
| 1305 |
|
|
r = __builtin_clzll (x); \
|
| 1306 |
|
|
else \
|
| 1307 |
|
|
abort (); \
|
| 1308 |
|
|
} while (0)
|
| 1309 |
|
|
#endif /* ndef __FP_CLZ */
|
| 1310 |
|
|
|
| 1311 |
|
|
#define _FP_DIV_HELP_imm(q, r, n, d) \
|
| 1312 |
|
|
do { \
|
| 1313 |
|
|
q = n / d, r = n % d; \
|
| 1314 |
|
|
} while (0)
|
| 1315 |
|
|
|
| 1316 |
|
|
|
| 1317 |
|
|
/* A restoring bit-by-bit division primitive. */
|
| 1318 |
|
|
|
| 1319 |
|
|
#define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \
|
| 1320 |
|
|
do { \
|
| 1321 |
|
|
int count = _FP_WFRACBITS_##fs; \
|
| 1322 |
|
|
_FP_FRAC_DECL_##wc (u); \
|
| 1323 |
|
|
_FP_FRAC_DECL_##wc (v); \
|
| 1324 |
|
|
_FP_FRAC_COPY_##wc (u, X); \
|
| 1325 |
|
|
_FP_FRAC_COPY_##wc (v, Y); \
|
| 1326 |
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
| 1327 |
|
|
/* Normalize U and V. */ \
|
| 1328 |
|
|
_FP_FRAC_SLL_##wc (u, _FP_WFRACXBITS_##fs); \
|
| 1329 |
|
|
_FP_FRAC_SLL_##wc (v, _FP_WFRACXBITS_##fs); \
|
| 1330 |
|
|
/* First round. Since the operands are normalized, either the \
|
| 1331 |
|
|
first or second bit will be set in the fraction. Produce a \
|
| 1332 |
|
|
normalized result by checking which and adjusting the loop \
|
| 1333 |
|
|
count and exponent accordingly. */ \
|
| 1334 |
|
|
if (_FP_FRAC_GE_1 (u, v)) \
|
| 1335 |
|
|
{ \
|
| 1336 |
|
|
_FP_FRAC_SUB_##wc (u, u, v); \
|
| 1337 |
|
|
_FP_FRAC_LOW_##wc (R) |= 1; \
|
| 1338 |
|
|
count--; \
|
| 1339 |
|
|
} \
|
| 1340 |
|
|
else \
|
| 1341 |
|
|
R##_e--; \
|
| 1342 |
|
|
/* Subsequent rounds. */ \
|
| 1343 |
|
|
do { \
|
| 1344 |
|
|
int msb = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (u) < 0; \
|
| 1345 |
|
|
_FP_FRAC_SLL_##wc (u, 1); \
|
| 1346 |
|
|
_FP_FRAC_SLL_##wc (R, 1); \
|
| 1347 |
|
|
if (msb || _FP_FRAC_GE_1 (u, v)) \
|
| 1348 |
|
|
{ \
|
| 1349 |
|
|
_FP_FRAC_SUB_##wc (u, u, v); \
|
| 1350 |
|
|
_FP_FRAC_LOW_##wc (R) |= 1; \
|
| 1351 |
|
|
} \
|
| 1352 |
|
|
} while (--count > 0); \
|
| 1353 |
|
|
/* If there's anything left in U, the result is inexact. */ \
|
| 1354 |
|
|
_FP_FRAC_LOW_##wc (R) |= !_FP_FRAC_ZEROP_##wc (u); \
|
| 1355 |
|
|
} while (0)
|
| 1356 |
|
|
|
| 1357 |
|
|
#define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
|
| 1358 |
|
|
#define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
|
| 1359 |
|
|
#define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)
|
