mirror of git://sourceware.org/git/glibc.git
1322 lines
41 KiB
C
1322 lines
41 KiB
C
/* Software floating-point emulation. Common operations.
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Copyright (C) 1997,1998,1999,2006 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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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, Inc., 59 Temple Place, Suite 330, Boston, MA
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02111-1307 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_SET_EXCEPTION(FP_EX_OVERFLOW); \
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FP_SET_EXCEPTION(FP_EX_INEXACT); \
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_FP_FRAC_SET_##wc(X, _FP_MAXFRAC_##wc); \
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} \
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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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/*
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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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} \
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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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FP_SET_EXCEPTION(FP_EX_UNDERFLOW); \
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} \
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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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|
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/* Addition on semi-raw values. */
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#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
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do { \
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if (X##_s == Y##_s) \
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{ \
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/* Addition. */ \
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R##_s = X##_s; \
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int ediff = X##_e - Y##_e; \
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if (ediff > 0) \
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{ \
|
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R##_e = X##_e; \
|
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if (Y##_e == 0) \
|
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{ \
|
|
/* Y is zero or denormalized. */ \
|
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if (_FP_FRAC_ZEROP_##wc(Y)) \
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{ \
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_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
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_FP_FRAC_COPY_##wc(R, X); \
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goto add_done; \
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} \
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else \
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{ \
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FP_SET_EXCEPTION(FP_EX_DENORM); \
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ediff--; \
|
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if (ediff == 0) \
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|
{ \
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
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|
goto add3; \
|
|
} \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc(R, X); \
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goto add_done; \
|
|
} \
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goto add1; \
|
|
} \
|
|
} \
|
|
else if (X##_e == _FP_EXPMAX_##fs) \
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{ \
|
|
/* X is NaN or Inf, Y is normal. */ \
|
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_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
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_FP_FRAC_COPY_##wc(R, X); \
|
|
goto add_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of Y. */ \
|
|
_FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \
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|
\
|
|
add1: \
|
|
/* Shift the mantissa of Y to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of X. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc(Y)) \
|
|
_FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
|
|
} \
|
|
else if (ediff < 0) \
|
|
{ \
|
|
ediff = -ediff; \
|
|
R##_e = Y##_e; \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X is zero or denormalized. */ \
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
ediff--; \
|
|
if (ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_ADD_##wc(R, Y, X); \
|
|
goto add3; \
|
|
} \
|
|
if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
goto add2; \
|
|
} \
|
|
} \
|
|
else if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* Y is NaN or Inf, X is normal. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of X. */ \
|
|
_FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
add2: \
|
|
/* Shift the mantissa of X to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of Y. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc(X)) \
|
|
_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_ADD_##wc(R, Y, X); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* ediff == 0. */ \
|
|
if (!_FP_EXP_NORMAL(fs, wc, X)) \
|
|
{ \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X and Y are zero or denormalized. */ \
|
|
R##_e = 0; \
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
|
{ \
|
|
if (!_FP_FRAC_ZEROP_##wc(Y)) \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
goto add_done; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc(Y)) \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
goto add_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* Normalized result. */ \
|
|
_FP_FRAC_HIGH_##fs(R) \
|
|
&= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
|
R##_e = 1; \
|
|
} \
|
|
goto add_done; \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* X and Y are NaN or Inf. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
R##_e = _FP_EXPMAX_##fs; \
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
else if (_FP_FRAC_ZEROP_##wc(Y)) \
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
else \
|
|
_FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \
|
|
goto add_done; \
|
|
} \
|
|
} \
|
|
/* The exponents of X and Y, both normal, are equal. The \
|
|
implicit MSBs will always add to increase the \
|
|
exponent. */ \
|
|
_FP_FRAC_ADD_##wc(R, X, Y); \
|
|
R##_e = X##_e + 1; \
|
|
_FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
|
|
if (R##_e == _FP_EXPMAX_##fs) \
|
|
/* Overflow to infinity (depending on rounding mode). */ \
|
|
_FP_OVERFLOW_SEMIRAW(fs, wc, R); \
|
|
goto add_done; \
|
|
} \
|
|
add3: \
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* Overflow. */ \
|
|
_FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
|
R##_e++; \
|
|
_FP_FRAC_SRS_##wc(R, 1, _FP_WFRACBITS_##fs); \
|
|
if (R##_e == _FP_EXPMAX_##fs) \
|
|
/* Overflow to infinity (depending on rounding mode). */ \
|
|
_FP_OVERFLOW_SEMIRAW(fs, wc, R); \
|
|
} \
|
|
add_done: ; \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* Subtraction. */ \
|
|
int ediff = X##_e - Y##_e; \
|
|
if (ediff > 0) \
|
|
{ \
|
|
R##_e = X##_e; \
|
|
R##_s = X##_s; \
|
|
if (Y##_e == 0) \
|
|
{ \
|
|
/* Y is zero or denormalized. */ \
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
goto sub_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
ediff--; \
|
|
if (ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
|
goto sub3; \
|
|
} \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
goto sub_done; \
|
|
} \
|
|
goto sub1; \
|
|
} \
|
|
} \
|
|
else if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* X is NaN or Inf, Y is normal. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
goto sub_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of Y. */ \
|
|
_FP_FRAC_HIGH_##fs(Y) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
sub1: \
|
|
/* Shift the mantissa of Y to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of X. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc(Y, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc(Y)) \
|
|
_FP_FRAC_SET_##wc(Y, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
|
} \
|
|
else if (ediff < 0) \
|
|
{ \
|
|
ediff = -ediff; \
|
|
R##_e = Y##_e; \
|
|
R##_s = Y##_s; \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X is zero or denormalized. */ \
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
goto sub_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
ediff--; \
|
|
if (ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
|
goto sub3; \
|
|
} \
|
|
if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
goto sub_done; \
|
|
} \
|
|
goto sub2; \
|
|
} \
|
|
} \
|
|
else if (Y##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* Y is NaN or Inf, X is normal. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
goto sub_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of X. */ \
|
|
_FP_FRAC_HIGH_##fs(X) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
sub2: \
|
|
/* Shift the mantissa of X to the right EDIFF steps; \
|
|
remember to account later for the implicit MSB of Y. */ \
|
|
if (ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc(X, ediff, _FP_WFRACBITS_##fs); \
|
|
else if (!_FP_FRAC_ZEROP_##wc(X)) \
|
|
_FP_FRAC_SET_##wc(X, _FP_MINFRAC_##wc); \
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* ediff == 0. */ \
|
|
if (!_FP_EXP_NORMAL(fs, wc, X)) \
|
|
{ \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
/* X and Y are zero or denormalized. */ \
|
|
R##_e = 0; \
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
|
{ \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
R##_s = Y##_s; \
|
|
} \
|
|
goto sub_done; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc(Y)) \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
R##_s = X##_s; \
|
|
goto sub_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
|
R##_s = X##_s; \
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* |X| < |Y|, negate result. */ \
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
|
R##_s = Y##_s; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc(R)) \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
goto sub_done; \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* X and Y are NaN or Inf, of opposite signs. */ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, X); \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(fs, wc, Y); \
|
|
R##_e = _FP_EXPMAX_##fs; \
|
|
if (_FP_FRAC_ZEROP_##wc(X)) \
|
|
{ \
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
|
{ \
|
|
/* Inf - Inf. */ \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
_FP_FRAC_SET_##wc(R, _FP_NANFRAC_##fs); \
|
|
_FP_FRAC_SLL_##wc(R, _FP_WORKBITS); \
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* Inf - NaN. */ \
|
|
R##_s = Y##_s; \
|
|
_FP_FRAC_COPY_##wc(R, Y); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
if (_FP_FRAC_ZEROP_##wc(Y)) \
|
|
{ \
|
|
/* NaN - Inf. */ \
|
|
R##_s = X##_s; \
|
|
_FP_FRAC_COPY_##wc(R, X); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* NaN - NaN. */ \
|
|
_FP_CHOOSENAN_SEMIRAW(fs, wc, R, X, Y, OP); \
|
|
} \
|
|
} \
|
|
goto sub_done; \
|
|
} \
|
|
} \
|
|
/* The exponents of X and Y, both normal, are equal. The \
|
|
implicit MSBs cancel. */ \
|
|
R##_e = X##_e; \
|
|
_FP_FRAC_SUB_##wc(R, X, Y); \
|
|
R##_s = X##_s; \
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
/* |X| < |Y|, negate result. */ \
|
|
_FP_FRAC_SUB_##wc(R, Y, X); \
|
|
R##_s = Y##_s; \
|
|
} \
|
|
else if (_FP_FRAC_ZEROP_##wc(R)) \
|
|
{ \
|
|
R##_e = 0; \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
goto sub_done; \
|
|
} \
|
|
goto norm; \
|
|
} \
|
|
sub3: \
|
|
if (_FP_FRAC_HIGH_##fs(R) & _FP_IMPLBIT_SH_##fs) \
|
|
{ \
|
|
int diff; \
|
|
/* Carry into most significant bit of larger one of X and Y, \
|
|
canceling it; renormalize. */ \
|
|
_FP_FRAC_HIGH_##fs(R) &= _FP_IMPLBIT_SH_##fs - 1; \
|
|
norm: \
|
|
_FP_FRAC_CLZ_##wc(diff, R); \
|
|
diff -= _FP_WFRACXBITS_##fs; \
|
|
_FP_FRAC_SLL_##wc(R, diff); \
|
|
if (R##_e <= diff) \
|
|
{ \
|
|
/* R is denormalized. */ \
|
|
diff = diff - R##_e + 1; \
|
|
_FP_FRAC_SRS_##wc(R, diff, _FP_WFRACBITS_##fs); \
|
|
R##_e = 0; \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_e -= diff; \
|
|
_FP_FRAC_HIGH_##fs(R) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
|
} \
|
|
} \
|
|
sub_done: ; \
|
|
} \
|
|
} 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##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))) 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)
|
|
|
|
/* Version to test unordered. */
|
|
|
|
#define _FP_CMP_UNORD(fs, wc, ret, X, Y) \
|
|
do { \
|
|
ret = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(X)) \
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc(Y))); \
|
|
} 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. Input is raw.
|
|
*/
|
|
|
|
/* 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.
|
|
* -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 { \
|
|
if (X##_e < _FP_EXPBIAS_##fs) \
|
|
{ \
|
|
r = 0; \
|
|
if (X##_e == 0) \
|
|
{ \
|
|
if (!_FP_FRAC_ZEROP_##wc(X)) \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
} \
|
|
} \
|
|
else \
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
|
} \
|
|
else if (X##_e >= _FP_EXPBIAS_##fs + rsize - (rsigned > 0 || X##_s) \
|
|
|| (!rsigned && X##_s)) \
|
|
{ \
|
|
/* Overflow or converting to the most negative integer. */ \
|
|
if (rsigned) \
|
|
{ \
|
|
r = 1; \
|
|
r <<= rsize - 1; \
|
|
r -= 1 - X##_s; \
|
|
} else { \
|
|
r = 0; \
|
|
if (X##_s) \
|
|
r = ~r; \
|
|
} \
|
|
\
|
|
if (rsigned && X##_s && X##_e == _FP_EXPBIAS_##fs + rsize - 1) \
|
|
{ \
|
|
/* Possibly converting to most negative integer; check the \
|
|
mantissa. */ \
|
|
int inexact = 0; \
|
|
(void)((_FP_FRACBITS_##fs > rsize) \
|
|
? ({ _FP_FRAC_SRST_##wc(X, inexact, \
|
|
_FP_FRACBITS_##fs - rsize, \
|
|
_FP_FRACBITS_##fs); 0; }) \
|
|
: 0); \
|
|
if (!_FP_FRAC_ZEROP_##wc(X)) \
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
else if (inexact) \
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
|
} \
|
|
else \
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_HIGH_RAW_##fs(X) |= _FP_IMPLBIT_##fs; \
|
|
if (X##_e >= _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1) \
|
|
{ \
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
r <<= X##_e - _FP_EXPBIAS_##fs - _FP_FRACBITS_##fs + 1; \
|
|
} \
|
|
else \
|
|
{ \
|
|
int inexact; \
|
|
_FP_FRAC_SRST_##wc(X, inexact, \
|
|
(_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
|
|
- X##_e), \
|
|
_FP_FRACBITS_##fs); \
|
|
if (inexact) \
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
|
_FP_FRAC_ASSEMBLE_##wc(r, X, rsize); \
|
|
} \
|
|
if (rsigned && X##_s) \
|
|
r = -r; \
|
|
} \
|
|
} while (0)
|
|
|
|
/* Convert integer to fp. Output is raw. RTYPE is unsigned even if
|
|
input is signed. */
|
|
#define _FP_FROM_INT(fs, wc, X, r, rsize, rtype) \
|
|
do { \
|
|
if (r) \
|
|
{ \
|
|
rtype ur_; \
|
|
\
|
|
if ((X##_s = (r < 0))) \
|
|
r = -(rtype)r; \
|
|
\
|
|
ur_ = (rtype) r; \
|
|
(void)((rsize <= _FP_W_TYPE_SIZE) \
|
|
? ({ \
|
|
int lz_; \
|
|
__FP_CLZ(lz_, (_FP_W_TYPE)ur_); \
|
|
X##_e = _FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 - lz_; \
|
|
}) \
|
|
: ((rsize <= 2 * _FP_W_TYPE_SIZE) \
|
|
? ({ \
|
|
int lz_; \
|
|
__FP_CLZ_2(lz_, (_FP_W_TYPE)(ur_ >> _FP_W_TYPE_SIZE), \
|
|
(_FP_W_TYPE)ur_); \
|
|
X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
|
|
- lz_); \
|
|
}) \
|
|
: (abort(), 0))); \
|
|
\
|
|
if (rsize - 1 + _FP_EXPBIAS_##fs >= _FP_EXPMAX_##fs \
|
|
&& X##_e >= _FP_EXPMAX_##fs) \
|
|
{ \
|
|
/* Exponent too big; overflow to infinity. (May also \
|
|
happen after rounding below.) */ \
|
|
_FP_OVERFLOW_SEMIRAW(fs, wc, X); \
|
|
goto pack_semiraw; \
|
|
} \
|
|
\
|
|
if (rsize <= _FP_FRACBITS_##fs \
|
|
|| X##_e < _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs) \
|
|
{ \
|
|
/* Exactly representable; shift left. */ \
|
|
_FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \
|
|
_FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \
|
|
+ _FP_FRACBITS_##fs - 1 - X##_e)); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* More bits in integer than in floating type; need to \
|
|
round. */ \
|
|
if (_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 < X##_e) \
|
|
ur_ = ((ur_ >> (X##_e - _FP_EXPBIAS_##fs \
|
|
- _FP_WFRACBITS_##fs + 1)) \
|
|
| ((ur_ << (rsize - (X##_e - _FP_EXPBIAS_##fs \
|
|
- _FP_WFRACBITS_##fs + 1))) \
|
|
!= 0)); \
|
|
_FP_FRAC_DISASSEMBLE_##wc(X, ur_, rsize); \
|
|
if ((_FP_EXPBIAS_##fs + _FP_WFRACBITS_##fs - 1 - X##_e) > 0) \
|
|
_FP_FRAC_SLL_##wc(X, (_FP_EXPBIAS_##fs \
|
|
+ _FP_WFRACBITS_##fs - 1 - X##_e)); \
|
|
_FP_FRAC_HIGH_##fs(X) &= ~(_FP_W_TYPE)_FP_IMPLBIT_SH_##fs; \
|
|
pack_semiraw: \
|
|
_FP_PACK_SEMIRAW(fs, wc, X); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
X##_s = 0; \
|
|
X##_e = 0; \
|
|
_FP_FRAC_SET_##wc(X, _FP_ZEROFRAC_##wc); \
|
|
} \
|
|
} while (0)
|
|
|
|
|
|
/* Extend from a narrower floating-point format to a wider one. Input
|
|
and output are raw. */
|
|
#define FP_EXTEND(dfs,sfs,dwc,swc,D,S) \
|
|
do { \
|
|
if (_FP_FRACBITS_##dfs < _FP_FRACBITS_##sfs \
|
|
|| (_FP_EXPMAX_##dfs - _FP_EXPBIAS_##dfs \
|
|
< _FP_EXPMAX_##sfs - _FP_EXPBIAS_##sfs) \
|
|
|| _FP_EXPBIAS_##dfs < _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \
|
|
abort(); \
|
|
D##_s = S##_s; \
|
|
_FP_FRAC_COPY_##dwc##_##swc(D, S); \
|
|
if (_FP_EXP_NORMAL(sfs, swc, S)) \
|
|
{ \
|
|
D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
|
|
_FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs - _FP_FRACBITS_##sfs)); \
|
|
} \
|
|
else \
|
|
{ \
|
|
if (S##_e == 0) \
|
|
{ \
|
|
if (_FP_FRAC_ZEROP_##swc(S)) \
|
|
D##_e = 0; \
|
|
else \
|
|
{ \
|
|
int _lz; \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
_FP_FRAC_CLZ_##swc(_lz, S); \
|
|
_FP_FRAC_SLL_##dwc(D, \
|
|
_lz + _FP_FRACBITS_##dfs \
|
|
- _FP_FRACTBITS_##sfs); \
|
|
D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
|
|
+ _FP_FRACXBITS_##sfs - _lz); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
D##_e = _FP_EXPMAX_##dfs; \
|
|
if (!_FP_FRAC_ZEROP_##swc(S)) \
|
|
{ \
|
|
if (!(_FP_FRAC_HIGH_RAW_##sfs(S) & _FP_QNANBIT_##sfs)) \
|
|
FP_SET_EXCEPTION(FP_EX_INVALID); \
|
|
_FP_FRAC_SLL_##dwc(D, (_FP_FRACBITS_##dfs \
|
|
- _FP_FRACBITS_##sfs)); \
|
|
} \
|
|
} \
|
|
} \
|
|
} while (0)
|
|
|
|
/* Truncate from a wider floating-point format to a narrower one.
|
|
Input and output are semi-raw. */
|
|
#define FP_TRUNC(dfs,sfs,dwc,swc,D,S) \
|
|
do { \
|
|
if (_FP_FRACBITS_##sfs < _FP_FRACBITS_##dfs \
|
|
|| _FP_EXPBIAS_##sfs < _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \
|
|
abort(); \
|
|
D##_s = S##_s; \
|
|
if (_FP_EXP_NORMAL(sfs, swc, S)) \
|
|
{ \
|
|
D##_e = S##_e + _FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs; \
|
|
if (D##_e >= _FP_EXPMAX_##dfs) \
|
|
_FP_OVERFLOW_SEMIRAW(dfs, dwc, D); \
|
|
else \
|
|
{ \
|
|
if (D##_e <= 0) \
|
|
{ \
|
|
if (D##_e <= 1 - _FP_FRACBITS_##dfs) \
|
|
_FP_FRAC_SET_##swc(S, _FP_ZEROFRAC_##swc); \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_HIGH_##sfs(S) |= _FP_IMPLBIT_SH_##sfs; \
|
|
_FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs + 1 - D##_e), \
|
|
_FP_WFRACBITS_##sfs); \
|
|
} \
|
|
D##_e = 0; \
|
|
} \
|
|
else \
|
|
_FP_FRAC_SRS_##swc(S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs), \
|
|
_FP_WFRACBITS_##sfs); \
|
|
_FP_FRAC_COPY_##dwc##_##swc(D, S); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
if (S##_e == 0) \
|
|
{ \
|
|
D##_e = 0; \
|
|
_FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
|
|
if (!_FP_FRAC_ZEROP_##swc(S)) \
|
|
{ \
|
|
FP_SET_EXCEPTION(FP_EX_DENORM); \
|
|
FP_SET_EXCEPTION(FP_EX_INEXACT); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
D##_e = _FP_EXPMAX_##dfs; \
|
|
if (_FP_FRAC_ZEROP_##swc(S)) \
|
|
_FP_FRAC_SET_##dwc(D, _FP_ZEROFRAC_##dwc); \
|
|
else \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW(sfs, swc, S); \
|
|
_FP_FRAC_SRL_##swc(S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs)); \
|
|
_FP_FRAC_COPY_##dwc##_##swc(D, S); \
|
|
_FP_FRAC_HIGH_##dfs(D) |= _FP_QNANBIT_SH_##dfs; \
|
|
} \
|
|
} \
|
|
} \
|
|
} while (0)
|
|
|
|
/*
|
|
* Helper primitives.
|
|
*/
|
|
|
|
/* Count leading zeros in a word. */
|
|
|
|
#ifndef __FP_CLZ
|
|
/* GCC 3.4 and later provide the builtins for us. */
|
|
#define __FP_CLZ(r, x) \
|
|
do { \
|
|
if (sizeof (_FP_W_TYPE) == sizeof (unsigned int)) \
|
|
r = __builtin_clz (x); \
|
|
else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long)) \
|
|
r = __builtin_clzl (x); \
|
|
else if (sizeof (_FP_W_TYPE) == sizeof (unsigned long long)) \
|
|
r = __builtin_clzll (x); \
|
|
else \
|
|
abort (); \
|
|
} while (0)
|
|
#endif /* ndef __FP_CLZ */
|
|
|
|
#define _FP_DIV_HELP_imm(q, r, n, d) \
|
|
do { \
|
|
q = n / d, r = n % d; \
|
|
} while (0)
|
|
|
|
|
|
/* A restoring bit-by-bit division primitive. */
|
|
|
|
#define _FP_DIV_MEAT_N_loop(fs, wc, R, X, Y) \
|
|
do { \
|
|
int count = _FP_WFRACBITS_##fs; \
|
|
_FP_FRAC_DECL_##wc (u); \
|
|
_FP_FRAC_DECL_##wc (v); \
|
|
_FP_FRAC_COPY_##wc (u, X); \
|
|
_FP_FRAC_COPY_##wc (v, Y); \
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
|
/* Normalize U and V. */ \
|
|
_FP_FRAC_SLL_##wc (u, _FP_WFRACXBITS_##fs); \
|
|
_FP_FRAC_SLL_##wc (v, _FP_WFRACXBITS_##fs); \
|
|
/* First round. Since the operands are normalized, either the \
|
|
first or second bit will be set in the fraction. Produce a \
|
|
normalized result by checking which and adjusting the loop \
|
|
count and exponent accordingly. */ \
|
|
if (_FP_FRAC_GE_1 (u, v)) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc (u, u, v); \
|
|
_FP_FRAC_LOW_##wc (R) |= 1; \
|
|
count--; \
|
|
} \
|
|
else \
|
|
R##_e--; \
|
|
/* Subsequent rounds. */ \
|
|
do { \
|
|
int msb = (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (u) < 0; \
|
|
_FP_FRAC_SLL_##wc (u, 1); \
|
|
_FP_FRAC_SLL_##wc (R, 1); \
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if (msb || _FP_FRAC_GE_1 (u, v)) \
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{ \
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_FP_FRAC_SUB_##wc (u, u, v); \
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_FP_FRAC_LOW_##wc (R) |= 1; \
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} \
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} while (--count > 0); \
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/* If there's anything left in U, the result is inexact. */ \
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_FP_FRAC_LOW_##wc (R) |= !_FP_FRAC_ZEROP_##wc (u); \
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} while (0)
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|
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#define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
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#define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
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#define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)
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