forked from KolibriOS/kolibrios
1847 lines
58 KiB
C
1847 lines
58 KiB
C
/* Software floating-point emulation. Common operations.
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Copyright (C) 1997-2014 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, see
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<http://www.gnu.org/licenses/>. */
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#define _FP_DECL(wc, X) \
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_FP_I_TYPE X##_c __attribute__ ((unused)); \
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_FP_I_TYPE X##_s __attribute__ ((unused)); \
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_FP_I_TYPE X##_e __attribute__ ((unused)); \
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_FP_FRAC_DECL_##wc (X)
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/* Test whether the qNaN bit denotes a signaling NaN. */
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#define _FP_FRAC_SNANP(fs, X) \
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((_FP_QNANNEGATEDP) \
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? (_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs) \
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: !(_FP_FRAC_HIGH_RAW_##fs (X) & _FP_QNANBIT_##fs))
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#define _FP_FRAC_SNANP_SEMIRAW(fs, X) \
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((_FP_QNANNEGATEDP) \
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? (_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs) \
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: !(_FP_FRAC_HIGH_##fs (X) & _FP_QNANBIT_SH_##fs))
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/* Finish truly 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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#define _FP_UNPACK_CANONICAL(fs, wc, X) \
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do \
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{ \
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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 if (FP_DENORM_ZERO) \
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{ \
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X##_c = FP_CLS_ZERO; \
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_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
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FP_SET_EXCEPTION (FP_EX_DENORM); \
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} \
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else \
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{ \
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/* A denormalized number. */ \
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_FP_I_TYPE _FP_UNPACK_CANONICAL_shift; \
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_FP_FRAC_CLZ_##wc (_FP_UNPACK_CANONICAL_shift, \
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X); \
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_FP_UNPACK_CANONICAL_shift -= _FP_FRACXBITS_##fs; \
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_FP_FRAC_SLL_##wc (X, (_FP_UNPACK_CANONICAL_shift \
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+ _FP_WORKBITS)); \
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X##_e -= (_FP_EXPBIAS_##fs - 1 \
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+ _FP_UNPACK_CANONICAL_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_SNANP (fs, X)) \
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FP_SET_EXCEPTION (FP_EX_INVALID \
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| FP_EX_INVALID_SNAN); \
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} \
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break; \
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} \
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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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/* Check whether a raw or semi-raw input value should be flushed to
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zero, and flush it to zero if so. */
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#define _FP_CHECK_FLUSH_ZERO(fs, wc, X) \
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do \
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{ \
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if (FP_DENORM_ZERO \
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&& X##_e == 0 \
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&& !_FP_FRAC_ZEROP_##wc (X)) \
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{ \
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_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
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FP_SET_EXCEPTION (FP_EX_DENORM); \
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} \
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} \
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while (0)
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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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{ \
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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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} \
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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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{ \
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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_SNANP_SEMIRAW (fs, X)) \
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FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
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} \
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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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{ \
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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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} \
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while (0)
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/* Make the fractional part a quiet NaN, preserving the payload
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if possible, otherwise make it the canonical quiet NaN and set
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the sign bit accordingly. */
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#define _FP_SETQNAN(fs, wc, X) \
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do \
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{ \
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if (_FP_QNANNEGATEDP) \
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{ \
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_FP_FRAC_HIGH_RAW_##fs (X) &= _FP_QNANBIT_##fs - 1; \
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if (_FP_FRAC_ZEROP_##wc (X)) \
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{ \
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X##_s = _FP_NANSIGN_##fs; \
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_FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
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} \
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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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while (0)
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#define _FP_SETQNAN_SEMIRAW(fs, wc, X) \
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do \
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{ \
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if (_FP_QNANNEGATEDP) \
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{ \
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_FP_FRAC_HIGH_##fs (X) &= _FP_QNANBIT_SH_##fs - 1; \
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if (_FP_FRAC_ZEROP_##wc (X)) \
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{ \
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X##_s = _FP_NANSIGN_##fs; \
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_FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
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_FP_FRAC_SLL_##wc (X, _FP_WORKBITS); \
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} \
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} \
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else \
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_FP_FRAC_HIGH_##fs (X) |= _FP_QNANBIT_SH_##fs; \
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} \
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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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{ \
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int _FP_PACK_SEMIRAW_is_tiny \
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= X##_e == 0 && !_FP_FRAC_ZEROP_##wc (X); \
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if (_FP_TININESS_AFTER_ROUNDING \
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&& _FP_PACK_SEMIRAW_is_tiny) \
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{ \
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FP_DECL_##fs (_FP_PACK_SEMIRAW_T); \
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_FP_FRAC_COPY_##wc (_FP_PACK_SEMIRAW_T, X); \
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_FP_PACK_SEMIRAW_T##_s = X##_s; \
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_FP_PACK_SEMIRAW_T##_e = X##_e; \
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_FP_FRAC_SLL_##wc (_FP_PACK_SEMIRAW_T, 1); \
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_FP_ROUND (wc, _FP_PACK_SEMIRAW_T); \
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if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_SEMIRAW_T)) \
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_FP_PACK_SEMIRAW_is_tiny = 0; \
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} \
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_FP_ROUND (wc, X); \
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if (_FP_PACK_SEMIRAW_is_tiny) \
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{ \
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if ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
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|| (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW)) \
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FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
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} \
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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 (X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
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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_SETQNAN (fs, wc, X); \
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} \
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} \
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while (0)
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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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#define _FP_PACK_CANONICAL(fs, wc, X) \
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do \
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{ \
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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) \
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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) \
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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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int _FP_PACK_CANONICAL_is_tiny = 1; \
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if (_FP_TININESS_AFTER_ROUNDING && X##_e == 0) \
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{ \
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FP_DECL_##fs (_FP_PACK_CANONICAL_T); \
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_FP_FRAC_COPY_##wc (_FP_PACK_CANONICAL_T, X); \
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_FP_PACK_CANONICAL_T##_s = X##_s; \
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_FP_PACK_CANONICAL_T##_e = X##_e; \
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_FP_ROUND (wc, _FP_PACK_CANONICAL_T); \
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if (_FP_FRAC_OVERP_##wc (fs, _FP_PACK_CANONICAL_T)) \
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_FP_PACK_CANONICAL_is_tiny = 0; \
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} \
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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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FP_SET_EXCEPTION (FP_EX_INEXACT); \
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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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if (_FP_PACK_CANONICAL_is_tiny \
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&& ((FP_CUR_EXCEPTIONS & FP_EX_INEXACT) \
|
|
|| (FP_TRAPPING_EXCEPTIONS \
|
|
& FP_EX_UNDERFLOW))) \
|
|
FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
|
|
} \
|
|
else \
|
|
{ \
|
|
/* Underflow to zero. */ \
|
|
X##_e = 0; \
|
|
if (!_FP_FRAC_ZEROP_##wc (X)) \
|
|
{ \
|
|
_FP_FRAC_SET_##wc (X, _FP_MINFRAC_##wc); \
|
|
_FP_ROUND (wc, X); \
|
|
_FP_FRAC_LOW_##wc (X) >>= (_FP_WORKBITS); \
|
|
} \
|
|
FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
|
|
} \
|
|
} \
|
|
break; \
|
|
\
|
|
case FP_CLS_ZERO: \
|
|
X##_e = 0; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
break; \
|
|
\
|
|
case FP_CLS_INF: \
|
|
X##_e = _FP_EXPMAX_##fs; \
|
|
_FP_FRAC_SET_##wc (X, _FP_ZEROFRAC_##wc); \
|
|
break; \
|
|
\
|
|
case FP_CLS_NAN: \
|
|
X##_e = _FP_EXPMAX_##fs; \
|
|
if (!_FP_KEEPNANFRACP) \
|
|
{ \
|
|
_FP_FRAC_SET_##wc (X, _FP_NANFRAC_##fs); \
|
|
X##_s = _FP_NANSIGN_##fs; \
|
|
} \
|
|
else \
|
|
_FP_SETQNAN (fs, wc, X); \
|
|
break; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* This one accepts raw argument and not cooked, returns
|
|
1 if X is a signaling NaN. */
|
|
#define _FP_ISSIGNAN(fs, wc, X) \
|
|
({ \
|
|
int _FP_ISSIGNAN_ret = 0; \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
if (!_FP_FRAC_ZEROP_##wc (X) \
|
|
&& _FP_FRAC_SNANP (fs, X)) \
|
|
_FP_ISSIGNAN_ret = 1; \
|
|
} \
|
|
_FP_ISSIGNAN_ret; \
|
|
})
|
|
|
|
|
|
|
|
|
|
|
|
/* Addition on semi-raw values. */
|
|
#define _FP_ADD_INTERNAL(fs, wc, R, X, Y, OP) \
|
|
do \
|
|
{ \
|
|
_FP_CHECK_FLUSH_ZERO (fs, wc, X); \
|
|
_FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
|
|
if (X##_s == Y##_s) \
|
|
{ \
|
|
/* Addition. */ \
|
|
R##_s = X##_s; \
|
|
int _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
|
|
if (_FP_ADD_INTERNAL_ediff > 0) \
|
|
{ \
|
|
R##_e = X##_e; \
|
|
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 add_done; \
|
|
} \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_ADD_INTERNAL_ediff--; \
|
|
if (_FP_ADD_INTERNAL_ediff == 0) \
|
|
{ \
|
|
_FP_FRAC_ADD_##wc (R, X, Y); \
|
|
goto add3; \
|
|
} \
|
|
if (X##_e == _FP_EXPMAX_##fs) \
|
|
{ \
|
|
_FP_CHECK_SIGNAN_SEMIRAW (fs, wc, X); \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
goto add_done; \
|
|
} \
|
|
goto add1; \
|
|
} \
|
|
} \
|
|
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 add_done; \
|
|
} \
|
|
\
|
|
/* Insert implicit MSB of Y. */ \
|
|
_FP_FRAC_HIGH_##fs (Y) |= _FP_IMPLBIT_SH_##fs; \
|
|
\
|
|
add1: \
|
|
/* Shift the mantissa of Y to the right \
|
|
_FP_ADD_INTERNAL_EDIFF steps; remember to account \
|
|
later for the implicit MSB of X. */ \
|
|
if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_ediff < 0) \
|
|
{ \
|
|
_FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_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); \
|
|
_FP_ADD_INTERNAL_ediff--; \
|
|
if (_FP_ADD_INTERNAL_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 \
|
|
_FP_ADD_INTERNAL_EDIFF steps; remember to account \
|
|
later for the implicit MSB of Y. */ \
|
|
if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_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 \
|
|
{ \
|
|
/* _FP_ADD_INTERNAL_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 _FP_ADD_INTERNAL_ediff = X##_e - Y##_e; \
|
|
if (_FP_ADD_INTERNAL_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); \
|
|
_FP_ADD_INTERNAL_ediff--; \
|
|
if (_FP_ADD_INTERNAL_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 \
|
|
_FP_ADD_INTERNAL_EDIFF steps; remember to account \
|
|
later for the implicit MSB of X. */ \
|
|
if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (Y, _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_ediff < 0) \
|
|
{ \
|
|
_FP_ADD_INTERNAL_ediff = -_FP_ADD_INTERNAL_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); \
|
|
_FP_ADD_INTERNAL_ediff--; \
|
|
if (_FP_ADD_INTERNAL_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 \
|
|
_FP_ADD_INTERNAL_EDIFF steps; remember to account \
|
|
later for the implicit MSB of Y. */ \
|
|
if (_FP_ADD_INTERNAL_ediff <= _FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SRS_##wc (X, _FP_ADD_INTERNAL_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 \
|
|
| FP_EX_INVALID_ISI); \
|
|
} \
|
|
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 _FP_ADD_INTERNAL_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 (_FP_ADD_INTERNAL_diff, R); \
|
|
_FP_ADD_INTERNAL_diff -= _FP_WFRACXBITS_##fs; \
|
|
_FP_FRAC_SLL_##wc (R, _FP_ADD_INTERNAL_diff); \
|
|
if (R##_e <= _FP_ADD_INTERNAL_diff) \
|
|
{ \
|
|
/* R is denormalized. */ \
|
|
_FP_ADD_INTERNAL_diff \
|
|
= _FP_ADD_INTERNAL_diff - R##_e + 1; \
|
|
_FP_FRAC_SRS_##wc (R, _FP_ADD_INTERNAL_diff, \
|
|
_FP_WFRACBITS_##fs); \
|
|
R##_e = 0; \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_e -= _FP_ADD_INTERNAL_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. The input value is raw. */
|
|
|
|
#define _FP_NEG(fs, wc, R, X) \
|
|
do \
|
|
{ \
|
|
_FP_FRAC_COPY_##wc (R, X); \
|
|
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; \
|
|
R##_e = X##_e + Y##_e + 1; \
|
|
switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
\
|
|
_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 | FP_EX_INVALID_IMZ); \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Fused multiply-add. The input values should be cooked. */
|
|
|
|
#define _FP_FMA(fs, wc, dwc, R, X, Y, Z) \
|
|
do \
|
|
{ \
|
|
FP_DECL_##fs (_FP_FMA_T); \
|
|
_FP_FMA_T##_s = X##_s ^ Y##_s; \
|
|
_FP_FMA_T##_e = X##_e + Y##_e + 1; \
|
|
switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
|
|
switch (Z##_c) \
|
|
{ \
|
|
case FP_CLS_INF: \
|
|
case FP_CLS_NAN: \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
break; \
|
|
\
|
|
case FP_CLS_ZERO: \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
R##_s = _FP_FMA_T##_s; \
|
|
R##_e = _FP_FMA_T##_e; \
|
|
\
|
|
_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_NORMAL:; \
|
|
_FP_FRAC_DECL_##dwc (_FP_FMA_TD); \
|
|
_FP_FRAC_DECL_##dwc (_FP_FMA_ZD); \
|
|
_FP_FRAC_DECL_##dwc (_FP_FMA_RD); \
|
|
_FP_MUL_MEAT_DW_##fs (_FP_FMA_TD, X, Y); \
|
|
R##_e = _FP_FMA_T##_e; \
|
|
int _FP_FMA_tsh \
|
|
= _FP_FRAC_HIGHBIT_DW_##dwc (fs, _FP_FMA_TD) == 0; \
|
|
_FP_FMA_T##_e -= _FP_FMA_tsh; \
|
|
int _FP_FMA_ediff = _FP_FMA_T##_e - Z##_e; \
|
|
if (_FP_FMA_ediff >= 0) \
|
|
{ \
|
|
int _FP_FMA_shift \
|
|
= _FP_WFRACBITS_##fs - _FP_FMA_tsh - _FP_FMA_ediff; \
|
|
if (_FP_FMA_shift <= -_FP_WFRACBITS_##fs) \
|
|
_FP_FRAC_SET_##dwc (_FP_FMA_ZD, _FP_MINFRAC_##dwc); \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
|
|
if (_FP_FMA_shift < 0) \
|
|
_FP_FRAC_SRS_##dwc (_FP_FMA_ZD, -_FP_FMA_shift, \
|
|
_FP_WFRACBITS_DW_##fs); \
|
|
else if (_FP_FMA_shift > 0) \
|
|
_FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_FMA_shift); \
|
|
} \
|
|
R##_s = _FP_FMA_T##_s; \
|
|
if (_FP_FMA_T##_s == Z##_s) \
|
|
_FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
|
|
_FP_FMA_ZD); \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_TD, \
|
|
_FP_FMA_ZD); \
|
|
if (_FP_FRAC_NEGP_##dwc (_FP_FMA_RD)) \
|
|
{ \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
|
|
_FP_FMA_TD); \
|
|
} \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_e = Z##_e; \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##dwc##_##wc (_FP_FMA_ZD, Z); \
|
|
_FP_FRAC_SLL_##dwc (_FP_FMA_ZD, _FP_WFRACBITS_##fs); \
|
|
int _FP_FMA_shift = -_FP_FMA_ediff - _FP_FMA_tsh; \
|
|
if (_FP_FMA_shift >= _FP_WFRACBITS_DW_##fs) \
|
|
_FP_FRAC_SET_##dwc (_FP_FMA_TD, _FP_MINFRAC_##dwc); \
|
|
else if (_FP_FMA_shift > 0) \
|
|
_FP_FRAC_SRS_##dwc (_FP_FMA_TD, _FP_FMA_shift, \
|
|
_FP_WFRACBITS_DW_##fs); \
|
|
if (Z##_s == _FP_FMA_T##_s) \
|
|
_FP_FRAC_ADD_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
|
|
_FP_FMA_TD); \
|
|
else \
|
|
_FP_FRAC_SUB_##dwc (_FP_FMA_RD, _FP_FMA_ZD, \
|
|
_FP_FMA_TD); \
|
|
} \
|
|
if (_FP_FRAC_ZEROP_##dwc (_FP_FMA_RD)) \
|
|
{ \
|
|
if (_FP_FMA_T##_s == Z##_s) \
|
|
R##_s = Z##_s; \
|
|
else \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
|
R##_c = FP_CLS_ZERO; \
|
|
} \
|
|
else \
|
|
{ \
|
|
int _FP_FMA_rlz; \
|
|
_FP_FRAC_CLZ_##dwc (_FP_FMA_rlz, _FP_FMA_RD); \
|
|
_FP_FMA_rlz -= _FP_WFRACXBITS_DW_##fs; \
|
|
R##_e -= _FP_FMA_rlz; \
|
|
int _FP_FMA_shift = _FP_WFRACBITS_##fs - _FP_FMA_rlz; \
|
|
if (_FP_FMA_shift > 0) \
|
|
_FP_FRAC_SRS_##dwc (_FP_FMA_RD, _FP_FMA_shift, \
|
|
_FP_WFRACBITS_DW_##fs); \
|
|
else if (_FP_FMA_shift < 0) \
|
|
_FP_FRAC_SLL_##dwc (_FP_FMA_RD, -_FP_FMA_shift); \
|
|
_FP_FRAC_COPY_##wc##_##dwc (R, _FP_FMA_RD); \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
} \
|
|
break; \
|
|
} \
|
|
goto done_fma; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
|
|
_FP_CHOOSENAN (fs, wc, _FP_FMA_T, 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): \
|
|
_FP_FMA_T##_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 (_FP_FMA_T, X); \
|
|
_FP_FMA_T##_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): \
|
|
_FP_FMA_T##_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 (_FP_FMA_T, Y); \
|
|
_FP_FMA_T##_c = Y##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
|
|
_FP_FMA_T##_s = _FP_NANSIGN_##fs; \
|
|
_FP_FMA_T##_c = FP_CLS_NAN; \
|
|
_FP_FRAC_SET_##wc (_FP_FMA_T, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_IMZ_FMA); \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
\
|
|
/* T = X * Y is zero, infinity or NaN. */ \
|
|
switch (_FP_CLS_COMBINE (_FP_FMA_T##_c, Z##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NAN, FP_CLS_NAN): \
|
|
_FP_CHOOSENAN (fs, wc, R, _FP_FMA_T, Z, '+'); \
|
|
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): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_ZERO): \
|
|
R##_s = _FP_FMA_T##_s; \
|
|
_FP_FRAC_COPY_##wc (R, _FP_FMA_T); \
|
|
R##_c = _FP_FMA_T##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NAN): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_NORMAL): \
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_INF): \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_INF, FP_CLS_INF): \
|
|
if (_FP_FMA_T##_s == Z##_s) \
|
|
{ \
|
|
R##_s = Z##_s; \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
} \
|
|
else \
|
|
{ \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
R##_c = FP_CLS_NAN; \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_ISI); \
|
|
} \
|
|
break; \
|
|
\
|
|
case _FP_CLS_COMBINE (FP_CLS_ZERO, FP_CLS_ZERO): \
|
|
if (_FP_FMA_T##_s == Z##_s) \
|
|
R##_s = Z##_s; \
|
|
else \
|
|
R##_s = (FP_ROUNDMODE == FP_RND_MINF); \
|
|
_FP_FRAC_COPY_##wc (R, Z); \
|
|
R##_c = Z##_c; \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
done_fma: ; \
|
|
} \
|
|
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; \
|
|
R##_e = X##_e - Y##_e; \
|
|
switch (_FP_CLS_COMBINE (X##_c, Y##_c)) \
|
|
{ \
|
|
case _FP_CLS_COMBINE (FP_CLS_NORMAL, FP_CLS_NORMAL): \
|
|
R##_c = FP_CLS_NORMAL; \
|
|
\
|
|
_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 \
|
|
| (X##_c == FP_CLS_INF \
|
|
? FP_EX_INVALID_IDI \
|
|
: FP_EX_INVALID_ZDZ)); \
|
|
break; \
|
|
\
|
|
default: \
|
|
abort (); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
|
|
/* Helper for comparisons. EX is 0 not to raise exceptions, 1 to
|
|
raise exceptions for signaling NaN operands, 2 to raise exceptions
|
|
for all NaN operands. Conditionals are organized to allow the
|
|
compiler to optimize away code based on the value of EX. */
|
|
|
|
#define _FP_CMP_CHECK_NAN(fs, wc, X, Y, ex) \
|
|
do \
|
|
{ \
|
|
/* The arguments are unordered, which may or may not result in \
|
|
an exception. */ \
|
|
if (ex) \
|
|
{ \
|
|
/* At least some cases of unordered arguments result in \
|
|
exceptions; check whether this is one. */ \
|
|
if (FP_EX_INVALID_SNAN || FP_EX_INVALID_VC) \
|
|
{ \
|
|
/* Check separately for each case of "invalid" \
|
|
exceptions. */ \
|
|
if ((ex) == 2) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_VC); \
|
|
if (_FP_ISSIGNAN (fs, wc, X) \
|
|
|| _FP_ISSIGNAN (fs, wc, Y)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SNAN); \
|
|
} \
|
|
/* Otherwise, we only need to check whether to raise an \
|
|
exception, not which case or cases it is. */ \
|
|
else if ((ex) == 2 \
|
|
|| _FP_ISSIGNAN (fs, wc, X) \
|
|
|| _FP_ISSIGNAN (fs, wc, Y)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID); \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
/* Main differential comparison routine. The inputs should be raw not
|
|
cooked. The return is -1, 0, 1 for normal values, UN
|
|
otherwise. */
|
|
|
|
#define _FP_CMP(fs, wc, ret, X, Y, un, ex) \
|
|
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); \
|
|
_FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
|
|
} \
|
|
else \
|
|
{ \
|
|
int _FP_CMP_is_zero_x; \
|
|
int _FP_CMP_is_zero_y; \
|
|
\
|
|
_FP_CHECK_FLUSH_ZERO (fs, wc, X); \
|
|
_FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
|
|
\
|
|
_FP_CMP_is_zero_x \
|
|
= (!X##_e && _FP_FRAC_ZEROP_##wc (X)) ? 1 : 0; \
|
|
_FP_CMP_is_zero_y \
|
|
= (!Y##_e && _FP_FRAC_ZEROP_##wc (Y)) ? 1 : 0; \
|
|
\
|
|
if (_FP_CMP_is_zero_x && _FP_CMP_is_zero_y) \
|
|
(ret) = 0; \
|
|
else if (_FP_CMP_is_zero_x) \
|
|
(ret) = Y##_s ? 1 : -1; \
|
|
else if (_FP_CMP_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, ex) \
|
|
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; \
|
|
_FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_CHECK_FLUSH_ZERO (fs, wc, X); \
|
|
_FP_CHECK_FLUSH_ZERO (fs, wc, Y); \
|
|
\
|
|
(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, ex) \
|
|
do \
|
|
{ \
|
|
(ret) = ((X##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (X)) \
|
|
|| (Y##_e == _FP_EXPMAX_##fs && !_FP_FRAC_ZEROP_##wc (Y))); \
|
|
if (ret) \
|
|
_FP_CMP_CHECK_NAN (fs, wc, X, Y, (ex)); \
|
|
} \
|
|
while (0)
|
|
|
|
/* Main square root routine. The input value should be cooked. */
|
|
|
|
#define _FP_SQRT(fs, wc, R, X) \
|
|
do \
|
|
{ \
|
|
_FP_FRAC_DECL_##wc (_FP_SQRT_T); \
|
|
_FP_FRAC_DECL_##wc (_FP_SQRT_S); \
|
|
_FP_W_TYPE _FP_SQRT_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 | FP_EX_INVALID_SQRT); \
|
|
} \
|
|
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; /* NAN */ \
|
|
R##_s = _FP_NANSIGN_##fs; \
|
|
_FP_FRAC_SET_##wc (R, _FP_NANFRAC_##fs); \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_SQRT); \
|
|
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 (_FP_SQRT_S, _FP_ZEROFRAC_##wc); \
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
|
_FP_SQRT_q = _FP_OVERFLOW_##fs >> 1; \
|
|
_FP_SQRT_MEAT_##wc (R, _FP_SQRT_S, _FP_SQRT_T, X, \
|
|
_FP_SQRT_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.
|
|
2: the number is required to be -(2^(rsize-1))..(2^(rsize-1))-1, if not,
|
|
NV is set plus the result is reduced modulo 2^rsize.
|
|
-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)) \
|
|
{ \
|
|
if (!FP_DENORM_ZERO) \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
} \
|
|
} \
|
|
else \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
} \
|
|
else if ((rsigned) == 2 \
|
|
&& (X##_e \
|
|
>= ((_FP_EXPMAX_##fs \
|
|
< _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1) \
|
|
? _FP_EXPMAX_##fs \
|
|
: _FP_EXPBIAS_##fs + _FP_FRACBITS_##fs + (rsize) - 1))) \
|
|
{ \
|
|
/* Overflow resulting in 0. */ \
|
|
(r) = 0; \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID \
|
|
| FP_EX_INVALID_CVI \
|
|
| ((FP_EX_INVALID_SNAN \
|
|
&& _FP_ISSIGNAN (fs, wc, X)) \
|
|
? FP_EX_INVALID_SNAN \
|
|
: 0)); \
|
|
} \
|
|
else if ((rsigned) != 2 \
|
|
&& (X##_e >= (_FP_EXPMAX_##fs < _FP_EXPBIAS_##fs + (rsize) \
|
|
? _FP_EXPMAX_##fs \
|
|
: (_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 (_FP_EXPBIAS_##fs + (rsize) - 1 < _FP_EXPMAX_##fs \
|
|
&& (rsigned) \
|
|
&& X##_s \
|
|
&& X##_e == _FP_EXPBIAS_##fs + (rsize) - 1) \
|
|
{ \
|
|
/* Possibly converting to most negative integer; check the \
|
|
mantissa. */ \
|
|
int _FP_TO_INT_inexact = 0; \
|
|
(void) ((_FP_FRACBITS_##fs > (rsize)) \
|
|
? ({ \
|
|
_FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
|
|
_FP_FRACBITS_##fs - (rsize), \
|
|
_FP_FRACBITS_##fs); \
|
|
0; \
|
|
}) \
|
|
: 0); \
|
|
if (!_FP_FRAC_ZEROP_##wc (X)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
|
|
else if (_FP_TO_INT_inexact) \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
} \
|
|
else \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID \
|
|
| FP_EX_INVALID_CVI \
|
|
| ((FP_EX_INVALID_SNAN \
|
|
&& _FP_ISSIGNAN (fs, wc, X)) \
|
|
? FP_EX_INVALID_SNAN \
|
|
: 0)); \
|
|
} \
|
|
else \
|
|
{ \
|
|
int _FP_TO_INT_inexact = 0; \
|
|
_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 \
|
|
{ \
|
|
_FP_FRAC_SRST_##wc (X, _FP_TO_INT_inexact, \
|
|
(_FP_FRACBITS_##fs + _FP_EXPBIAS_##fs - 1 \
|
|
- X##_e), \
|
|
_FP_FRACBITS_##fs); \
|
|
_FP_FRAC_ASSEMBLE_##wc ((r), X, (rsize)); \
|
|
} \
|
|
if ((rsigned) && X##_s) \
|
|
(r) = -(r); \
|
|
if ((rsigned) == 2 && X##_e >= _FP_EXPBIAS_##fs + (rsize) - 1) \
|
|
{ \
|
|
/* Overflow or converting to the most negative integer. */ \
|
|
if (X##_e > _FP_EXPBIAS_##fs + (rsize) - 1 \
|
|
|| !X##_s \
|
|
|| (r) != (((typeof (r)) 1) << ((rsize) - 1))) \
|
|
{ \
|
|
_FP_TO_INT_inexact = 0; \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID | FP_EX_INVALID_CVI); \
|
|
} \
|
|
} \
|
|
if (_FP_TO_INT_inexact) \
|
|
FP_SET_EXCEPTION (FP_EX_INEXACT); \
|
|
} \
|
|
} \
|
|
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 _FP_FROM_INT_ur; \
|
|
\
|
|
if ((X##_s = ((r) < 0))) \
|
|
(r) = -(rtype) (r); \
|
|
\
|
|
_FP_FROM_INT_ur = (rtype) (r); \
|
|
(void) (((rsize) <= _FP_W_TYPE_SIZE) \
|
|
? ({ \
|
|
int _FP_FROM_INT_lz; \
|
|
__FP_CLZ (_FP_FROM_INT_lz, \
|
|
(_FP_W_TYPE) _FP_FROM_INT_ur); \
|
|
X##_e = (_FP_EXPBIAS_##fs + _FP_W_TYPE_SIZE - 1 \
|
|
- _FP_FROM_INT_lz); \
|
|
}) \
|
|
: (((rsize) <= 2 * _FP_W_TYPE_SIZE) \
|
|
? ({ \
|
|
int _FP_FROM_INT_lz; \
|
|
__FP_CLZ_2 (_FP_FROM_INT_lz, \
|
|
(_FP_W_TYPE) (_FP_FROM_INT_ur \
|
|
>> _FP_W_TYPE_SIZE), \
|
|
(_FP_W_TYPE) _FP_FROM_INT_ur); \
|
|
X##_e = (_FP_EXPBIAS_##fs + 2 * _FP_W_TYPE_SIZE - 1 \
|
|
- _FP_FROM_INT_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, _FP_FROM_INT_ur, (rsize)); \
|
|
if (_FP_EXPBIAS_##fs + _FP_FRACBITS_##fs - 1 - X##_e > 0) \
|
|
_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) \
|
|
_FP_FROM_INT_ur \
|
|
= ((_FP_FROM_INT_ur >> (X##_e - _FP_EXPBIAS_##fs \
|
|
- _FP_WFRACBITS_##fs + 1)) \
|
|
| ((_FP_FROM_INT_ur \
|
|
<< ((rsize) - (X##_e - _FP_EXPBIAS_##fs \
|
|
- _FP_WFRACBITS_##fs + 1))) \
|
|
!= 0)); \
|
|
_FP_FRAC_DISASSEMBLE_##wc (X, _FP_FROM_INT_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 \
|
|
&& _FP_EXPBIAS_##dfs != _FP_EXPBIAS_##sfs)) \
|
|
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) \
|
|
{ \
|
|
_FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
|
|
if (_FP_FRAC_ZEROP_##swc (S)) \
|
|
D##_e = 0; \
|
|
else if (_FP_EXPBIAS_##dfs \
|
|
< _FP_EXPBIAS_##sfs + _FP_FRACBITS_##sfs - 1) \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
|
|
- _FP_FRACBITS_##sfs)); \
|
|
D##_e = 0; \
|
|
if (FP_TRAPPING_EXCEPTIONS & FP_EX_UNDERFLOW) \
|
|
FP_SET_EXCEPTION (FP_EX_UNDERFLOW); \
|
|
} \
|
|
else \
|
|
{ \
|
|
int FP_EXTEND_lz; \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
_FP_FRAC_CLZ_##swc (FP_EXTEND_lz, S); \
|
|
_FP_FRAC_SLL_##dwc (D, \
|
|
FP_EXTEND_lz + _FP_FRACBITS_##dfs \
|
|
- _FP_FRACTBITS_##sfs); \
|
|
D##_e = (_FP_EXPBIAS_##dfs - _FP_EXPBIAS_##sfs + 1 \
|
|
+ _FP_FRACXBITS_##sfs - FP_EXTEND_lz); \
|
|
} \
|
|
} \
|
|
else \
|
|
{ \
|
|
D##_e = _FP_EXPMAX_##dfs; \
|
|
if (!_FP_FRAC_ZEROP_##swc (S)) \
|
|
{ \
|
|
if (_FP_FRAC_SNANP (sfs, S)) \
|
|
FP_SET_EXCEPTION (FP_EX_INVALID \
|
|
| FP_EX_INVALID_SNAN); \
|
|
_FP_FRAC_SLL_##dwc (D, (_FP_FRACBITS_##dfs \
|
|
- _FP_FRACBITS_##sfs)); \
|
|
_FP_SETQNAN (dfs, dwc, D); \
|
|
} \
|
|
} \
|
|
} \
|
|
} \
|
|
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 \
|
|
&& _FP_EXPBIAS_##sfs != _FP_EXPBIAS_##dfs)) \
|
|
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); \
|
|
_FP_FRAC_LOW_##swc (S) |= 1; \
|
|
} \
|
|
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) \
|
|
{ \
|
|
_FP_CHECK_FLUSH_ZERO (sfs, swc, S); \
|
|
D##_e = 0; \
|
|
if (_FP_FRAC_ZEROP_##swc (S)) \
|
|
_FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
|
|
else \
|
|
{ \
|
|
FP_SET_EXCEPTION (FP_EX_DENORM); \
|
|
if (_FP_EXPBIAS_##sfs \
|
|
< _FP_EXPBIAS_##dfs + _FP_FRACBITS_##dfs - 1) \
|
|
{ \
|
|
_FP_FRAC_SRS_##swc (S, (_FP_WFRACBITS_##sfs \
|
|
- _FP_WFRACBITS_##dfs), \
|
|
_FP_WFRACBITS_##sfs); \
|
|
_FP_FRAC_COPY_##dwc##_##swc (D, S); \
|
|
} \
|
|
else \
|
|
{ \
|
|
_FP_FRAC_SET_##dwc (D, _FP_ZEROFRAC_##dwc); \
|
|
_FP_FRAC_LOW_##dwc (D) |= 1; \
|
|
} \
|
|
} \
|
|
} \
|
|
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); \
|
|
/* Semi-raw NaN must have all workbits cleared. */ \
|
|
_FP_FRAC_LOW_##dwc (D) \
|
|
&= ~(_FP_W_TYPE) ((1 << _FP_WORKBITS) - 1); \
|
|
_FP_SETQNAN_SEMIRAW (dfs, dwc, D); \
|
|
} \
|
|
} \
|
|
} \
|
|
} \
|
|
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 _FP_DIV_MEAT_N_loop_count = _FP_WFRACBITS_##fs; \
|
|
_FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_u); \
|
|
_FP_FRAC_DECL_##wc (_FP_DIV_MEAT_N_loop_v); \
|
|
_FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_u, X); \
|
|
_FP_FRAC_COPY_##wc (_FP_DIV_MEAT_N_loop_v, Y); \
|
|
_FP_FRAC_SET_##wc (R, _FP_ZEROFRAC_##wc); \
|
|
/* Normalize _FP_DIV_MEAT_N_LOOP_U and _FP_DIV_MEAT_N_LOOP_V. */ \
|
|
_FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, _FP_WFRACXBITS_##fs); \
|
|
_FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_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 (_FP_DIV_MEAT_N_loop_u, _FP_DIV_MEAT_N_loop_v)) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
|
|
_FP_DIV_MEAT_N_loop_u, \
|
|
_FP_DIV_MEAT_N_loop_v); \
|
|
_FP_FRAC_LOW_##wc (R) |= 1; \
|
|
_FP_DIV_MEAT_N_loop_count--; \
|
|
} \
|
|
else \
|
|
R##_e--; \
|
|
/* Subsequent rounds. */ \
|
|
do \
|
|
{ \
|
|
int _FP_DIV_MEAT_N_loop_msb \
|
|
= (_FP_WS_TYPE) _FP_FRAC_HIGH_##wc (_FP_DIV_MEAT_N_loop_u) < 0; \
|
|
_FP_FRAC_SLL_##wc (_FP_DIV_MEAT_N_loop_u, 1); \
|
|
_FP_FRAC_SLL_##wc (R, 1); \
|
|
if (_FP_DIV_MEAT_N_loop_msb \
|
|
|| _FP_FRAC_GE_1 (_FP_DIV_MEAT_N_loop_u, \
|
|
_FP_DIV_MEAT_N_loop_v)) \
|
|
{ \
|
|
_FP_FRAC_SUB_##wc (_FP_DIV_MEAT_N_loop_u, \
|
|
_FP_DIV_MEAT_N_loop_u, \
|
|
_FP_DIV_MEAT_N_loop_v); \
|
|
_FP_FRAC_LOW_##wc (R) |= 1; \
|
|
} \
|
|
} \
|
|
while (--_FP_DIV_MEAT_N_loop_count > 0); \
|
|
/* If there's anything left in _FP_DIV_MEAT_N_LOOP_U, the result \
|
|
is inexact. */ \
|
|
_FP_FRAC_LOW_##wc (R) \
|
|
|= !_FP_FRAC_ZEROP_##wc (_FP_DIV_MEAT_N_loop_u); \
|
|
} \
|
|
while (0)
|
|
|
|
#define _FP_DIV_MEAT_1_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 1, R, X, Y)
|
|
#define _FP_DIV_MEAT_2_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 2, R, X, Y)
|
|
#define _FP_DIV_MEAT_4_loop(fs, R, X, Y) _FP_DIV_MEAT_N_loop (fs, 4, R, X, Y)
|