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518 lines
14 KiB
C
518 lines
14 KiB
C
/* Software floating-point emulation.
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Definitions for IEEE Extended Precision.
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Copyright (C) 1999-2016 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by Jakub Jelinek (jj@ultra.linux.cz).
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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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#ifndef SOFT_FP_EXTENDED_H
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#define SOFT_FP_EXTENDED_H 1
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#if _FP_W_TYPE_SIZE < 32
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# error "Here's a nickel, kid. Go buy yourself a real computer."
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#endif
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#if _FP_W_TYPE_SIZE < 64
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# define _FP_FRACTBITS_E (4*_FP_W_TYPE_SIZE)
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# define _FP_FRACTBITS_DW_E (8*_FP_W_TYPE_SIZE)
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#else
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# define _FP_FRACTBITS_E (2*_FP_W_TYPE_SIZE)
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# define _FP_FRACTBITS_DW_E (4*_FP_W_TYPE_SIZE)
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#endif
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#define _FP_FRACBITS_E 64
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#define _FP_FRACXBITS_E (_FP_FRACTBITS_E - _FP_FRACBITS_E)
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#define _FP_WFRACBITS_E (_FP_WORKBITS + _FP_FRACBITS_E)
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#define _FP_WFRACXBITS_E (_FP_FRACTBITS_E - _FP_WFRACBITS_E)
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#define _FP_EXPBITS_E 15
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#define _FP_EXPBIAS_E 16383
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#define _FP_EXPMAX_E 32767
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#define _FP_QNANBIT_E \
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((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-2) % _FP_W_TYPE_SIZE)
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#define _FP_QNANBIT_SH_E \
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((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-2+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
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#define _FP_IMPLBIT_E \
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((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-1) % _FP_W_TYPE_SIZE)
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#define _FP_IMPLBIT_SH_E \
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((_FP_W_TYPE) 1 << (_FP_FRACBITS_E-1+_FP_WORKBITS) % _FP_W_TYPE_SIZE)
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#define _FP_OVERFLOW_E \
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((_FP_W_TYPE) 1 << (_FP_WFRACBITS_E % _FP_W_TYPE_SIZE))
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#define _FP_WFRACBITS_DW_E (2 * _FP_WFRACBITS_E)
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#define _FP_WFRACXBITS_DW_E (_FP_FRACTBITS_DW_E - _FP_WFRACBITS_DW_E)
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#define _FP_HIGHBIT_DW_E \
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((_FP_W_TYPE) 1 << (_FP_WFRACBITS_DW_E - 1) % _FP_W_TYPE_SIZE)
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typedef float XFtype __attribute__ ((mode (XF)));
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#if _FP_W_TYPE_SIZE < 64
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union _FP_UNION_E
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{
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XFtype flt;
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struct _FP_STRUCT_LAYOUT
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{
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# if __BYTE_ORDER == __BIG_ENDIAN
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unsigned long pad1 : _FP_W_TYPE_SIZE;
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unsigned long pad2 : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
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unsigned long sign : 1;
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unsigned long exp : _FP_EXPBITS_E;
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unsigned long frac1 : _FP_W_TYPE_SIZE;
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unsigned long frac0 : _FP_W_TYPE_SIZE;
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# else
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unsigned long frac0 : _FP_W_TYPE_SIZE;
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unsigned long frac1 : _FP_W_TYPE_SIZE;
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unsigned exp : _FP_EXPBITS_E;
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unsigned sign : 1;
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# endif /* not bigendian */
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} bits __attribute__ ((packed));
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};
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# define FP_DECL_E(X) _FP_DECL (4, X)
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# define FP_UNPACK_RAW_E(X, val) \
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do \
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{ \
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union _FP_UNION_E FP_UNPACK_RAW_E_flo; \
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FP_UNPACK_RAW_E_flo.flt = (val); \
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\
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X##_f[2] = 0; \
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X##_f[3] = 0; \
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X##_f[0] = FP_UNPACK_RAW_E_flo.bits.frac0; \
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X##_f[1] = FP_UNPACK_RAW_E_flo.bits.frac1; \
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X##_f[1] &= ~_FP_IMPLBIT_E; \
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X##_e = FP_UNPACK_RAW_E_flo.bits.exp; \
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X##_s = FP_UNPACK_RAW_E_flo.bits.sign; \
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} \
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while (0)
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# define FP_UNPACK_RAW_EP(X, val) \
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do \
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{ \
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union _FP_UNION_E *FP_UNPACK_RAW_EP_flo \
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= (union _FP_UNION_E *) (val); \
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\
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X##_f[2] = 0; \
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X##_f[3] = 0; \
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X##_f[0] = FP_UNPACK_RAW_EP_flo->bits.frac0; \
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X##_f[1] = FP_UNPACK_RAW_EP_flo->bits.frac1; \
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X##_f[1] &= ~_FP_IMPLBIT_E; \
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X##_e = FP_UNPACK_RAW_EP_flo->bits.exp; \
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X##_s = FP_UNPACK_RAW_EP_flo->bits.sign; \
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} \
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while (0)
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# define FP_PACK_RAW_E(val, X) \
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do \
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{ \
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union _FP_UNION_E FP_PACK_RAW_E_flo; \
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\
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if (X##_e) \
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X##_f[1] |= _FP_IMPLBIT_E; \
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else \
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X##_f[1] &= ~(_FP_IMPLBIT_E); \
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FP_PACK_RAW_E_flo.bits.frac0 = X##_f[0]; \
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FP_PACK_RAW_E_flo.bits.frac1 = X##_f[1]; \
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FP_PACK_RAW_E_flo.bits.exp = X##_e; \
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FP_PACK_RAW_E_flo.bits.sign = X##_s; \
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\
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(val) = FP_PACK_RAW_E_flo.flt; \
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} \
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while (0)
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# define FP_PACK_RAW_EP(val, X) \
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do \
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{ \
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if (!FP_INHIBIT_RESULTS) \
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{ \
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union _FP_UNION_E *FP_PACK_RAW_EP_flo \
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= (union _FP_UNION_E *) (val); \
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\
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if (X##_e) \
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X##_f[1] |= _FP_IMPLBIT_E; \
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else \
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X##_f[1] &= ~(_FP_IMPLBIT_E); \
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FP_PACK_RAW_EP_flo->bits.frac0 = X##_f[0]; \
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FP_PACK_RAW_EP_flo->bits.frac1 = X##_f[1]; \
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FP_PACK_RAW_EP_flo->bits.exp = X##_e; \
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FP_PACK_RAW_EP_flo->bits.sign = X##_s; \
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} \
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} \
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while (0)
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# define FP_UNPACK_E(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_E (X, (val)); \
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_FP_UNPACK_CANONICAL (E, 4, X); \
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} \
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while (0)
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# define FP_UNPACK_EP(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_EP (X, (val)); \
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_FP_UNPACK_CANONICAL (E, 4, X); \
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} \
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while (0)
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# define FP_UNPACK_SEMIRAW_E(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_E (X, (val)); \
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_FP_UNPACK_SEMIRAW (E, 4, X); \
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} \
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while (0)
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# define FP_UNPACK_SEMIRAW_EP(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_EP (X, (val)); \
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_FP_UNPACK_SEMIRAW (E, 4, X); \
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} \
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while (0)
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# define FP_PACK_E(val, X) \
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do \
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{ \
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_FP_PACK_CANONICAL (E, 4, X); \
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FP_PACK_RAW_E ((val), X); \
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} \
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while (0)
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# define FP_PACK_EP(val, X) \
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do \
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{ \
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_FP_PACK_CANONICAL (E, 4, X); \
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FP_PACK_RAW_EP ((val), X); \
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} \
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while (0)
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# define FP_PACK_SEMIRAW_E(val, X) \
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do \
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{ \
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_FP_PACK_SEMIRAW (E, 4, X); \
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FP_PACK_RAW_E ((val), X); \
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} \
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while (0)
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# define FP_PACK_SEMIRAW_EP(val, X) \
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do \
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{ \
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_FP_PACK_SEMIRAW (E, 4, X); \
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FP_PACK_RAW_EP ((val), X); \
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} \
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while (0)
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# define FP_ISSIGNAN_E(X) _FP_ISSIGNAN (E, 4, X)
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# define FP_NEG_E(R, X) _FP_NEG (E, 4, R, X)
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# define FP_ADD_E(R, X, Y) _FP_ADD (E, 4, R, X, Y)
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# define FP_SUB_E(R, X, Y) _FP_SUB (E, 4, R, X, Y)
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# define FP_MUL_E(R, X, Y) _FP_MUL (E, 4, R, X, Y)
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# define FP_DIV_E(R, X, Y) _FP_DIV (E, 4, R, X, Y)
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# define FP_SQRT_E(R, X) _FP_SQRT (E, 4, R, X)
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# define FP_FMA_E(R, X, Y, Z) _FP_FMA (E, 4, 8, R, X, Y, Z)
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/* Square root algorithms:
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We have just one right now, maybe Newton approximation
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should be added for those machines where division is fast.
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This has special _E version because standard _4 square
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root would not work (it has to start normally with the
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second word and not the first), but as we have to do it
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anyway, we optimize it by doing most of the calculations
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in two UWtype registers instead of four. */
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# define _FP_SQRT_MEAT_E(R, S, T, X, q) \
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do \
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{ \
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(q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
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_FP_FRAC_SRL_4 (X, (_FP_WORKBITS)); \
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while (q) \
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{ \
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T##_f[1] = S##_f[1] + (q); \
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if (T##_f[1] <= X##_f[1]) \
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{ \
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S##_f[1] = T##_f[1] + (q); \
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X##_f[1] -= T##_f[1]; \
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R##_f[1] += (q); \
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} \
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_FP_FRAC_SLL_2 (X, 1); \
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(q) >>= 1; \
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} \
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(q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
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while (q) \
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{ \
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T##_f[0] = S##_f[0] + (q); \
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T##_f[1] = S##_f[1]; \
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if (T##_f[1] < X##_f[1] \
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|| (T##_f[1] == X##_f[1] \
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&& T##_f[0] <= X##_f[0])) \
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{ \
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S##_f[0] = T##_f[0] + (q); \
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S##_f[1] += (T##_f[0] > S##_f[0]); \
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_FP_FRAC_DEC_2 (X, T); \
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R##_f[0] += (q); \
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} \
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_FP_FRAC_SLL_2 (X, 1); \
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(q) >>= 1; \
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} \
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_FP_FRAC_SLL_4 (R, (_FP_WORKBITS)); \
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if (X##_f[0] | X##_f[1]) \
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{ \
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if (S##_f[1] < X##_f[1] \
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|| (S##_f[1] == X##_f[1] \
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&& S##_f[0] < X##_f[0])) \
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R##_f[0] |= _FP_WORK_ROUND; \
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R##_f[0] |= _FP_WORK_STICKY; \
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} \
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} \
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while (0)
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# define FP_CMP_E(r, X, Y, un, ex) _FP_CMP (E, 4, (r), X, Y, (un), (ex))
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# define FP_CMP_EQ_E(r, X, Y, ex) _FP_CMP_EQ (E, 4, (r), X, Y, (ex))
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# define FP_CMP_UNORD_E(r, X, Y, ex) _FP_CMP_UNORD (E, 4, (r), X, Y, (ex))
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# define FP_TO_INT_E(r, X, rsz, rsg) _FP_TO_INT (E, 4, (r), X, (rsz), (rsg))
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# define FP_TO_INT_ROUND_E(r, X, rsz, rsg) \
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_FP_TO_INT_ROUND (E, 4, (r), X, (rsz), (rsg))
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# define FP_FROM_INT_E(X, r, rs, rt) _FP_FROM_INT (E, 4, X, (r), (rs), rt)
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# define _FP_FRAC_HIGH_E(X) (X##_f[2])
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# define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1])
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# define _FP_FRAC_HIGH_DW_E(X) (X##_f[4])
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#else /* not _FP_W_TYPE_SIZE < 64 */
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union _FP_UNION_E
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{
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XFtype flt;
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struct _FP_STRUCT_LAYOUT
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{
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# if __BYTE_ORDER == __BIG_ENDIAN
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_FP_W_TYPE pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
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unsigned sign : 1;
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unsigned exp : _FP_EXPBITS_E;
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_FP_W_TYPE frac : _FP_W_TYPE_SIZE;
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# else
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_FP_W_TYPE frac : _FP_W_TYPE_SIZE;
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unsigned exp : _FP_EXPBITS_E;
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unsigned sign : 1;
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# endif
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} bits;
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};
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# define FP_DECL_E(X) _FP_DECL (2, X)
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# define FP_UNPACK_RAW_E(X, val) \
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do \
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{ \
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union _FP_UNION_E FP_UNPACK_RAW_E_flo; \
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FP_UNPACK_RAW_E_flo.flt = (val); \
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\
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X##_f0 = FP_UNPACK_RAW_E_flo.bits.frac; \
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X##_f0 &= ~_FP_IMPLBIT_E; \
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X##_f1 = 0; \
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X##_e = FP_UNPACK_RAW_E_flo.bits.exp; \
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X##_s = FP_UNPACK_RAW_E_flo.bits.sign; \
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} \
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while (0)
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# define FP_UNPACK_RAW_EP(X, val) \
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do \
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{ \
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union _FP_UNION_E *FP_UNPACK_RAW_EP_flo \
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= (union _FP_UNION_E *) (val); \
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\
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X##_f0 = FP_UNPACK_RAW_EP_flo->bits.frac; \
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X##_f0 &= ~_FP_IMPLBIT_E; \
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X##_f1 = 0; \
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X##_e = FP_UNPACK_RAW_EP_flo->bits.exp; \
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X##_s = FP_UNPACK_RAW_EP_flo->bits.sign; \
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} \
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while (0)
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# define FP_PACK_RAW_E(val, X) \
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do \
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{ \
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union _FP_UNION_E FP_PACK_RAW_E_flo; \
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\
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if (X##_e) \
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X##_f0 |= _FP_IMPLBIT_E; \
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else \
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X##_f0 &= ~(_FP_IMPLBIT_E); \
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FP_PACK_RAW_E_flo.bits.frac = X##_f0; \
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FP_PACK_RAW_E_flo.bits.exp = X##_e; \
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FP_PACK_RAW_E_flo.bits.sign = X##_s; \
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\
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(val) = FP_PACK_RAW_E_flo.flt; \
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} \
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while (0)
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# define FP_PACK_RAW_EP(fs, val, X) \
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do \
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{ \
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if (!FP_INHIBIT_RESULTS) \
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{ \
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union _FP_UNION_E *FP_PACK_RAW_EP_flo \
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= (union _FP_UNION_E *) (val); \
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\
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if (X##_e) \
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X##_f0 |= _FP_IMPLBIT_E; \
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else \
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X##_f0 &= ~(_FP_IMPLBIT_E); \
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FP_PACK_RAW_EP_flo->bits.frac = X##_f0; \
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FP_PACK_RAW_EP_flo->bits.exp = X##_e; \
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FP_PACK_RAW_EP_flo->bits.sign = X##_s; \
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} \
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} \
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while (0)
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# define FP_UNPACK_E(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_E (X, (val)); \
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_FP_UNPACK_CANONICAL (E, 2, X); \
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} \
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while (0)
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# define FP_UNPACK_EP(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_EP (X, (val)); \
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_FP_UNPACK_CANONICAL (E, 2, X); \
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} \
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while (0)
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# define FP_UNPACK_SEMIRAW_E(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_E (X, (val)); \
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_FP_UNPACK_SEMIRAW (E, 2, X); \
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} \
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while (0)
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# define FP_UNPACK_SEMIRAW_EP(X, val) \
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do \
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{ \
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FP_UNPACK_RAW_EP (X, (val)); \
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_FP_UNPACK_SEMIRAW (E, 2, X); \
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} \
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while (0)
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# define FP_PACK_E(val, X) \
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do \
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{ \
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_FP_PACK_CANONICAL (E, 2, X); \
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FP_PACK_RAW_E ((val), X); \
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} \
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while (0)
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# define FP_PACK_EP(val, X) \
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do \
|
|
{ \
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|
_FP_PACK_CANONICAL (E, 2, X); \
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|
FP_PACK_RAW_EP ((val), X); \
|
|
} \
|
|
while (0)
|
|
|
|
# define FP_PACK_SEMIRAW_E(val, X) \
|
|
do \
|
|
{ \
|
|
_FP_PACK_SEMIRAW (E, 2, X); \
|
|
FP_PACK_RAW_E ((val), X); \
|
|
} \
|
|
while (0)
|
|
|
|
# define FP_PACK_SEMIRAW_EP(val, X) \
|
|
do \
|
|
{ \
|
|
_FP_PACK_SEMIRAW (E, 2, X); \
|
|
FP_PACK_RAW_EP ((val), X); \
|
|
} \
|
|
while (0)
|
|
|
|
# define FP_ISSIGNAN_E(X) _FP_ISSIGNAN (E, 2, X)
|
|
# define FP_NEG_E(R, X) _FP_NEG (E, 2, R, X)
|
|
# define FP_ADD_E(R, X, Y) _FP_ADD (E, 2, R, X, Y)
|
|
# define FP_SUB_E(R, X, Y) _FP_SUB (E, 2, R, X, Y)
|
|
# define FP_MUL_E(R, X, Y) _FP_MUL (E, 2, R, X, Y)
|
|
# define FP_DIV_E(R, X, Y) _FP_DIV (E, 2, R, X, Y)
|
|
# define FP_SQRT_E(R, X) _FP_SQRT (E, 2, R, X)
|
|
# define FP_FMA_E(R, X, Y, Z) _FP_FMA (E, 2, 4, R, X, Y, Z)
|
|
|
|
/* Square root algorithms:
|
|
We have just one right now, maybe Newton approximation
|
|
should be added for those machines where division is fast.
|
|
We optimize it by doing most of the calculations
|
|
in one UWtype registers instead of two, although we don't
|
|
have to. */
|
|
# define _FP_SQRT_MEAT_E(R, S, T, X, q) \
|
|
do \
|
|
{ \
|
|
(q) = (_FP_W_TYPE) 1 << (_FP_W_TYPE_SIZE - 1); \
|
|
_FP_FRAC_SRL_2 (X, (_FP_WORKBITS)); \
|
|
while (q) \
|
|
{ \
|
|
T##_f0 = S##_f0 + (q); \
|
|
if (T##_f0 <= X##_f0) \
|
|
{ \
|
|
S##_f0 = T##_f0 + (q); \
|
|
X##_f0 -= T##_f0; \
|
|
R##_f0 += (q); \
|
|
} \
|
|
_FP_FRAC_SLL_1 (X, 1); \
|
|
(q) >>= 1; \
|
|
} \
|
|
_FP_FRAC_SLL_2 (R, (_FP_WORKBITS)); \
|
|
if (X##_f0) \
|
|
{ \
|
|
if (S##_f0 < X##_f0) \
|
|
R##_f0 |= _FP_WORK_ROUND; \
|
|
R##_f0 |= _FP_WORK_STICKY; \
|
|
} \
|
|
} \
|
|
while (0)
|
|
|
|
# define FP_CMP_E(r, X, Y, un, ex) _FP_CMP (E, 2, (r), X, Y, (un), (ex))
|
|
# define FP_CMP_EQ_E(r, X, Y, ex) _FP_CMP_EQ (E, 2, (r), X, Y, (ex))
|
|
# define FP_CMP_UNORD_E(r, X, Y, ex) _FP_CMP_UNORD (E, 2, (r), X, Y, (ex))
|
|
|
|
# define FP_TO_INT_E(r, X, rsz, rsg) _FP_TO_INT (E, 2, (r), X, (rsz), (rsg))
|
|
# define FP_TO_INT_ROUND_E(r, X, rsz, rsg) \
|
|
_FP_TO_INT_ROUND (E, 2, (r), X, (rsz), (rsg))
|
|
# define FP_FROM_INT_E(X, r, rs, rt) _FP_FROM_INT (E, 2, X, (r), (rs), rt)
|
|
|
|
# define _FP_FRAC_HIGH_E(X) (X##_f1)
|
|
# define _FP_FRAC_HIGH_RAW_E(X) (X##_f0)
|
|
|
|
# define _FP_FRAC_HIGH_DW_E(X) (X##_f[2])
|
|
|
|
#endif /* not _FP_W_TYPE_SIZE < 64 */
|
|
|
|
#endif /* !SOFT_FP_EXTENDED_H */
|