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734 |
jeremybenn |
/* Software floating-point emulation.
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Definitions for IEEE Extended Precision.
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Copyright (C) 1999,2006,2007 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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Contributed by 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, write to the Free
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Software Foundation, 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#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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#else
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#define _FP_FRACTBITS_E (2*_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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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
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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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union _FP_UNION_E _flo; _flo.flt = (val); \
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\
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X##_f[2] = 0; X##_f[3] = 0; \
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X##_f[0] = _flo.bits.frac0; \
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X##_f[1] = _flo.bits.frac1; \
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X##_e = _flo.bits.exp; \
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X##_s = _flo.bits.sign; \
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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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union _FP_UNION_E *_flo = \
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(union _FP_UNION_E *)(val); \
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\
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X##_f[2] = 0; X##_f[3] = 0; \
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X##_f[0] = _flo->bits.frac0; \
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X##_f[1] = _flo->bits.frac1; \
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X##_e = _flo->bits.exp; \
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X##_s = _flo->bits.sign; \
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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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union _FP_UNION_E _flo; \
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\
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if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
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else X##_f[1] &= ~(_FP_IMPLBIT_E); \
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_flo.bits.frac0 = X##_f[0]; \
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_flo.bits.frac1 = X##_f[1]; \
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_flo.bits.exp = X##_e; \
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_flo.bits.sign = X##_s; \
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\
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(val) = _flo.flt; \
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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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if (!FP_INHIBIT_RESULTS) \
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{ \
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union _FP_UNION_E *_flo = \
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(union _FP_UNION_E *)(val); \
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\
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if (X##_e) X##_f[1] |= _FP_IMPLBIT_E; \
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else X##_f[1] &= ~(_FP_IMPLBIT_E); \
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_flo->bits.frac0 = X##_f[0]; \
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_flo->bits.frac1 = X##_f[1]; \
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_flo->bits.exp = X##_e; \
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_flo->bits.sign = X##_s; \
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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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FP_UNPACK_RAW_E(X,val); \
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_FP_UNPACK_CANONICAL(E,4,X); \
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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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FP_UNPACK_RAW_EP(X,val); \
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_FP_UNPACK_CANONICAL(E,4,X); \
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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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FP_UNPACK_RAW_E(X,val); \
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_FP_UNPACK_SEMIRAW(E,4,X); \
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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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FP_UNPACK_RAW_EP(X,val); \
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_FP_UNPACK_SEMIRAW(E,4,X); \
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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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_FP_PACK_CANONICAL(E,4,X); \
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FP_PACK_RAW_E(val,X); \
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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,4,X); \
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FP_PACK_RAW_EP(val,X); \
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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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_FP_PACK_SEMIRAW(E,4,X); \
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FP_PACK_RAW_E(val,X); \
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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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_FP_PACK_SEMIRAW(E,4,X); \
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FP_PACK_RAW_EP(val,X); \
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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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/*
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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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*/
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#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
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do { \
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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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| 233 |
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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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| 236 |
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R##_f[0] += q; \
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} \
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| 238 |
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_FP_FRAC_SLL_2(X, 1); \
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| 239 |
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q >>= 1; \
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| 240 |
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} \
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_FP_FRAC_SLL_4(R, (_FP_WORKBITS)); \
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| 242 |
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if (X##_f[0] | X##_f[1]) \
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| 243 |
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{ \
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| 244 |
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if (S##_f[1] < X##_f[1] || \
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| 245 |
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(S##_f[1] == X##_f[1] && \
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| 246 |
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S##_f[0] < X##_f[0])) \
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| 247 |
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R##_f[0] |= _FP_WORK_ROUND; \
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| 248 |
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R##_f[0] |= _FP_WORK_STICKY; \
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| 249 |
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} \
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| 250 |
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} while (0)
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| 251 |
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| 252 |
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#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,4,r,X,Y,un)
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| 253 |
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#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,4,r,X,Y)
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| 254 |
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#define FP_CMP_UNORD_E(r,X,Y) _FP_CMP_UNORD(E,4,r,X,Y)
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| 255 |
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| 256 |
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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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| 257 |
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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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| 258 |
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| 259 |
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#define _FP_FRAC_HIGH_E(X) (X##_f[2])
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| 260 |
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#define _FP_FRAC_HIGH_RAW_E(X) (X##_f[1])
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| 261 |
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| 262 |
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#else /* not _FP_W_TYPE_SIZE < 64 */
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| 263 |
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union _FP_UNION_E
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| 264 |
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{
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| 265 |
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XFtype flt;
|
| 266 |
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struct {
|
| 267 |
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#if __BYTE_ORDER == __BIG_ENDIAN
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| 268 |
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_FP_W_TYPE pad : (_FP_W_TYPE_SIZE - 1 - _FP_EXPBITS_E);
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| 269 |
|
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unsigned sign : 1;
|
| 270 |
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unsigned exp : _FP_EXPBITS_E;
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| 271 |
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_FP_W_TYPE frac : _FP_W_TYPE_SIZE;
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| 272 |
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#else
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| 273 |
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_FP_W_TYPE frac : _FP_W_TYPE_SIZE;
|
| 274 |
|
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unsigned exp : _FP_EXPBITS_E;
|
| 275 |
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unsigned sign : 1;
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| 276 |
|
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#endif
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| 277 |
|
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} bits;
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| 278 |
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};
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| 279 |
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| 280 |
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#define FP_DECL_E(X) _FP_DECL(2,X)
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| 281 |
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| 282 |
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#define FP_UNPACK_RAW_E(X, val) \
|
| 283 |
|
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do { \
|
| 284 |
|
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union _FP_UNION_E _flo; _flo.flt = (val); \
|
| 285 |
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\
|
| 286 |
|
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X##_f0 = _flo.bits.frac; \
|
| 287 |
|
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X##_f1 = 0; \
|
| 288 |
|
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X##_e = _flo.bits.exp; \
|
| 289 |
|
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X##_s = _flo.bits.sign; \
|
| 290 |
|
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} while (0)
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| 291 |
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|
| 292 |
|
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#define FP_UNPACK_RAW_EP(X, val) \
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| 293 |
|
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do { \
|
| 294 |
|
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union _FP_UNION_E *_flo = \
|
| 295 |
|
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(union _FP_UNION_E *)(val); \
|
| 296 |
|
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\
|
| 297 |
|
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X##_f0 = _flo->bits.frac; \
|
| 298 |
|
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X##_f1 = 0; \
|
| 299 |
|
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X##_e = _flo->bits.exp; \
|
| 300 |
|
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X##_s = _flo->bits.sign; \
|
| 301 |
|
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} while (0)
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| 302 |
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|
| 303 |
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#define FP_PACK_RAW_E(val, X) \
|
| 304 |
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|
do { \
|
| 305 |
|
|
union _FP_UNION_E _flo; \
|
| 306 |
|
|
\
|
| 307 |
|
|
if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
|
| 308 |
|
|
else X##_f0 &= ~(_FP_IMPLBIT_E); \
|
| 309 |
|
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_flo.bits.frac = X##_f0; \
|
| 310 |
|
|
_flo.bits.exp = X##_e; \
|
| 311 |
|
|
_flo.bits.sign = X##_s; \
|
| 312 |
|
|
\
|
| 313 |
|
|
(val) = _flo.flt; \
|
| 314 |
|
|
} while (0)
|
| 315 |
|
|
|
| 316 |
|
|
#define FP_PACK_RAW_EP(fs, val, X) \
|
| 317 |
|
|
do { \
|
| 318 |
|
|
if (!FP_INHIBIT_RESULTS) \
|
| 319 |
|
|
{ \
|
| 320 |
|
|
union _FP_UNION_E *_flo = \
|
| 321 |
|
|
(union _FP_UNION_E *)(val); \
|
| 322 |
|
|
\
|
| 323 |
|
|
if (X##_e) X##_f0 |= _FP_IMPLBIT_E; \
|
| 324 |
|
|
else X##_f0 &= ~(_FP_IMPLBIT_E); \
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| 325 |
|
|
_flo->bits.frac = X##_f0; \
|
| 326 |
|
|
_flo->bits.exp = X##_e; \
|
| 327 |
|
|
_flo->bits.sign = X##_s; \
|
| 328 |
|
|
} \
|
| 329 |
|
|
} while (0)
|
| 330 |
|
|
|
| 331 |
|
|
|
| 332 |
|
|
#define FP_UNPACK_E(X,val) \
|
| 333 |
|
|
do { \
|
| 334 |
|
|
FP_UNPACK_RAW_E(X,val); \
|
| 335 |
|
|
_FP_UNPACK_CANONICAL(E,2,X); \
|
| 336 |
|
|
} while (0)
|
| 337 |
|
|
|
| 338 |
|
|
#define FP_UNPACK_EP(X,val) \
|
| 339 |
|
|
do { \
|
| 340 |
|
|
FP_UNPACK_RAW_EP(X,val); \
|
| 341 |
|
|
_FP_UNPACK_CANONICAL(E,2,X); \
|
| 342 |
|
|
} while (0)
|
| 343 |
|
|
|
| 344 |
|
|
#define FP_UNPACK_SEMIRAW_E(X,val) \
|
| 345 |
|
|
do { \
|
| 346 |
|
|
FP_UNPACK_RAW_E(X,val); \
|
| 347 |
|
|
_FP_UNPACK_SEMIRAW(E,2,X); \
|
| 348 |
|
|
} while (0)
|
| 349 |
|
|
|
| 350 |
|
|
#define FP_UNPACK_SEMIRAW_EP(X,val) \
|
| 351 |
|
|
do { \
|
| 352 |
|
|
FP_UNPACK_RAW_EP(X,val); \
|
| 353 |
|
|
_FP_UNPACK_SEMIRAW(E,2,X); \
|
| 354 |
|
|
} while (0)
|
| 355 |
|
|
|
| 356 |
|
|
#define FP_PACK_E(val,X) \
|
| 357 |
|
|
do { \
|
| 358 |
|
|
_FP_PACK_CANONICAL(E,2,X); \
|
| 359 |
|
|
FP_PACK_RAW_E(val,X); \
|
| 360 |
|
|
} while (0)
|
| 361 |
|
|
|
| 362 |
|
|
#define FP_PACK_EP(val,X) \
|
| 363 |
|
|
do { \
|
| 364 |
|
|
_FP_PACK_CANONICAL(E,2,X); \
|
| 365 |
|
|
FP_PACK_RAW_EP(val,X); \
|
| 366 |
|
|
} while (0)
|
| 367 |
|
|
|
| 368 |
|
|
#define FP_PACK_SEMIRAW_E(val,X) \
|
| 369 |
|
|
do { \
|
| 370 |
|
|
_FP_PACK_SEMIRAW(E,2,X); \
|
| 371 |
|
|
FP_PACK_RAW_E(val,X); \
|
| 372 |
|
|
} while (0)
|
| 373 |
|
|
|
| 374 |
|
|
#define FP_PACK_SEMIRAW_EP(val,X) \
|
| 375 |
|
|
do { \
|
| 376 |
|
|
_FP_PACK_SEMIRAW(E,2,X); \
|
| 377 |
|
|
FP_PACK_RAW_EP(val,X); \
|
| 378 |
|
|
} while (0)
|
| 379 |
|
|
|
| 380 |
|
|
#define FP_ISSIGNAN_E(X) _FP_ISSIGNAN(E,2,X)
|
| 381 |
|
|
#define FP_NEG_E(R,X) _FP_NEG(E,2,R,X)
|
| 382 |
|
|
#define FP_ADD_E(R,X,Y) _FP_ADD(E,2,R,X,Y)
|
| 383 |
|
|
#define FP_SUB_E(R,X,Y) _FP_SUB(E,2,R,X,Y)
|
| 384 |
|
|
#define FP_MUL_E(R,X,Y) _FP_MUL(E,2,R,X,Y)
|
| 385 |
|
|
#define FP_DIV_E(R,X,Y) _FP_DIV(E,2,R,X,Y)
|
| 386 |
|
|
#define FP_SQRT_E(R,X) _FP_SQRT(E,2,R,X)
|
| 387 |
|
|
|
| 388 |
|
|
/*
|
| 389 |
|
|
* Square root algorithms:
|
| 390 |
|
|
* We have just one right now, maybe Newton approximation
|
| 391 |
|
|
* should be added for those machines where division is fast.
|
| 392 |
|
|
* We optimize it by doing most of the calculations
|
| 393 |
|
|
* in one UWtype registers instead of two, although we don't
|
| 394 |
|
|
* have to.
|
| 395 |
|
|
*/
|
| 396 |
|
|
#define _FP_SQRT_MEAT_E(R, S, T, X, q) \
|
| 397 |
|
|
do { \
|
| 398 |
|
|
q = (_FP_W_TYPE)1 << (_FP_W_TYPE_SIZE - 1); \
|
| 399 |
|
|
_FP_FRAC_SRL_2(X, (_FP_WORKBITS)); \
|
| 400 |
|
|
while (q) \
|
| 401 |
|
|
{ \
|
| 402 |
|
|
T##_f0 = S##_f0 + q; \
|
| 403 |
|
|
if (T##_f0 <= X##_f0) \
|
| 404 |
|
|
{ \
|
| 405 |
|
|
S##_f0 = T##_f0 + q; \
|
| 406 |
|
|
X##_f0 -= T##_f0; \
|
| 407 |
|
|
R##_f0 += q; \
|
| 408 |
|
|
} \
|
| 409 |
|
|
_FP_FRAC_SLL_1(X, 1); \
|
| 410 |
|
|
q >>= 1; \
|
| 411 |
|
|
} \
|
| 412 |
|
|
_FP_FRAC_SLL_2(R, (_FP_WORKBITS)); \
|
| 413 |
|
|
if (X##_f0) \
|
| 414 |
|
|
{ \
|
| 415 |
|
|
if (S##_f0 < X##_f0) \
|
| 416 |
|
|
R##_f0 |= _FP_WORK_ROUND; \
|
| 417 |
|
|
R##_f0 |= _FP_WORK_STICKY; \
|
| 418 |
|
|
} \
|
| 419 |
|
|
} while (0)
|
| 420 |
|
|
|
| 421 |
|
|
#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,2,r,X,Y,un)
|
| 422 |
|
|
#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,2,r,X,Y)
|
| 423 |
|
|
#define FP_CMP_UNORD_E(r,X,Y) _FP_CMP_UNORD(E,2,r,X,Y)
|
| 424 |
|
|
|
| 425 |
|
|
#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,2,r,X,rsz,rsg)
|
| 426 |
|
|
#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,2,X,r,rs,rt)
|
| 427 |
|
|
|
| 428 |
|
|
#define _FP_FRAC_HIGH_E(X) (X##_f1)
|
| 429 |
|
|
#define _FP_FRAC_HIGH_RAW_E(X) (X##_f0)
|
| 430 |
|
|
|
| 431 |
|
|
#endif /* not _FP_W_TYPE_SIZE < 64 */
|
