431 lines
12 KiB
C
431 lines
12 KiB
C
/* Software floating-point emulation.
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Definitions for IEEE Extended Precision.
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Copyright (C) 1999,2006,2007,2012 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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#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 _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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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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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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} while (0)
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#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,4,r,X,Y,un)
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#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,4,r,X,Y)
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#define FP_CMP_UNORD_E(r,X,Y) _FP_CMP_UNORD(E,4,r,X,Y)
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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_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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#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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#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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union _FP_UNION_E _flo; _flo.flt = (val); \
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\
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X##_f0 = _flo.bits.frac; \
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X##_f1 = 0; \
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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##_f0 = _flo->bits.frac; \
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X##_f1 = 0; \
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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##_f0 |= _FP_IMPLBIT_E; \
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else X##_f0 &= ~(_FP_IMPLBIT_E); \
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_flo.bits.frac = X##_f0; \
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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(fs, 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##_f0 |= _FP_IMPLBIT_E; \
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else X##_f0 &= ~(_FP_IMPLBIT_E); \
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_flo->bits.frac = X##_f0; \
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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,2,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,2,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,2,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,2,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,2,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,2,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,2,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,2,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,2,X)
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#define FP_NEG_E(R,X) _FP_NEG(E,2,R,X)
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#define FP_ADD_E(R,X,Y) _FP_ADD(E,2,R,X,Y)
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#define FP_SUB_E(R,X,Y) _FP_SUB(E,2,R,X,Y)
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#define FP_MUL_E(R,X,Y) _FP_MUL(E,2,R,X,Y)
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#define FP_DIV_E(R,X,Y) _FP_DIV(E,2,R,X,Y)
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#define FP_SQRT_E(R,X) _FP_SQRT(E,2,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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* We optimize it by doing most of the calculations
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* in one UWtype registers instead of two, although we don't
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* have to.
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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_2(X, (_FP_WORKBITS)); \
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while (q) \
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{ \
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T##_f0 = S##_f0 + q; \
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if (T##_f0 <= X##_f0) \
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{ \
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S##_f0 = T##_f0 + q; \
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X##_f0 -= T##_f0; \
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R##_f0 += q; \
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} \
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_FP_FRAC_SLL_1(X, 1); \
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q >>= 1; \
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} \
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_FP_FRAC_SLL_2(R, (_FP_WORKBITS)); \
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if (X##_f0) \
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{ \
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if (S##_f0 < X##_f0) \
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R##_f0 |= _FP_WORK_ROUND; \
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R##_f0 |= _FP_WORK_STICKY; \
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} \
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} while (0)
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#define FP_CMP_E(r,X,Y,un) _FP_CMP(E,2,r,X,Y,un)
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#define FP_CMP_EQ_E(r,X,Y) _FP_CMP_EQ(E,2,r,X,Y)
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#define FP_CMP_UNORD_E(r,X,Y) _FP_CMP_UNORD(E,2,r,X,Y)
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#define FP_TO_INT_E(r,X,rsz,rsg) _FP_TO_INT(E,2,r,X,rsz,rsg)
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#define FP_FROM_INT_E(X,r,rs,rt) _FP_FROM_INT(E,2,X,r,rs,rt)
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#define _FP_FRAC_HIGH_E(X) (X##_f1)
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#define _FP_FRAC_HIGH_RAW_E(X) (X##_f0)
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#endif /* not _FP_W_TYPE_SIZE < 64 */
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